Sustainability assessment of concrete bridge deck designs in coastal environments using neutrosophic criteria weights

"This is an Accepted Manuscript of an article published by Taylor & Francis in Structure and Infrastructure Engineering on 02/07/2020, available online: https://doi.org/10.1080/15732479.2019.1676791."[EN] Essential infrastructures such as bridges are designed to provide a long-lasting and intergenerational functionality. In those cases, sustainability becomes of paramount importance when the infrastructure is exposed to aggressive environments, which can jeopardise their durability and lead to significant maintenance demands. The assessment of sustainability is however often complex and uncertain. The present study assesses the sustainability performance of 16 alternative designs of a concrete bridge deck in a coastal environment on the basis of a neutrosophic group analytic hierarchy process (AHP). The use of neutrosophic logic in the field of multi-criteria decision-making, as a generalisation of the widely used fuzzy logic, allows for a proper capture of the vagueness and uncertainties of the judgements emitted by the decision-makers. TOPSIS technique is then used to aggregate the different sustainability criteria. From the results, it is derived that only the simultaneous consideration of the economic, environmental and social life cycle impacts of a design shall lead to adequate sustainable designs. Choices made based on the optimality of a design in only some of the sustainability pillars will lead to erroneous conclusions. The use of concrete with silica fume has resulted in a sustainability performance of 46.3% better than conventional concrete designs.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).Navarro, I.; Yepes, V.; Martí, J. (2020). Sustainability assessment of concrete bridge deck designs in coastal environments using neutrosophic criteria weights. Structure and Infrastructure Engineering. 16(7):949-967. https://doi.org/10.1080/15732479.2019.1676791S949967167Abdel-Basset, M., Manogaran, G., Mohamed, M., & Chilamkurti, N. (2018). Three-way decisions based on neutrosophic sets and AHP-QFD framework for supplier selection problem. Future Generation Computer Systems, 89, 19-30. doi:10.1016/j.future.2018.06.024Abdullah, L., & Najib, L. (2014). Sustainable energy planning decision using the intuitionistic fuzzy analytic hierarchy process: choosing energy technology in Malaysia. International Journal of Sustainable Energy, 35(4), 360-377. doi:10.1080/14786451.2014.907292Ali, M. S., Aslam, M. S., & Mirza, M. S. (2015). A sustainability assessment framework for bridges – a case study: Victoria and Champlain Bridges, Montreal. Structure and Infrastructure Engineering, 1-14. doi:10.1080/15732479.2015.1120754Allacker, K. (2012). Environmental and economic optimisation of the floor on grade in residential buildings. The International Journal of Life Cycle Assessment, 17(6), 813-827. doi:10.1007/s11367-012-0402-2Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. doi:10.1016/s0165-0114(86)80034-3Barone, G., & Frangopol, D. M. (2014). Life-cycle maintenance of deteriorating structures by multi-objective optimization involving reliability, risk, availability, hazard and cost. Structural Safety, 48, 40-50. doi:10.1016/j.strusafe.2014.02.002Biswas, P., Pramanik, S., & Giri, B. C. (2015). TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Computing and Applications, 27(3), 727-737. doi:10.1007/s00521-015-1891-2Bolturk, E., & Kahraman, C. (2018). A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft Computing, 22(15), 4941-4958. doi:10.1007/s00500-018-3140-yBuckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17(3), 233-247. doi:10.1016/0165-0114(85)90090-9Büyüközkan, G., & Göçer, F. (2017). Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem. Applied Soft Computing, 52, 1222-1238. doi:10.1016/j.asoc.2016.08.051Cebeci, U. (2009). Fuzzy AHP-based decision support system for selecting ERP systems in textile industry by using balanced scorecard. Expert Systems with Applications, 36(5), 8900-8909. doi:10.1016/j.eswa.2008.11.046Chen, C., Habert, G., Bouzidi, Y., Jullien, A., & Ventura, A. (2010). LCA allocation procedure used as an incitative method for waste recycling: An application to mineral additions in concrete. Resources, Conservation and Recycling, 54(12), 1231-1240. doi:10.1016/j.resconrec.2010.04.001Chu, T.-C., & Tsao, C.-T. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & Mathematics with Applications, 43(1-2), 111-117. doi:10.1016/s0898-1221(01)00277-2Cope, A., Bai, Q., Samdariya, A., & Labi, S. (2013). Assessing the efficacy of stainless steel for bridge deck reinforcement under uncertainty using Monte Carlo simulation. Structure and Infrastructure Engineering, 9(7), 634-647. doi:10.1080/15732479.2011.602418De la Fuente, A., Pons, O., Josa, A., & Aguado, A. (2016). Multi-Criteria Decision Making in the sustainability assessment of sewerage pipe systems. Journal of Cleaner Production, 112, 4762-4770. doi:10.1016/j.jclepro.2015.07.002Deli, I., & Şubaş, Y. (2016). A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8(4), 1309-1322. doi:10.1007/s13042-016-0505-3Dong, Y., Zhang, G., Hong, W.-C., & Xu, Y. (2010). Consensus models for AHP group decision making under row geometric mean prioritization method. Decision Support Systems, 49(3), 281-289. doi:10.1016/j.dss.2010.03.003Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184(1), 3-28. doi:10.1016/j.fss.2011.06.003Eamon, C. D., Jensen, E. A., Grace, N. F., & Shi, X. (2012). Life-Cycle Cost Analysis of Alternative Reinforcement Materials for Bridge Superstructures Considering Cost and Maintenance Uncertainties. Journal of Materials in Civil Engineering, 24(4), 373-380. doi:10.1061/(asce)mt.1943-5533.0000398Enea, M., & Piazza, T. (2004). Project Selection by Constrained Fuzzy AHP. Fuzzy Optimization and Decision Making, 3(1), 39-62. doi:10.1023/b:fodm.0000013071.63614.3dGarcía-Segura, T., Penadés-Plà, V., & Yepes, V. (2018). Sustainable bridge design by metamodel-assisted multi-objective optimization and decision-making under uncertainty. Journal of Cleaner Production, 202, 904-915. doi:10.1016/j.jclepro.2018.08.177García-Segura, T., & Yepes, V. (2016). Multiobjective optimization of post-tensioned concrete box-girder road bridges considering cost, CO2 emissions, and safety. Engineering Structures, 125, 325-336. doi:10.1016/j.engstruct.2016.07.012García-Segura, T., Yepes, V., Frangopol, D. M., & Yang, D. Y. (2017). Lifetime reliability-based optimization of post-tensioned box-girder bridges. Engineering Structures, 145, 381-391. doi:10.1016/j.engstruct.2017.05.013Gervásio, H., & Simões da Silva, L. (2012). A probabilistic decision-making approach for the sustainable assessment of infrastructures. Expert Systems with Applications, 39(8), 7121-7131. doi:10.1016/j.eswa.2012.01.032Guzmán-Sánchez, S., Jato-Espino, D., Lombillo, I., & Diaz-Sarachaga, J. M. (2018). Assessment of the contributions of different flat roof types to achieving sustainable development. Building and Environment, 141, 182-192. doi:10.1016/j.buildenv.2018.05.063Heravi, G., Fathi, M., & Faeghi, S. (2017). Multi-criteria group decision-making method for optimal selection of sustainable industrial building options focused on petrochemical projects. Journal of Cleaner Production, 142, 2999-3013. doi:10.1016/j.jclepro.2016.10.168Invidiata, A., Lavagna, M., & Ghisi, E. (2018). Selecting design strategies using multi-criteria decision making to improve the sustainability of buildings. Building and Environment, 139, 58-68. doi:10.1016/j.buildenv.2018.04.041Jakiel, P., & Fabianowski, D. (2015). FAHP model used for assessment of highway RC bridge structural and technological arrangements. Expert Systems with Applications, 42(8), 4054-4061. doi:10.1016/j.eswa.2014.12.039Kahraman, C., Cebi, S., Onar, S. C., & Oztaysi, B. (2018). A novel trapezoidal intuitionistic fuzzy information axiom approach: An application to multicriteria landfill site selection. Engineering Applications of Artificial Intelligence, 67, 157-172. doi:10.1016/j.engappai.2017.09.009Kere, K. J., & Huang, Q. (2019). Life-Cycle Cost Comparison of Corrosion Management Strategies for Steel Bridges. Journal of Bridge Engineering, 24(4), 04019007. doi:10.1061/(asce)be.1943-5592.0001361Liang, R., Wang, J., & Zhang, H. (2017). A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Computing and Applications, 30(11), 3383-3398. doi:10.1007/s00521-017-2925-8Liu, P., & Liu, X. (2016). The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making. International Journal of Machine Learning and Cybernetics, 9(2), 347-358. doi:10.1007/s13042-016-0508-0Martí, J. V., García-Segura, T., & Yepes, V. (2016). Structural design of precast-prestressed concrete U-beam road bridges based on embodied energy. Journal of Cleaner Production, 120, 231-240. doi:10.1016/j.jclepro.2016.02.024Martínez-Blanco, J., Lehmann, A., Muñoz, P., Antón, A., Traverso, M., Rieradevall, J., & Finkbeiner, M. (2014). Application challenges for the social Life Cycle Assessment of fertilizers within life cycle sustainability assessment. Journal of Cleaner Production, 69, 34-48. doi:10.1016/j.jclepro.2014.01.044Mistry, M., Koffler, C., & Wong, S. (2016). LCA and LCC of the world’s longest pier: a case study on nickel-containing stainless steel rebar. The International Journal of Life Cycle Assessment, 21(11), 1637-1644. doi:10.1007/s11367-016-1080-2Moazami, D., Behbahani, H., & Muniandy, R. (2011). Pavement rehabilitation and maintenance prioritization of urban roads using fuzzy logic. Expert Systems with Applications, 38(10), 12869-12879. doi:10.1016/j.eswa.2011.04.079Mosalam, K. M., Alibrandi, U., Lee, H., & Armengou, J. (2018). Performance-based engineering and multi-criteria decision analysis for sustainable and resilient building design. Structural Safety, 74, 1-13. doi:10.1016/j.strusafe.2018.03.005Navarro, I., Yepes, V., & Martí, J. (2018). Life Cycle Cost Assessment of Preventive Strategies Applied to Prestressed Concrete Bridges Exposed to Chlorides. Sustainability, 10(3), 845. doi:10.3390/su10030845Navarro, I. J., Martí, J. V., & Yepes, V. (2019). Reliability-based maintenance optimization of corrosion preventive designs under a life cycle perspective. Environmental Impact Assessment Review, 74, 23-34. doi:10.1016/j.eiar.2018.10.001Navarro, I. J., Yepes, V., & Martí, J. V. (2018). Social life cycle assessment of concrete bridge decks exposed to aggressive environments. Environmental Impact Assessment Review, 72, 50-63. doi:10.1016/j.eiar.2018.05.003Navarro, I. J., Yepes, V., Martí, J. V., & González-Vidosa, F. (2018). Life cycle impact assessment of corrosion preventive designs applied to prestressed concrete bridge decks. Journal of Cleaner Production, 196, 698-713. doi:10.1016/j.jclepro.2018.06.110Nogueira, C. G., Leonel, E. D., & Coda, H. B. (2012). Reliability algorithms applied to reinforced concrete structures durability assessment. Revista IBRACON de Estruturas e Materiais, 5(4), 440-450. doi:10.1590/s1983-41952012000400003Pamučar, D., Badi, I., Sanja, K., & Obradović, R. (2018). A Novel Approach for the Selection of Power-Generation Technology Using a Linguistic Neutrosophic CODAS Method: A Case Study in Libya. Energies, 11(9), 2489. doi:10.3390/en11092489Penadés-Plà, V., García-Segura, T., Martí, J., & Yepes, V. (2016). A Review of Multi-Criteria Decision-Making Methods Applied to the Sustainable Bridge Design. Sustainability, 8(12), 1295. doi:10.3390/su8121295Peng, J., Wang, J., & Yang, W.-E. (2016). A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. International Journal of Systems Science, 48(2), 425-435. doi:10.1080/00207721.2016.1218975Petcherdchoo, A. (2015). Environmental Impacts of Combined Repairs on Marine Concrete Structures. Journal of Advanced Concrete Technology, 13(3), 205-213. doi:10.3151/jact.13.205PRASCEVIC, N., & PRASCEVIC, Z. (2017). APPLICATION OF FUZZY AHP FOR RANKING AND SELECTION OF ALTERNATIVES IN CONSTRUCTION PROJECT MANAGEMENT. Journal of Civil Engineering and Management, 23(8), 1123-1135. doi:10.3846/13923730.2017.1388278Pryn, M. R., Cornet, Y., & Salling, K. B. (2015). APPLYING SUSTAINABILITY THEORY TO TRANSPORT INFRASTRUCTURE ASSESSMENT USING A MULTIPLICATIVE AHP DECISION SUPPORT MODEL. TRANSPORT, 30(3), 330-341. doi:10.3846/16484142.2015.1081281Rashidi, M., Samali, B., & Sharafi, P. (2015). A new model for bridge management: Part B: decision support system for remediation planning. Australian Journal of Civil Engineering, 14(1), 46-53. doi:10.1080/14488353.2015.1092642Sabatino, S., Frangopol, D. M., & Dong, Y. (2015). Life cycle utility-informed maintenance planning based on lifetime functions: optimum balancing of cost, failure consequences and performance benefit. Structure and Infrastructure Engineering, 12(7), 830-847. doi:10.1080/15732479.2015.1064968Safi, M., Sundquist, H., & Karoumi, R. (2015). Cost-Efficient Procurement of Bridge Infrastructures by Incorporating Life-Cycle Cost Analysis with Bridge Management Systems. Journal of Bridge Engineering, 20(6), 04014083. doi:10.1061/(asce)be.1943-5592.0000673Sajedi, S., & Huang, Q. (2019). Reliability-based life-cycle-cost comparison of different corrosion management strategies. Engineering Structures, 186, 52-63. doi:10.1016/j.engstruct.2019.02.018Sierra, L. A., Pellicer, E., & Yepes, V. (2016). Social Sustainability in the Lifecycle of Chilean Public Infrastructure. Journal of Construction Engineering and Management, 142(5), 05015020. doi:10.1061/(asce)co.1943-7862.0001099Sierra, L. A., Yepes, V., García-Segura, T., & Pellicer, E. (2018). Bayesian network method for decision-making about the social sustainability of infrastructure projects. Journal of Cleaner Production, 176, 521-534. doi:10.1016/j.jclepro.2017.12.140Sodenkamp, M. A., Tavana, M., & Di Caprio, D. (2018). An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets. Applied Soft Computing, 71, 715-727. doi:10.1016/j.asoc.2018.07.020Stewart, M. G., Estes, A. C., & Frangopol, D. M. (2004). Bridge Deck Replacement for Minimum Expected Cost Under Multiple Reliability Constraints. Journal of Structural Engineering, 130(9), 1414-1419. doi:10.1061/(asce)0733-9445(2004)130:9(1414)Swarr, T. E., Hunkeler, D., Klöpffer, W., Pesonen, H.-L., Ciroth, A., Brent, A. C., & Pagan, R. (2011). Environmental life-cycle costing: a code of practice. The International Journal of Life Cycle Assessment, 16(5), 389-391. doi:10.1007/s11367-011-0287-5Tahmasebi Birgani, Y., & Yazdandoost, F. (2018). An Integrated Framework to Evaluate Resilient-Sustainable Urban Drainage Management Plans Using a Combined-adaptive MCDM Technique. Water Resources Management, 32(8), 2817-2835. doi:10.1007/s11269-018-1960-2Tesfamariam, S., & Sadiq, R. (2006). Risk-based environmental decision-making using fuzzy analytic hierarchy process (F-AHP). Stochastic Environmental Research and Risk Assessment, 21(1), 35-50. doi:10.1007/s00477-006-0042-9Wang, Y.-M., & Elhag, T. M. S. (2006). On the normalization of interval and fuzzy weights. Fuzzy Sets and Systems, 157(18), 2456-2471. doi:10.1016/j.fss.2006.06.008Yang, Z., Shi, X., Creighton, A. T., & Peterson, M. M. (2009). Effect of styrene–butadiene rubber latex on the chloride permeability and microstructure of Portland cement mortar. Construction and Building Materials, 23(6), 2283-2290. doi:10.1016/j.conbuildmat.2008.11.011Ye, J. (2013). Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. International Journal of General Systems, 42(4), 386-394. doi:10.1080/03081079.2012.761609Ye, J. (2017). Subtraction and Division Operations of Simplified Neutrosophic Sets. Information, 8(2), 51. doi:10.3390/info8020051Yepes, V., García-Segura, T., & Moreno-Jiménez, J. M. (2015). A cognitive approach for the multi-objective optimization of RC structural problems. Archives of Civil and Mechanical Engineering, 15(4), 1024-1036. doi:10.1016/j.acme.2015.05.001Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xZadeh, L. A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man, and Cybernetics, SMC-3(1), 28-44. doi:10.1109/tsmc.1973.5408575Zavadskas, E. K., Mardani, A., Turskis, Z., Jusoh, A., & Nor, K. M. (2016). Development of TOPSIS Method to Solve Complicated Decision-Making Problems — An Overview on Developments from 2000 to 2015. International Journal of Information Technology & Decision Making, 15(03), 645-682. doi:10.1142/s021962201630001

Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices

[EN] After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, by definition, a wide variety in number and nature of conflicting criteria, thus pushing the limits of conventional multicriteria decision-making tools practices. The greater the number of criteria and the more complex the relations existing between them in a decisional problem, the less accurate and certain are the judgments required by usual methods, such as the analytic hierarchy process (AHP). The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%.The authors acknowledge the financial support of the Spanish Ministry of Economy and Business, along with FEDER funding (DIMALIFE Project: BIA2017-85098-R).Navarro, IJ.; Martí Albiñana, JV.; Yepes, V. (2021). Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices. Mathematics. 9(5):1-19. https://doi.org/10.3390/math905049611995Worrell, E., Price, L., Martin, N., Hendriks, C., & Meida, L. O. (2001). CARBON DIOXIDE EMISSIONS FROM THE GLOBAL CEMENT INDUSTRY. Annual Review of Energy and the Environment, 26(1), 303-329. doi:10.1146/annurev.energy.26.1.303García, J., Yepes, V., & Martí, J. V. (2020). A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem. Mathematics, 8(4), 555. doi:10.3390/math8040555Penadés-Plà, V., García-Segura, T., & Yepes, V. (2020). Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge. Mathematics, 8(3), 398. doi:10.3390/math8030398Kim, S., & Frangopol, D. M. (2017). Multi-objective probabilistic optimum monitoring planning considering fatigue damage detection, maintenance, reliability, service life and cost. Structural and Multidisciplinary Optimization, 57(1), 39-54. doi:10.1007/s00158-017-1849-3García-Segura, T., Yepes, V., & Frangopol, D. M. (2017). Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Structural and Multidisciplinary Optimization, 56(1), 139-150. doi:10.1007/s00158-017-1653-0Van den Heede, P., & De Belie, N. (2014). A service life based global warming potential for high-volume fly ash concrete exposed to carbonation. Construction and Building Materials, 55, 183-193. doi:10.1016/j.conbuildmat.2014.01.033García, J., Martí, J. V., & Yepes, V. (2020). The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm. Mathematics, 8(6), 862. doi:10.3390/math8060862García-Segura, T., Penadés-Plà, V., & Yepes, V. (2018). Sustainable bridge design by metamodel-assisted multi-objective optimization and decision-making under uncertainty. Journal of Cleaner Production, 202, 904-915. doi:10.1016/j.jclepro.2018.08.177Gursel, A. P., & Ostertag, C. (2016). Comparative life-cycle impact assessment of concrete manufacturing in Singapore. The International Journal of Life Cycle Assessment, 22(2), 237-255. doi:10.1007/s11367-016-1149-yPenadés-Plà, V., Martí, J. V., García-Segura, T., & Yepes, V. (2017). Life-Cycle Assessment: A Comparison between Two Optimal Post-Tensioned Concrete Box-Girder Road Bridges. Sustainability, 9(10), 1864. doi:10.3390/su9101864Navarro, I. J., Yepes, V., & Martí, J. V. (2018). Social life cycle assessment of concrete bridge decks exposed to aggressive environments. Environmental Impact Assessment Review, 72, 50-63. doi:10.1016/j.eiar.2018.05.003Sierra, L. A., Pellicer, E., & Yepes, V. (2017). Method for estimating the social sustainability of infrastructure projects. Environmental Impact Assessment Review, 65, 41-53. doi:10.1016/j.eiar.2017.02.004Navarro, I. J., Yepes, V., & Martí, J. V. (2019). Sustainability assessment of concrete bridge deck designs in coastal environments using neutrosophic criteria weights. Structure and Infrastructure Engineering, 16(7), 949-967. doi:10.1080/15732479.2019.1676791Tavana, M., Shaabani, A., Javier Santos-Arteaga, F., & Raeesi Vanani, I. (2020). A Review of Uncertain Decision-Making Methods in Energy Management Using Text Mining and Data Analytics. Energies, 13(15), 3947. doi:10.3390/en13153947Yannis, G., Kopsacheili, A., Dragomanovits, A., & Petraki, V. (2020). State-of-the-art review on multi-criteria decision-making in the transport sector. Journal of Traffic and Transportation Engineering (English Edition), 7(4), 413-431. doi:10.1016/j.jtte.2020.05.005Navarro, I. J., Penadés-Plà, V., Martínez-Muñoz, D., Rempling, R., & Yepes, V. (2020). LIFE CYCLE SUSTAINABILITY ASSESSMENT FOR MULTI-CRITERIA DECISION MAKING IN BRIDGE DESIGN: A REVIEW. JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT, 26(7), 690-704. doi:10.3846/jcem.2020.13599Hedelin, B. (2018). Complexity is no excuse. Sustainability Science, 14(3), 733-749. doi:10.1007/s11625-018-0635-5Zadeh, L. A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man, and Cybernetics, SMC-3(1), 28-44. doi:10.1109/tsmc.1973.5408575Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xMilošević, D. M., Milošević, M. R., & Simjanović, D. J. (2020). Implementation of Adjusted Fuzzy AHP Method in the Assessment for Reuse of Industrial Buildings. Mathematics, 8(10), 1697. doi:10.3390/math8101697Lin, C.-N. (2020). A Fuzzy Analytic Hierarchy Process-Based Analysis of the Dynamic Sustainable Management Index in Leisure Agriculture. Sustainability, 12(13), 5395. doi:10.3390/su12135395Salehi, S., Jalili Ghazizadeh, M., Tabesh, M., Valadi, S., & Salamati Nia, S. P. (2020). A risk component-based model to determine pipes renewal strategies in water distribution networks. Structure and Infrastructure Engineering, 17(10), 1338-1359. doi:10.1080/15732479.2020.1842466Liu, P., & Liu, X. (2016). The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making. International Journal of Machine Learning and Cybernetics, 9(2), 347-358. doi:10.1007/s13042-016-0508-0Peng, J., Wang, J., & Yang, W.-E. (2016). A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. International Journal of Systems Science, 48(2), 425-435. doi:10.1080/00207721.2016.1218975Saaty, T. L., & Ozdemir, M. S. (2003). Why the magic number seven plus or minus two. Mathematical and Computer Modelling, 38(3-4), 233-244. doi:10.1016/s0895-7177(03)90083-5Harker, P. T. (1987). Incomplete pairwise comparisons in the analytic hierarchy process. Mathematical Modelling, 9(11), 837-848. doi:10.1016/0270-0255(87)90503-3Chen, K., Kou, G., Michael Tarn, J., & Song, Y. (2015). Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices. Annals of Operations Research, 235(1), 155-175. doi:10.1007/s10479-015-1997-zBozóki, S., Fülöp, J., & Rónyai, L. (2010). On optimal completion of incomplete pairwise comparison matrices. Mathematical and Computer Modelling, 52(1-2), 318-333. doi:10.1016/j.mcm.2010.02.047Dong, M., Li, S., & Zhang, H. (2015). Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP. Expert Systems with Applications, 42(21), 7846-7857. doi:10.1016/j.eswa.2015.06.007Zhou, X., Hu, Y., Deng, Y., Chan, F. T. S., & Ishizaka, A. (2018). A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP. Annals of Operations Research, 271(2), 1045-1066. doi:10.1007/s10479-018-2769-3Sumathi, I. R., & Antony Crispin Sweety, C. (2019). New approach on differential equation via trapezoidal neutrosophic number. Complex & Intelligent Systems, 5(4), 417-424. doi:10.1007/s40747-019-00117-3Deli, I., & Şubaş, Y. (2016). A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8(4), 1309-1322. doi:10.1007/s13042-016-0505-3Ye, J. (2017). Subtraction and Division Operations of Simplified Neutrosophic Sets. Information, 8(2), 51. doi:10.3390/info8020051Liang, R., Wang, J., & Zhang, H. (2017). A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Computing and Applications, 30(11), 3383-3398. doi:10.1007/s00521-017-2925-8Sodenkamp, M. A., Tavana, M., & Di Caprio, D. (2018). An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets. Applied Soft Computing, 71, 715-727. doi:10.1016/j.asoc.2018.07.020Sierra, L. A., Pellicer, E., & Yepes, V. (2016). Social Sustainability in the Lifecycle of Chilean Public Infrastructure. Journal of Construction Engineering and Management, 142(5), 05015020. doi:10.1061/(asce)co.1943-7862.0001099Abdel-Basset, M., Manogaran, G., Mohamed, M., & Chilamkurti, N. (2018). RETRACTED: Three-way decisions based on neutrosophic sets and AHP-QFD framework for supplier selection problem. Future Generation Computer Systems, 89, 19-30. doi:10.1016/j.future.2018.06.024Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184(1), 3-28. doi:10.1016/j.fss.2011.06.003Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17(3), 233-247. doi:10.1016/0165-0114(85)90090-9Wang, Y.-M., & Elhag, T. M. S. (2006). On the normalization of interval and fuzzy weights. Fuzzy Sets and Systems, 157(18), 2456-2471. doi:10.1016/j.fss.2006.06.008Enea, M., & Piazza, T. (2004). Project Selection by Constrained Fuzzy AHP. Fuzzy Optimization and Decision Making, 3(1), 39-62. doi:10.1023/b:fodm.0000013071.63614.3dChu, T.-C., & Tsao, C.-T. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & Mathematics with Applications, 43(1-2), 111-117. doi:10.1016/s0898-1221(01)00277-

A prescriptive approach to qualify and quantify customer value for value-based requirements engineering

Recently, customer-based product development is becoming a popular paradigm. Customer expectations and needs can be identified and transformed into requirements for product design with the help of various methods and tools. However, in many cases, these models fail to focus on the perceived value that is crucial when customers make the decision of purchasing a product. In this paper, a prescriptive approach to support value-based requirements engineering (RE) is proposed, describing the foundations, procedures and initial applications in the context of RE for commercial aircraft. An integrated set of techniques, such as means-ends analysis, part-whole analysis and multi-attribute utility theory is introduced in order to understand customer values in depth and width. Technically, this enables identifying the implicit value, structuring logically collected statements of customer expectations and performing value modelling and simulation. Additionally, it helps to put in place a system to measure customer satisfaction that is derived from the proposed approach. The approach offers significant potential to develop effective value creation strategies for the development of new product

Decision making with Dempster-Shafer belief structure and the OWAWA operator

[EN] A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging ¿ weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Spanish Ministry of Education under project JC2009-00189 , the University of Barcelona (099311) and the European Commission (PIEFGA-2011-300062) is gratefully acknowledgedMerigó, JM.; Engemann, KJ.; Palacios Marqués, D. (2013). Decision making with Dempster-Shafer belief structure and the OWAWA operator. Technological and Economic Development of Economy. 19(sup 1):S100-S118. https://doi.org/10.3846/20294913.2013.869517SS100S11819sup 1Antuchevičienė, J., Zavadskas, E. K., & Zakarevičius, A. (2010). MULTIPLE CRITERIA CONSTRUCTION MANAGEMENT DECISIONS CONSIDERING RELATIONS BETWEEN CRITERIA / DAUGIATIKSLIAI STATYBOS VALDYMO SPRENDIMAI ATSIŽVELGIANT Į RODIKLIŲ TARPUSAVIO PRIKLAUSOMYBĘ. Technological and Economic Development of Economy, 16(1), 109-125. doi:10.3846/tede.2010.07Brauers, W. K. M., & Zavadskas, E. K. (2010). PROJECT MANAGEMENT BY MULTIMOORA AS AN INSTRUMENT FOR TRANSITION ECONOMIES / PROJEKTŲ VADYBA SU MULTIMOORA KAIP PRIEMONĖ PEREINAMOJO LAIKOTARPIO ŪKIAMS. Technological and Economic Development of Economy, 16(1), 5-24. doi:10.3846/tede.2010.01Dempster, A. P. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. The Annals of Mathematical Statistics, 38(2), 325-339. doi:10.1214/aoms/1177698950ENGEMANN, K. J., MILLER, H. E., & YAGER, R. R. (1996). DECISION MAKING WITH BELIEF STRUCTURES: AN APPLICATION IN RISK MANAGEMENT. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 04(01), 1-25. doi:10.1142/s0218488596000020ENGEMANN, K. J., FILEV, D. P., & YAGER, R. R. (1996). MODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES. International Journal of General Systems, 24(3), 281-294. doi:10.1080/03081079608945123Engemann, K. J., & Miller, H. E. (2009). Critical infrastructure and smart technology risk modelling using computational intelligence. International Journal of Business Continuity and Risk Management, 1(1), 91. doi:10.1504/ijbcrm.2009.028953Fodor, J., Marichal, J.-L., & Roubens, M. (1995). Characterization of the ordered weighted averaging operators. IEEE Transactions on Fuzzy Systems, 3(2), 236-240. doi:10.1109/91.388176Han, Z., & Liu, P. (2011). A FUZZY MULTI-ATTRIBUTE DECISION-MAKING METHOD UNDER RISK WITH UNKNOWN ATTRIBUTE WEIGHTS / NERAIŠKUSIS MAŽESNĖS RIZIKOS DAUGIATIKSLIS SPRENDIMŲ PRIĖMIMO METODAS SU NEŽINOMAIS PRISKIRIAMAIS REIKŠMINGUMAIS. Technological and Economic Development of Economy, 17(2), 246-258. doi:10.3846/20294913.2011.580575Keršulienė, V., Zavadskas, E. K., & Turskis, Z. (2010). SELECTION OF RATIONAL DISPUTE RESOLUTION METHOD BY APPLYING NEW STEP‐WISE WEIGHT ASSESSMENT RATIO ANALYSIS (SWARA). Journal of Business Economics and Management, 11(2), 243-258. doi:10.3846/jbem.2010.12Liu, P. (2009). MULTI‐ATTRIBUTE DECISION‐MAKING METHOD RESEARCH BASED ON INTERVAL VAGUE SET AND TOPSIS METHOD. Technological and Economic Development of Economy, 15(3), 453-463. doi:10.3846/1392-8619.2009.15.453-463Liu, P. (2011). A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Systems with Applications, 38(1), 1053-1060. doi:10.1016/j.eswa.2010.07.144Merigó, J. M. (2011). A unified model between the weighted average and the induced OWA operator. Expert Systems with Applications, 38(9), 11560-11572. doi:10.1016/j.eswa.2011.03.034Merigó, J. M. (2012). The probabilistic weighted average and its application in multiperson decision making. International Journal of Intelligent Systems, 27(5), 457-476. doi:10.1002/int.21531Merigó, J. M., & Casanovas, M. (2009). Induced aggregation operators in decision making with the Dempster-Shafer belief structure. International Journal of Intelligent Systems, 24(8), 934-954. doi:10.1002/int.20368Merigó, J. M., & Casanovas, M. (2010). The uncertain induced quasi-arithmetic OWA operator. International Journal of Intelligent Systems, 26(1), 1-24. doi:10.1002/int.20444MERIGÓ, J. M., & CASANOVAS, M. (2011). THE UNCERTAIN GENERALIZED OWA OPERATOR AND ITS APPLICATION TO FINANCIAL DECISION MAKING. International Journal of Information Technology & Decision Making, 10(02), 211-230. doi:10.1142/s0219622011004300MERIGÓ, J. M., CASANOVAS, M., & MARTÍNEZ, L. (2010). LINGUISTIC AGGREGATION OPERATORS FOR LINGUISTIC DECISION MAKING BASED ON THE DEMPSTER-SHAFER THEORY OF EVIDENCE. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(03), 287-304. doi:10.1142/s0218488510006544MERIGO, J., & GILLAFUENTE, A. (2009). The induced generalized OWA operator. Information Sciences, 179(6), 729-741. doi:10.1016/j.ins.2008.11.013Merigó, J. M., & Gil-Lafuente, A. M. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085-2094. doi:10.1016/j.ins.2010.01.028Merigó, J. M., & Wei, G. (2011). PROBABILISTIC AGGREGATION OPERATORS AND THEIR APPLICATION IN UNCERTAIN MULTI-PERSON DECISION-MAKING / TIKIMYBINIAI SUMAVIMO OPERATORIAI IR JŲ TAIKYMAS PRIIMANT GRUPINIUS SPRENDIMUS NEAPIBRĖŽTOJE APLINKOJE. Technological and Economic Development of Economy, 17(2), 335-351. doi:10.3846/20294913.2011.584961Podvezko, V. (2009). Application of AHP technique. Journal of Business Economics and Management, 10(2), 181-189. doi:10.3846/1611-1699.2009.10.181-189Reformat, M., & Yager, R. R. (2007). Building ensemble classifiers using belief functions and OWA operators. Soft Computing, 12(6), 543-558. doi:10.1007/s00500-007-0227-2Srivastava, R. P., & Mock, T. J. (Eds.). (2002). Belief Functions in Business Decisions. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-7908-1798-0Torra, V. (1997). The weighted OWA operator. International Journal of Intelligent Systems, 12(2), 153-166. doi:10.1002/(sici)1098-111x(199702)12:23.0.co;2-pWei, G.-W. (2011). Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Computers & Industrial Engineering, 61(1), 32-38. doi:10.1016/j.cie.2011.02.007Wei, G., Zhao, X., & Lin, R. (2010). Some Induced Aggregating Operators with Fuzzy Number Intuitionistic Fuzzy Information and their Applications to Group Decision Making. International Journal of Computational Intelligence Systems, 3(1), 84-95. doi:10.1080/18756891.2010.9727679Xu, Z. (2005). An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20(8), 843-865. doi:10.1002/int.20097Xu, Z. (2009). A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making. Group Decision and Negotiation, 19(1), 57-76. doi:10.1007/s10726-009-9164-zXu, Z. S., & Da, Q. L. (2003). An overview of operators for aggregating information. International Journal of Intelligent Systems, 18(9), 953-969. doi:10.1002/int.10127Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183-190. doi:10.1109/21.87068YAGER, R. R. (1992). DECISION MAKING UNDER DEMPSTER-SHAFER UNCERTAINTIES. International Journal of General Systems, 20(3), 233-245. doi:10.1080/03081079208945033Yager, R. R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59(2), 125-148. doi:10.1016/0165-0114(93)90194-mYager, R. R. (1998). Including importances in OWA aggregations using fuzzy systems modeling. IEEE Transactions on Fuzzy Systems, 6(2), 286-294. doi:10.1109/91.669028Yager, R. R. (2004). Generalized OWA Aggregation Operators. Fuzzy Optimization and Decision Making, 3(1), 93-107. doi:10.1023/b:fodm.0000013074.68765.97Yager, R. R., Engemann, K. J., & Filev, D. P. (1995). On the concept of immediate probabilities. International Journal of Intelligent Systems, 10(4), 373-397. doi:10.1002/int.4550100403Yager, R. R., & Kacprzyk, J. (Eds.). (1997). The Ordered Weighted Averaging Operators. doi:10.1007/978-1-4615-6123-1Yager, R. R., Kacprzyk, J., & Beliakov, G. (Eds.). (2011). Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-642-17910-5Yager, R. R., & Liu, L. (Eds.). (2008). Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-44792-4Zavadskas, E. K., & Turskis, Z. (2011). MULTIPLE CRITERIA DECISION MAKING (MCDM) METHODS IN ECONOMICS: AN OVERVIEW / DAUGIATIKSLIAI SPRENDIMŲ PRIĖMIMO METODAI EKONOMIKOJE: APŽVALGA. Technological and Economic Development of Economy, 17(2), 397-427. doi:10.3846/20294913.2011.593291Zavadskas, E. K., Vilutienė, T., Turskis, Z., & Tamosaitienė, J. (2010). CONTRACTOR SELECTION FOR CONSTRUCTION WORKS BY APPLYING SAW‐G AND TOPSIS GREY TECHNIQUES. Journal of Business Economics and Management, 11(1), 34-55. doi:10.3846/jbem.2010.03Zeng, S., & Su, W. (2011). Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems, 24(8), 1224-1232. doi:10.1016/j.knosys.2011.05.013Zhang, X., & Liu, P. (2010). METHOD FOR AGGREGATING TRIANGULAR FUZZY INTUITIONISTIC FUZZY INFORMATION AND ITS APPLICATION TO DECISION MAKING / NUMANOMŲ NEAPIBRĖŽTŲJŲ AIBIŲ TEORIJA IR JOS TAIKYMAS PRIIMANT SPRENDIMUS. Technological and Economic Development of Economy, 16(2), 280-290. doi:10.3846/tede.2010.18Zhao, H., Xu, Z., Ni, M., & Liu, S. (2010). Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 25(1), 1-30. doi:10.1002/int.20386Zhou, L.-G., & Chen, H. (2010). Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. International Journal of Intelligent Systems, n/a-n/a. doi:10.1002/int.20419Zhou, L.-G., & Chen, H.-Y. (2011). Continuous generalized OWA operator and its application to decision making. Fuzzy Sets and Systems, 168(1), 18-34. doi:10.1016/j.fss.2010.05.009Zhou, L., & Chen, H. (2012). A generalization of the power aggregation operators for linguistic environment and its application in group decision making. Knowledge-Based Systems, 26, 216-224. doi:10.1016/j.knosys.2011.08.004Zhou, L., Chen, H., & Liu, J. (2011). Generalized Multiple Averaging Operators and their Applications to Group Decision Making. Group Decision and Negotiation, 22(2), 331-358. doi:10.1007/s10726-011-9267-1Zhou, L., Chen, H., & Liu, J. (2012). Generalized power aggregation operators and their applications in group decision making. Computers & Industrial Engineering, 62(4), 989-999. doi:10.1016/j.cie.2011.12.025Zhou, L.-G., Chen, H.-Y., Merigó, J. M., & Gil-Lafuente, A. M. (2012). Uncertain generalized aggregation operators. Expert Systems with Applications, 39(1), 1105-1117. doi:10.1016/j.eswa.2011.07.11

Improving Distributed Decision Making in Inventory Management: A Combined ABC-AHP Approach Supported by Teamwork

[EN] The need of organizations to ensure service levels that impact on customer satisfaction has required the design of collaborative processes among stakeholders involved in inventory decision making. The increase of quantity and variety of items, on the one hand, and demand and customer expectations, on the other hand, are transformed into a greater complexity in inventory management, requiring effective communication and agreements between the leaders of the logistics processes. Traditionally, decision making in inventory management was based on approaches conditioned only by cost or sales volume. These approaches must be overcome by others that consider multiple criteria, involving several areas of the companies and taking into account the opinions of the stakeholders involved in these decisions. Inventory management becomes part of a complex system that involves stakeholders from different areas of the company, where each agent has limited information and where the cooperation between such agents is key for the system's performance. In this paper, a distributed inventory control approach was used with the decisions allowing communication between the stakeholders and with a multicriteria group decision-making perspective. This work proposes a methodology that combines the analysis of the value chain and the AHP technique, in order to improve communication and the performance of the areas related to inventory management decision making. This methodology uses the areas of the value chain as a theoretical framework to identify the criteria necessary for the application of the AHP multicriteria group decision-making technique. These criteria were defined as indicators that measure the performance of the areas of the value chain related to inventory management and were used to classify ABC inventory of the products according to these selected criteria. Therefore, the methodology allows us to solve inventory management DDM based on multicriteria ABC classification and was validated in a Colombian company belonging to the graphic arts sector.Pérez Vergara, IG.; Arias Sánchez, JA.; Poveda Bautista, R.; Diego-Mas, JA. (2020). Improving Distributed Decision Making in Inventory Management: A Combined ABC-AHP Approach Supported by Teamwork. Complexity. 2020:1-13. https://doi.org/10.1155/2020/6758108S1132020Poveda-Bautista, R., Baptista, D. C., & García-Melón, M. (2012). Setting competitiveness indicators using BSC and ANP. International Journal of Production Research, 50(17), 4738-4752. doi:10.1080/00207543.2012.657964Castro Zuluaga, C. A., Velez Gallego, M. C., & Catro Urrego, J. A. (2011). Clasificación ABC Multicriterio: Tipos de Criterios y efectos en la asignación de pesos. ITECKNE, 8(2). doi:10.15332/iteckne.v8i2.35Morash, E. A., & Clinton, S. R. (1998). Supply Chain Integration: Customer Value through Collaborative Closeness versus Operational Excellence. Journal of Marketing Theory and Practice, 6(4), 104-120. doi:10.1080/10696679.1998.11501814Fabbe-Costes, N. (2015). Évaluer la création de valeurdu Supply Chain Management. Logistique & Management, 23(4), 41-50. doi:10.1080/12507970.2015.11758621Flores, B. E., & Clay Whybark, D. (1986). Multiple Criteria ABC Analysis. International Journal of Operations & Production Management, 6(3), 38-46. doi:10.1108/eb054765Partovi, F. Y., & Burton, J. (1993). Using the Analytic Hierarchy Process for ABC Analysis. International Journal of Operations & Production Management, 13(9), 29-44. doi:10.1108/01443579310043619Balaji, K., & Kumar, V. S. S. (2014). Multicriteria Inventory ABC Classification in an Automobile Rubber Components Manufacturing Industry. Procedia CIRP, 17, 463-468. doi:10.1016/j.procir.2014.02.044Ramanathan, R. (2006). ABC inventory classification with multiple-criteria using weighted linear optimization. Computers & Operations Research, 33(3), 695-700. doi:10.1016/j.cor.2004.07.014Van Kampen, T. J., Akkerman, R., & Pieter van Donk, D. (2012). SKU classification: a literature review and conceptual framework. International Journal of Operations & Production Management, 32(7), 850-876. doi:10.1108/01443571211250112Flores, B. E., Olson, D. L., & Dorai, V. K. (1992). Management of multicriteria inventory classification. Mathematical and Computer Modelling, 16(12), 71-82. doi:10.1016/0895-7177(92)90021-cGajpal, P. P., Ganesh, L. S., & Rajendran, C. (1994). Criticality analysis of spare parts using the analytic hierarchy process. International Journal of Production Economics, 35(1-3), 293-297. doi:10.1016/0925-5273(94)90095-7Scala, N. M., Rajgopal, J., & Needy, K. L. (2014). Managing Nuclear Spare Parts Inventories: A Data Driven Methodology. IEEE Transactions on Engineering Management, 61(1), 28-37. doi:10.1109/tem.2013.2283170Hadad, Y., & Keren, B. (2013). ABC inventory classification via linear discriminant analysis and ranking methods. International Journal of Logistics Systems and Management, 14(4), 387. doi:10.1504/ijlsm.2013.052744Altay Guvenir, H., & Erel, E. (1998). Multicriteria inventory classification using a genetic algorithm. European Journal of Operational Research, 105(1), 29-37. doi:10.1016/s0377-2217(97)00039-8Rezaei, J., & Dowlatshahi, S. (2010). A rule-based multi-criteria approach to inventory classification. International Journal of Production Research, 48(23), 7107-7126. doi:10.1080/00207540903348361Hatefi, S. M., Torabi, S. A., & Bagheri, P. (2013). Multi-criteria ABC inventory classification with mixed quantitative and qualitative criteria. International Journal of Production Research, 52(3), 776-786. doi:10.1080/00207543.2013.838328Ishizaka, A., Pearman, C., & Nemery, P. (2012). AHPSort: an AHP-based method for sorting problems. International Journal of Production Research, 50(17), 4767-4784. doi:10.1080/00207543.2012.657966Yu, M.-C. (2011). Multi-criteria ABC analysis using artificial-intelligence-based classification techniques. Expert Systems with Applications, 38(4), 3416-3421. doi:10.1016/j.eswa.2010.08.127Tsai, C.-Y., & Yeh, S.-W. (2008). A multiple objective particle swarm optimization approach for inventory classification. International Journal of Production Economics, 114(2), 656-666. doi:10.1016/j.ijpe.2008.02.017Aydin Keskin, G., & Ozkan, C. (2013). Multiple Criteria ABC Analysis with FCM Clustering. Journal of Industrial Engineering, 2013, 1-7. doi:10.1155/2013/827274Lolli, F., Ishizaka, A., & Gamberini, R. (2014). New AHP-based approaches for multi-criteria inventory classification. International Journal of Production Economics, 156, 62-74. doi:10.1016/j.ijpe.2014.05.015Raja, A. M. L., Ai, T. J., & Astanti, R. D. (2016). A Clustering Classification of Spare Parts for Improving Inventory Policies. IOP Conference Series: Materials Science and Engineering, 114, 012075. doi:10.1088/1757-899x/114/1/012075Zowid, F. M., Babai, M. Z., Douissa, M. R., & Ducq, Y. (2019). Multi-criteria inventory ABC classification using Gaussian Mixture Model. IFAC-PapersOnLine, 52(13), 1925-1930. doi:10.1016/j.ifacol.2019.11.484Babai, M. Z., Ladhari, T., & Lajili, I. (2014). On the inventory performance of multi-criteria classification methods: empirical investigation. International Journal of Production Research, 53(1), 279-290. doi:10.1080/00207543.2014.952791Schneeweiss, C. (2003). Distributed decision making––a unified approach. European Journal of Operational Research, 150(2), 237-252. doi:10.1016/s0377-2217(02)00501-5Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), 83. doi:10.1504/ijssci.2008.017590Cakir, O., & Canbolat, M. S. (2008). A web-based decision support system for multi-criteria inventory classification using fuzzy AHP methodology. Expert Systems with Applications, 35(3), 1367-1378. doi:10.1016/j.eswa.2007.08.041Liu, J., Liao, X., Zhao, W., & Yang, N. (2016). A classification approach based on the outranking model for multiple criteria ABC analysis. Omega, 61, 19-34. doi:10.1016/j.omega.2015.07.004Douissa, M. R., & Jabeur, K. (2016). A New Model for Multi-criteria ABC Inventory Classification: PROAFTN Method. Procedia Computer Science, 96, 550-559. doi:10.1016/j.procs.2016.08.233Lolli, F., Balugani, E., Ishizaka, A., Gamberini, R., Rimini, B., & Regattieri, A. (2018). Machine learning for multi-criteria inventory classification applied to intermittent demand. Production Planning & Control, 30(1), 76-89. doi:10.1080/09537287.2018.1525506Kartal, H., Oztekin, A., Gunasekaran, A., & Cebi, F. (2016). An integrated decision analytic framework of machine learning with multi-criteria decision making for multi-attribute inventory classification. Computers & Industrial Engineering, 101, 599-613. doi:10.1016/j.cie.2016.06.004López-Soto, D., Angel-Bello, F., Yacout, S., & Alvarez, A. (2017). A multi-start algorithm to design a multi-class classifier for a multi-criteria ABC inventory classification problem. Expert Systems with Applications, 81, 12-21. doi:10.1016/j.eswa.2017.02.048Dweiri, F., Kumar, S., Khan, S. A., & Jain, V. (2016). Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Systems with Applications, 62, 273-283. doi:10.1016/j.eswa.2016.06.030Bruno, G., Esposito, E., Genovese, A., & Simpson, M. (2016). Applying supplier selection methodologies in a multi-stakeholder environment: A case study and a critical assessment. Expert Systems with Applications, 43, 271-285. doi:10.1016/j.eswa.2015.07.016Poza, C. (2020). A Conceptual Model to Measure Football Player’s Market Value. A Proposal by means of an Analytic Hierarchy Process. [Un modelo conceptual para medir el valor de mercado de los futbolistas. Una propuesta a través de un proceso analítico jerárquico]. RICYDE. Revista internacional de ciencias del deporte, 16(59), 24-42. doi:10.5232/ricyde2020.05903Guarnieri, P., Sobreiro, V. A., Nagano, M. S., & Marques Serrano, A. L. (2015). The challenge of selecting and evaluating third-party reverse logistics providers in a multicriteria perspective: a Brazilian case. Journal of Cleaner Production, 96, 209-219. doi:10.1016/j.jclepro.2014.05.040Ishizaka, A., & Labib, A. (2011). Selection of new production facilities with the Group Analytic Hierarchy Process Ordering method. Expert Systems with Applications, 38(6), 7317-7325. doi:10.1016/j.eswa.2010.12.004Partovi, F. Y., & Anandarajan, M. (2002). Classifying inventory using an artificial neural network approach. Computers & Industrial Engineering, 41(4), 389-404. doi:10.1016/s0360-8352(01)00064-xAlonso-Manzanedo, M., De-la -Fuente-Aragon, M. V., & Ros-McDonnell, L. (2013). A Proposed Collaborative Network Enterprise Model in the Fruit-and-Vegetable Sector Using Maturity Models. Annals of Industrial Engineering 2012, 359-366. doi:10.1007/978-1-4471-5349-8_42Augusto, M., Lisboa, J., Yasin, M., & Figueira, J. R. (2008). Benchmarking in a multiple criteria performance context: An application and a conceptual framework. European Journal of Operational Research, 184(1), 244-254. doi:10.1016/j.ejor.2006.10.05

Ranking Alternatives on the Basis of a Dominance Intensity Measure

The additive multi-attribute utility model is widely used within MultiAttribute Utility Theory (MAUT), demanding all the information describing the decision-making situation. However, these information requirements can obviously be far too strict in many practical situations. Consequently, incomplete information about input parameters has been incorporated into the decisionmaking process. We propose an approach based on a dominance intensity measure to deal with such situations. The approach is based on the dominance values between pairs of alternatives that can be computed by linear programming. These dominance values are transformed into dominance intensities from which a dominance intensity measure is derived. It is used to analyze the robustness of a ranking of technologies for the disposition of surplus weapons-grade plutonium by the Department of Energy in the USA, and compared with other dominance measuring methods

A REVIEW OF APPLICATIONS OF MULTIPLE - CRITERIA DECISION-MAKING TECHNIQUES TO FISHERIES

Management of public resources, such as fisheries, is a complex task. Society, in general, has a number of goals that it hopes to achieve from the use of public resources. These include conservation, economic, and social objectives. However, these objectives often conflict, due to the varying opinions of the many stakeholders. It would appear that the techniques available in the field of multiple-criteria decision-making (MCDM) are well suited to the analysis and determination of fisheries management regimes. However, to date, relatively few publications exist using such MCDM methods compared to other applicational fields, such as forestry, agriculture, and finance. This paper reviews MCDM applied to fishery management by providing an overview of the research published to date. Conclusions are drawn regarding the success and applicability of these techniques to analyzing fisheries management problems.Resource /Energy Economics and Policy,

Decision support model for the selection of asphalt wearing courses in highly trafficked roads

The suitable choice of the materials forming the wearing course of highly trafficked roads is a delicate task because of their direct interaction with vehicles. Furthermore, modern roads must be planned according to sustainable development goals, which is complex because some of these might be in conflict. Under this premise, this paper develops a multi-criteria decision support model based on the analytic hierarchy process and the technique for order of preference by similarity to ideal solution to facilitate the selection of wearing courses in European countries. Variables were modelled using either fuzzy logic or Monte Carlo methods, depending on their nature. The views of a panel of experts on the problem were collected and processed using the generalized reduced gradient algorithm and a distance-based aggregation approach. The results showed a clear preponderance by stone mastic asphalt over the remaining alternatives in different scenarios evaluated through sensitivity analysis. The research leading to these results was framed in the European FP7 Project DURABROADS (No. 605404).The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 605404

Dominance Measuring Approach using Stochastic Weights

In this paper we propose an approach to obtain a ranking of alternatives in multicriteria decision-making problems when there is imprecision concerning the alternative performances, component utility functions and weights. We assume decision maker's preferences are represented by an additive multi-attribute utility function, in which weights are modeled by independent normal variables, the performance in each attribute for each alternative is an interval value and classes of utility functions are available for each attribute. The approach we propose is based on dominance measures, which are computed in a similar way that when the imprecision concerning weights is modeled by uniform distributions or by an ordinal relation. In this paper we will show how the approach can be applied when the imprecision concerning weights are represented by normal distributions. Extensions to other distributions, such as truncated normal or beta, can be feasible using Monte Carlo simulation techniques

A comparison of TOPSIS, grey relational analysis and COPRAS methods for machine selection problem in the food industry of Turkey

[EN] The paper aims to compare the results of the selection/choice of cream separators by using multi-criteria decision-making methods in an integrated manner for an enterprise with a dairy processing capacity of 80 to 100 tons per day operating in the Turkish food sector. A total of 7 alternative products and 7 criteria for milk processing were determined. Criterion weights were calculated using entropy method and then integrated into TOPSIS (Technique for Order Preference by Similarity to Ideal Solutions), GRA (Grey Relational Analysis) and COPRAS (Complex Proportional Assessment) methods. Sensitivity analyses were carried out on the results obtained from the three methods to check for their reliability. At the end of the study, similar alternative and appropriate results were found from the TOPSIS and COPRAS methods. However, different alternative but appropriate or suitable results were obtained from the GRA method. Sensitivity analysis of the three methods showed that all the methods used were valid. In the review of available and related literature, very few studies on machine selection in the dairy and food sector in general were found. For this reason, it is thought that the study will contribute to the decision-making process of companies in the dairy sector in their choice of machinery selections. As far as is known, this paper is the first attempt in extant literature to compare in an integrated manner the results of TOPSIS, COPRAS and GRA methods considered in the study.Özcan, S.; Çelik, AK. (2021). A comparison of TOPSIS, grey relational analysis and COPRAS methods for machine selection problem in the food industry of Turkey. International Journal of Production Management and Engineering. 9(2):81-92. https://doi.org/10.4995/ijpme.2021.14734OJS819292Ahmed, M., Qureshi, M.N., Mallick, J., Kahla, N.B. (2019). Selection of sustainable supplementary concrete materials using OSM-AHP-TOPSIS approach. Advances in Materials Science and Engineering, 2019, 1-12. https://doi.org/10.1155/2019/2850480Aloini, D., Dulmin, R., Mininno, V. (2014). A peer IF-TOPSIS based decision support system for packaging machine selection. Expert Systems with Applications, 41(5), 2157-2165https://doi.org/10.1016/j.eswa.2013.09.014Alpay, S., Ihpar, M. (2018). Equipment selection based on two different fuzzy multi criteria decision making methods: Fuzzy TOPSIS and fuzzy VIKOR. Open Geosciences, 10(1), 661-677. https://doi.org/10.1515/geo-2018-0053Antucheviciene, J., Zavadskas, E.K., Zakarevičius, A. (2012). Ranking redevelopment decisions of derelict buildings and analysis of ranking results. Economic Computation and Economic Cybernetics Studies and Research, 46(2), 37-63. Retrieved June 08, 2020 from http://www.ecocyb.ase.ro/22012/Edmundas%20ZAVADSKAS%20_DA_.pdfAyağ, Z., Özdemir, R.G. (2006). A fuzzy AHP approach to evaluating machine tool alternatives. Journal of Intelligent Manufacturing, 17(2), 179-190. https://doi.org/10.1007/s10845-005-6635-1Belton, V., Stewart, T.J. (2002). Multiple criteria decision analysis: An integrated approach. Berlin: Kluwer Academic Publishers.https://doi.org/10.1007/978-1-4615-1495-4Camcı, A., Temur, G.T., Beşkese, A. (2018). CNC router selection for SMEs in woodwork manufacturing using hesitant fuzzy AHP method. Journal of Enterprise Information Management, 31(4), 529-549. https://doi.org/10.1108/JEIM-01-2018-0017Çakır, S. (2018). An integrated approach to machine selection problem using fuzzy SMART-fuzzy weighted axiomatic design. Journal of Intelligent Manufacturing, 29(7), 1433-1445. https://doi.org/10.1007/s10845-015-1189-3Çelen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: With an application to Turkish deposit banking market. Informatica, 25(2), 185-208. https://doi.org/10.15388/Informatica.2014.10Chandan, R.C. (2008). Dairy Processing and Quality Assurance: An Overview. Ramesh C. Chandan, Arun Kilara, Nagendra Shah (Eds.), In Dairy Processing and Quality Assurance (pp. 1-40). New Jersey: Wiley-Blackwell. https://doi.org/10.1002/9780813804033Chatterjee, P., Chakraborty, S. (2014). Investigating the effect of normalization norms in flexible manfacturing sytem selection using Multi-Criteria Decision-Making methods. Journal of Engineering Science and Technology Review, 7(3), 141-150. https://doi.org/10.25103/jestr.073.23Clarke, M.P., Denby, B., Schofield, D. (1990). Decision making tools for surface mine equipment selection. Mining Science and Technology, 10(3), 323-335. https://doi.org/10.1016/0167-9031(90)90530-6Datta, S., Sahu, N., Mahapatra, S. (2013). Robot selection based on grey-MULTIMOORA approach. Grey Systems: Theory and Application, 3(2), 201-232. https://doi.org/10.1108/GS-05-2013-0008Deng, H., Yeh, C.H., Willis, R. J. (2000). Inter-company comparison using modified TOPSIS with objective weights. Computers and Operations Research, 27(10), 963-973. https://doi.org/10.1016/S0305-0548(99)00069-6Doğan, M., Aslan, D., Aktar, T., Sarac, M.G. (2016). A methodology to evaluate the sensory properties of instant hot chocolate beverage with different fat contents: multi-criteria decision-making techniques approach. European Food Research and Technology, 242(6), 953-966. https://doi.org/10.1007/s00217-015-2602-zErtuğrul, İ., Güneş, M. (2007). Fuzzy multi-criteria decision making method for machine selection. P. Melin, O. Castillo, E.G. Ramirez, J. Kacprzyk and W. Pedrycz (Eds.), In Analysis and Design of Intelligent Systems Using Soft Computing Techniques (pp. 638-648). Berlin, Germany: Springer. https://doi.org/10.1007/978-3-540-72432-2_65Ertuğrul, İ., Öztaş, T. (2015). The application of sewing machine selection with the multi-objective optimization on the basis of ratio analysis method (MOORA) in apparel sector. Textile and Apparel, 25(1), 80-85. Retrieved May 17, 2020 from https://dergipark.org.tr/tr/pub/tekstilvekonfeksiyon/issue/23647/251887FAO. (2019a). Dairy Market Review. FAO Publishing, Rome.FAO. (2019b). Food Outlook - Biannual Report on Global Food Markets. FAO Publishing, Rome.Feizabadi, A., Doolabi, M.S., Sadrnezhaad, S.K., Zafarani, H.R., Doolabi, D.S. (2017). MCDM selection of pulse parameters for best tribological performance of Cr-Al2O3 nano-composite co-deposited from trivalent chromium bath. Journal of Alloys and Compounds, 727, 286-296. https://doi.org/10.1016/j.jallcom.2017.08.098Feng, C.M., Wang, R.T. (2000). Performance evaluation for airlines including the consideration of financial ratios. Journal of Air Transport Management, 6(3), 133-142. https://doi.org/10.1016/S0969-6997(00)00003-XGuo, X., Sun, Z. (2016). A novel evaluation approach for tourist choice of destination based on grey relation analysis. Scientific Programming, 2016, 1-10. https://doi.org/10.1155/2016/1812094Gurmeric, V.E., Dogan, M., Toker, O.S., Senyigit, E., Ersoz, N.B. (2013). Application of different multi-criteria decision techniques to determine optimum flavour of prebiotic pudding based on sensory analyses. Food and Bioprocess Technology, 6(10), 2844-2859. https://doi.org/10.1007/s11947-012-0972-9Hwang, C.L., Yoon, K. (1980). Multiple attribute decision making methods and applications: A state-of-the-art survey. New York: Springer-Verlag.Jahan, A., Yazdani, M., Edwards, K.L. (2021). TOPSIS-RTCID for range target-based criteria and interval data. International Journal of Production Management and Engineering, 9(1), 1-14. https://doi.org/10.4995/ijpme.2021.13323Kabak, M., Dağdeviren, M. (2017). A hybrid approach based on ANP and Grey Relational Analysis for machine selection. Technical Gazette, 24(Supplement 1), 109-118. https://doi.org/10.17559/TV-20141123105333Kang, H.Y., Lee, A.H.I., Yang, C.Y. (2012). A fuzzy ANP model for supplier selection as applied to IC packaging. Journal of Intelligent Manufacturing, 23(5), 1477-1488.https://doi.org/10.1007/s10845-010-0448-6Karaman, S.,Toker, Ö.S., Yüksel, F., Çam, M., Kayacier, A., Dogan, M. (2014). Physicochemical, bioactive, and sensory properties of persimmon-based ice cream: Technique for order preference by similarity to ideal solution to determine optimum concentration. Journal of Dairy Science, 97(1), 97-110. https://doi.org/10.3168/jds.2013-7111Karim, R., Karmaker, C.L. (2016). Machine selection by AHP and TOPSIS methods. American Journal of Industrial Engineering, 4(1), 7-13. https://doi.org/10.12691/ajie-4-1-2Kumru, M., Kumru, P.Y. (2015). A fuzzy ANP model for the selection of 3D coordinate-measuring machine. Journal of Intelligent Manufacturing, 26(5), 999-1010. https://doi.org/10.1007/s10845-014-0882-yNguyen, H.T., Dawal, S. Z. Md., Nukman, Y., Aoyama, H. (2014). A hybrid approach for fuzzy multi-attribute decision making in machine tool selection with consideration of the interactions of attributes. Expert Systems with Applications, 41(6), 3078-3090. https://doi.org/10.1016/j.eswa.2013.10.039OECD/FAO. (2019). OECD-FAO Agricultural Outlook 2019-2028. OECD Publishing, Paris.Önüt, S., Kara, S.S., Işik, E. (2009). Long term supplier selection using a combined fuzzy MCDM approach: A case study for a telecommunication company. Expert Systems with Applications, 36(2), 3887-3895. https://doi.org/10.1016/j.eswa.2008.02.045Özceylan, E., Kabak, M., Dağdeviren, M. (2016). A fuzzy-based decision making procedure for machine selection problem. Journal of Intelligent and Fuzzy Systems, 30(3), 1841-1856. https://doi.org/10.3233/IFS-151895Özdağoğlu, A., Yakut, E., Bahar, S. (2017). Machine selection in a dairy product company with Entropy and SAW methods integration. Faculty of Economics and Administrative Sciences Journal, 32(1), 341-359. https://doi.org/10.24988/deuiibf.2017321605Özgen, A., Tuzkaya, G., Tuzkaya, U.R., Özgen, D. (2011). A multi-criteria decision making approach for machine tool selection problem in a fuzzy environment. International Journal of Computational Intelligence Systems, 4(4), 431-445. https://doi.org/10.1080/18756891.2011.9727802Ozturk, G., Dogan, M., Toker, O.S. (2014). Physicochemical, functional and sensory properties of mellorine enriched with different vegetable juices and TOPSIS approach to determine optimum juice concentration. Food Bioscience, 7, 45-55. https://doi.org/10.1016/j.fbio.2014.05.001Pang, B., Bai, S. (2013). An integrated fuzzy synthetic evaluation approach for supplier selection based on analytic network process. Journal of Intelligent Manufacturing, 23(5), 163-174. https://doi.org/10.1007/s10845-011-0551-3Paramasivam, V., Senthil, V., Ramasamy, N.R. (2011). Decision making in equipment selection: an integrated approach with digraph and matrix approach, AHP and ANP. The International Journal of Advanced Manufacturing Technology, 54(9-12), 1233-1244. https://doi.org/10.1007/s00170-010-2997-4Pavličić, D.M. (2001). Normalisation affects the results of MADM methods. Yugoslav Journal of Operations Research, 11(2), 251-265. Retrieved May 6, 2020 from http://scindeks.ceon.rs/article.aspx?artid=0354-02430102251PSamanta, B., Sarkar, B., Mukherjee, S.K. (2002). Selection of opencast mining equipment by a multi-criteria decision-making process. Mining Technology, 111(2), 136-142. https://doi.org/10.1179/mnt.2002.111.2.136Seçme, N.Y., Bayrakdaroğlu, A., Kahraman, C. (2009). Fuzzy performance evaluation in Turkish Banking Sector using Analytic Hierarchy Process and TOPSIS. Expert Systems with Applications, 36(9), 11699-11709. https://doi.org/10.1016/j.eswa.2009.03.013Sharma, A., Yadava, V. (2011). Optimization of cut quality characteristics during nd:yag laser straight cutting of ni-based superalloy thin sheet using grey relational analysis with entropy measurement. Materials and Manufacturing Processes, 26(12), 1522-1529. https://doi.org/10.1080/10426914.2011.551910Shih, H. S., Shyur, H.J., Lee, E.S. (2007). An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45(7-8), 801-813. https://doi.org/10.1016/j.mcm.2006.03.023Stanujkic, D., Đorđević, B., Đorđević, M. (2013). Comparative analysis of some prominent MCDM methods: A case of ranking Serbian Banks. Serbian Journal of Management, 8(2), 213-241. https://doi.org/10.5937/sjm8-3774Štirbanović, Z., Stanujkić, D., Miljanović, I., Milanović, D. (2019). Application of MCDM methods for flotation machine selection. Minerals Engineering, 137, 140-146. https://doi.org/10.1016/j.mineng.2019.04.014Sun, C.C. (2014). Combining grey relation analysis and entropy model for evaluating the operational performance: An empirical study. Quality and Quantity, 48(3), 1589-1600. https://doi.org/10.1007/s11135-013-9854-0Taha, Z., Rostam, S. (2011). A fuzzy AHP-ANN-based decision support system for machine tool selection in a flexible manufacturing cell. International Journal of Advanced Manufacturing Technology, 57(5-8), 719-733. https://doi.org/10.1007/s00170-011-3323-5Temiz, I., Çalış, G. (2017). Selection of construction equipment by using multi-criteria decision making methods. Procedia Engineering, 196, 286-293. https://doi.org/10.1016/j.proeng.2017.07.201Tosun, N. (2006). Determination of optimum parameters for multi-performance characteristics in drilling by using grey relational analysis. The International Journal of Advanced Manufacturing Technology, 28(5-6), 450-455. https://doi.org/10.1007/s00170-004-2386-yUğur, L.O. (2017). Application of the VIKOR multi-criteria decision method for construction machine buying. Journal of Polytechnic, 20(4), 879-885. https://doi.org/10.2339/politeknik.369058Ulubeyli, S., Kazaz, A. (2009). A multiple criteria decision-making approach to the selection of concrete pumps. Journal of Civil Engineering and Management, 15(4), 369-376. https://doi.org/10.3846/1392-3730.2009.15.369-376Vafaei, N., Ribeiro, R.A., Camarinha-Matos, L.M. (2018). Data normalisation techniques in decision making: Case study with TOPSIS method. International Journal of Information and Decision Sciences, 10(1), 19-38. https://doi.org/10.1504/IJIDS.2018.090667Vatansever, K., Kazançoğlu, Y. (2014). Integrated usage of fuzzy multi criteria decision making techniques for machine selection problems and an application. International Journal of Business and Social Science, 5(9), 12-24. https://doi.org/10.1504/IJIDS.2018.090667https://doi.org/10.1504/IJIDS.2018.090667Wang, T.C., Lee, H.D. (2009). Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Systems with Applications, 36(5), 8980-8985. https://doi.org/10.1016/j.eswa.2008.11.035Wu, J., Sun, J., Liang, L., Zha, Y. (2011). Determination of weights for ultimate cross efficiency using Shannon entropy. Expert Systems with Applications, 38(5), 5162-5165. https://doi.org/10.1016/j.eswa.2010.10.046Wu, W., Peng, Y. (2016). Extension of grey relational analysis for facilitating group consensus to oil spill emergency management. Annals of Operations Research, 238(1-2), 615-635. https://doi.org/10.1007/s10479-015-2067-2Wu, Z., Ahmad, J., Xu, J. (2016). A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information. Applied Soft Computing, 42, 314-324. https://doi.org/10.1016/j.asoc.2016.02.007Yazdani-Chamzini, A., Yakhchali, S.H. (2012). Tunnel Boring Machine (TBM) selection using fuzzy multicriteria decision making methods. Tunnelling and Underground Space Technology, 30, 194-204. https://doi.org/10.1016/j.tust.2012.02.021Yılmaz, B., Dağdeviren, M. (2010). Comparative analysis of PROMETHEE and fuzzy PROMETHEE methods in equipment selection problem. Journal of the Faculty of Engineering and Architecture of Gazi University, 25(4), 811-826. Retrieved May 6, 2020 from https://avesis.gazi.edu.tr/yayin/989e528e-9184-4d8e-8970-fccfabbbed73/comparative-analysis-of-promethee-and-fuzzy-promethee-methods-in-equipment-selection-problemYılmaz, B., Dağdeviren, M. (2011). A combined approach for equipment selection: F-PROMETHEE method and zero-one goal programming. Expert Systems with Applications, 38(9), 11641-11650. https://doi.org/10.1016/j.eswa.2011.03.043Zavadskas, E.K., Kaklauskas, A., Banaitis, A., Kvederyte, N. (2004). Housing credit access model: The case for Lithuania. European Journal of Operational Research, 155(2), 335-352. https://doi.org/10.1016/S0377-2217(03)00091-2Zhang, H., Gu, C.L., Gu, L. W., Zhang, Y. (2011). The evaluation of tourism destination competitiveness by TOPSIS and information entropy: A case in the Yangtze River Delta of China. Tourism Management, 32(2), 443-451. https://doi.org/10.1016/j.tourman.2010.02.00