Extensions of LINMAP model for multi criteria decision making with grey numbers

The linear programming technique for multidimensional analysis of preference, known as LINMAP is one of the existing well-known ideal seeking methods for multi attribute decision making problems. This method originally is proposed under crisp and deterministic circumstances. However, uncertainty is an indubitable property of decision making problems. In this paper, a new version of LINMAP-G is proposed where the decision maker's judgments are expressed as grey numbers. Like original LINMAP method, the grey ideal solution and attributes weight vector is determined and alternatives are ranked according to their weighted distance from determined ideal point. Application of the proposed method is illustrated in two numerical examples

Interval Type-2 Fuzzy Programming Method for Risky Multicriteria Decision-Making with Heterogeneous Relationship

We propose a new interval type-2 fuzzy (IT2F) programming method for risky multicriteria decision-making (MCDM) problems with IT2F truth degrees, where the criteria exhibit a heterogeneous relationship and decision-makers behave according to bounded rationality. First, we develop a technique to calculate the Banzhaf-based overall perceived utility values of alternatives based on 2-additive fuzzy measures and regret theory. Subsequently, considering pairwise comparisons of alternatives with IT2F truth degrees, we define the Banzhaf-based IT2F risky consistency index (BIT2FRCI) and the Banzhaf-based IT2F risky inconsistency index (BIT2FRII). Next, to identify the optimal weights, an IT2F programming model is established based on the concept that BIT2FRII must be minimized and must not exceed the BIT2FRCI using a fixed IT2F set. Furthermore, we design an effective algorithm using an external archive-based constrained state transition algorithm to solve the established model. Accordingly, the ranking order of alternatives is derived using the Banzhaf-based overall perceived utility values. Experimental studies pertaining to investment selection problems demonstrate the state-of-the-art performance of the proposed method, that is, its strong capability in addressing risky MCDM problems

THE USE OF THE PIVOT PAIRWISE RELATIVE CRITERIA IMPORTANCE ASSESSMENT METHOD FOR DETERMINING THE WEIGHTS OF CRITERIA

The weights of evaluation criteria could have a significant impact on the results obtained by applying multiple criteria decision-making methods. Therefore, the two extensions of the SWARA method that can be used in cases when it is not easy, or even is impossible to reach a consensus on the expected importance of the evaluation criteria are proposed in this paper. The primary objective of the proposed extensions is to provide an understandable and easy-to-use approach to the collecting of respondents’ real attitudes towards the significance of evaluation criteria and to also provide an approach to the checking of the reliability of the data collected

TOPSIS-RTCID for range target-based criteria and interval data

[EN] The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is receiving considerable attention as an essential decision analysis technique and becoming a leading method. This paper describes a new version of TOPSIS with interval data and capability to deal with all types of criteria. An improved structure of the TOPSIS is presented to deal with high uncertainty in engineering and engineering decision-making. The proposed Range Target-based Criteria and Interval Data model of TOPSIS (TOPSIS-RTCID) achieves the core contribution in decision making theories through a distinct normalization formula for cost and benefits criteria in scale of point and range target-based values. It is important to notice a very interesting property of the proposed normalization formula being opposite to the usual one. This property can explain why the rank reversal problem is limited. The applicability of the proposed TOPSIS-RTCID method is examined with several empirical litreture’s examples with comparisons, sensitivity analysis, and simulation. The authors have developed a new tool with more efficient, reliable and robust outcomes compared to that from other available tools. The complexity of an engineering design decision problem can be resolved through the development of a well-structured decision making method with multiple attributes. Various decision approches developed for engineering design have neglected elements that should have been taken into account. Through this study, engineering design problems can be resolved with greater reliability and confidence.Jahan, A.; Yazdani, M.; Edwards, K. (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.2021.13323OJS11491Ahn, B.S. (2017). The analytic hierarchy process with interval preference statements. Omega, 67, 177-185. https://doi.org/10.1016/j.omega.2016.05.004Alemi-Ardakani, M., Milani, A.S., Yannacopoulos, S., Shokouhi, G. (2016). On the effect of subjective, objective and combinative weighting in multiple criteria decision making: A case study on impact optimization of composites. Expert Systems With Applications, 46, 426-438. https://doi.org/10.1016/j.eswa.2015.11.003Amiri, M., Nosratian, N.E., Jamshidi, A., Kazemi, A. (2008). Developing a new ELECTRE method with interval data in multiple attribute decision making problems. Journal of Applied Sciences, 8, 4017-4028. https://doi.org/10.3923/jas.2008.4017.4028Bahraminasab, M., Jahan, A. (2011). Material selection for femoral component of total knee replacement using comprehensive VIKOR. Materials & Design, 32, 4471-4477. https://doi.org/10.1016/j.matdes.2011.03.046Baradaran, V., Azarnia, S. (2013). An Approach to Test Consistency and Generate Weights from Grey Pairwise Matrices in Grey Analytical Hierarchy Process. Journal of Grey System, 25.Behzadian, M., Otaghsara, S.K., Yazdani, M., Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 39, 13051-13069. https://doi.org/10.1016/j.eswa.2012.05.056Cables, E., Lamata, M.T., Verdegay, J.L. (2018). FRIM-Fuzzy Reference Ideal Method in Multicriteria Decision Making. In Collan, M. & Kacprzyk, J. (Eds.) Soft Computing Applications for Group Decision-making and Consensus Modeling. Cham, Springer International Publishing. https://doi.org/10.1007/978-3-319-60207-3_19Çakır, S. (2016). An integrated approach to machine selection problem using fuzzy SMART-fuzzy weighted axiomatic design. Journal of Intelligent Manufacturing, 1-13. https://doi.org/10.1007/s10845-015-1189-3Celen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: with an application to Turkish deposit banking market. Informatica, 25, 185-208. https://doi.org/10.15388/Informatica.2014.10Celik, E., Erdogan, M., Gumus, A. (2016). An extended fuzzy TOPSIS-GRA method based on different separation measures for green logistics service provider selection. International Journal of Environmental Science and Technology, 13, 1377-1392. https://doi.org/10.1007/s13762-016-0977-4Dymova, L., Sevastjanov, P., Tikhonenko, A. (2013). A direct interval extension of TOPSIS method. Expert Systems With Applications, 40, 4841-4847. https://doi.org/10.1016/j.eswa.2013.02.022Garca-Cascales, M.S., Lamata, M.T. (2012). On rank reversal and TOPSIS method. Mathematical and Computer Modelling, 56, 123-132. https://doi.org/10.1016/j.mcm.2011.12.022Hafezalkotob, A., Hafezalkotob, A. (2015). Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications. Materials & Design, 87, 949-959. https://doi.org/10.1016/j.matdes.2015.08.087Hafezalkotob, A., Hafezalkotob, A. (2016). Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection. Journal of Industrial Engineering International, 13, 181-198. https://doi.org/10.1007/s40092-016-0176-4Hafezalkotob, A., Hafezalkotob, A. (2017). Interval target-based VIKOR method supported on interval distance and preference degree for machine selection. Engineering Applications of Artificial Intelligence, 57, 184-196. https://doi.org/10.1016/j.engappai.2016.10.018Hafezalkotob, A., Hafezalkotob, A., Sayadi, M.K. (2016). Extension of MULTIMOORA method with interval numbers: An application in materials selection. Applied Mathematical Modelling, 40, 1372-1386. https://doi.org/10.1016/j.apm.2015.07.019Hajiagha, S.H.R., Hashemi, S.S., Zavadskas, E.K., Akrami, H. (2012). Extensions of LINMAP model for multi criteria decision making with grey numbers. Technological and Economic Development of Economy, 18, 636-650. https://doi.org/10.3846/20294913.2012.740518Hazelrigg, G.A. (2003). Validation of engineering design alternative selection methods. Engineering Optimization, 35, 103-120. https://doi.org/10.1080/0305215031000097059Hu, J., Du, Y., Mo, H., Wei, D., Deng, Y. (2016). A modified weighted TOPSIS to identify influential nodes in complex networks. Physica A: Statistical Mechanics and its Applications, 444, 73-85. https://doi.org/10.1016/j.physa.2015.09.028Huang, Y., Jiang, W. (2018). Extension of TOPSIS Method and its Application in Investment. Arabian Journal for Science and Engineering, 43, 693-705. https://doi.org/10.1007/s13369-017-2736-3Jahan, A. (2018). Developing WASPAS-RTB method for range target-based criteria: toward selection for robust design. Technological and Economic Development of Economy, 24, 1362-1387. https://doi.org/10.3846/20294913.2017.1295288Jahan, A., Bahraminasab, M., Edwards, K.L. (2012). A target-based normalization technique for materials selection. Materials & Design, 35, 647-654. https://doi.org/10.1016/j.matdes.2011.09.005Jahan, A., Edwards, K.L. (2013). VIKOR method for material selection problems with interval numbers and target-based criteria. Materials & Design, 47, 759-765. https://doi.org/10.1016/j.matdes.2012.12.072Jahan, A., Edwards, K.L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design, 65, 335-342. https://doi.org/10.1016/j.matdes.2014.09.022Jahan, A., Edwards, K.L., Bahraminasab, M. (2016). Multi-criteria decision analysis for supporting the selection of engineering materials in product design, Oxford, Butterworth-Heinemann.Jahan, A., Mustapha, F., Ismail, M.Y., Sapuan, S.M., Bahraminasab, M. (2011). A comprehensive VIKOR method for material selection. Materials & Design, 32, 1215-1221. https://doi.org/10.1016/j.matdes.2010.10.015Jahan, A., Zavadskas, E.K. (2018). ELECTRE-IDAT for design decision-making problems with interval data and target-based criteria. Soft Computing, 23, 129-143. https://doi.org/10.1007/s00500-018-3501-6Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Davoodi, A.R. (2009). Extension of TOPSIS for decision-making problems with interval data: Interval efficiency. Mathematical and Computer Modelling, 49, 1137-1142. https://doi.org/10.1016/j.mcm.2008.07.009Jahanshahloo, G.R., Lotfi, F.H., Izadikhah, M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation, 175, 1375-1384. https://doi.org/10.1016/j.amc.2005.08.048Kasirian, M., Yusuff, R. (2013). An integration of a hybrid modified TOPSIS with a PGP model for the supplier selection with interdependent criteria. International Journal of Production Research, 51, 1037-1054. https://doi.org/10.1080/00207543.2012.663107Kuo, T. (2017). A modified TOPSIS with a different ranking index. European Journal of Operational Research, 260, 152-160. https://doi.org/10.1016/j.ejor.2016.11.052Liang, D., Xu, Z. (2017). The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Applied Soft Computing, 60, 167-179. https://doi.org/10.1016/j.asoc.2017.06.034Liao, H., Wu, X. (2019). DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega, 94. 102058. https://doi.org/10.1016/j.omega.2019.04.001Liu, H.C., You, J.X., Zhen, L., Fan, X.J. (2014). A novel hybrid multiple criteria decision making model for material selection with targetbased criteria. Materials & Design, 60, 380-390. https://doi.org/10.1016/j.matdes.2014.03.071Maghsoodi, A.I., Maghsoodi, A.I., Poursoltan, P., Antucheviciene, J., Turskis, Z. (2019). Dam construction material selection by implementing the integrated SWARA-CODAS approach with target-based attributes. Archives of Civil and Mechanical Engineering, 19, 1194-1210. https://doi.org/10.1016/j.acme.2019.06.010Milani, A.S., Shanian, A., Madoliat, R., Nemes, J.A. (2005). The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection. Structural and Multidisciplinary Optimization, 29, 312-318. https://doi.org/10.1007/s00158-004-0473-1Peldschus, F. (2009). The analysis of the quality of the results obtained with the methods of multi-criteria decisions. Technological and Economic Development of Economy, 15, 580-592. https://doi.org/10.3846/1392-8619.2009.15.580-592Peldschus, F. (2018). Recent findings from numerical analysis in multi-criteria decision making. Technological and Economic Development of Economy, 24, 1695-1717. https://doi.org/10.3846/20294913.2017.1356761Perez, E.C., Lamata, M., Verdegay, J. (2016). RIM-Reference Ideal Method in Multicriteria Decision Making. Information Sciences, 337- 338, 1-10. https://doi.org/10.1016/j.ins.2015.12.011Sayadi, M.K., Heydari, M., Shahanaghi, K. (2009). Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 33, 2257-2262. https://doi.org/10.1016/j.apm.2008.06.002Sen, P., Yang, J.B. (1998). MCDM and the Nature of Decision Making in Design, Springer. https://doi.org/10.1007/978-1-4471-3020-8_2Sevastianov, P. (2007). Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster- Shafer theory. Information Sciences, 177, 4645-4661. https://doi.org/10.1016/j.ins.2007.05.001Shanian, A., Savadogo, O. (2009). A methodological concept for material selection of highly sensitive components based on multiple criteria decision analysis. Expert Systems With Applications, 36, 1362-1370. https://doi.org/10.1016/j.eswa.2007.11.052Shen, F., Ma, X., Li, Z., Xu, Z., Cai, D. (2018). An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Information Sciences, 428, 105-119. https://doi.org/10.1016/j.ins.2017.10.045Shishank, S., Dekkers, R. (2013). Outsourcing: decision-making methods and criteria during design and engineering. Production Planning & Control, 24, 318-336. https://doi.org/10.1080/09537287.2011.648544Shouzhen, Z., Yao, X. (2018). A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making. Technological and Economic Development of Economy, 24, 969-983. https://doi.org/10.3846/20294913.2016.1216472Stanujkic, D., Magdalinovic, N., Jovanovic, R., Stojanovic, S. (2012). An objective multi-criteria approach to optimization using MOORA method and interval grey numbers. Technological and Economic Development of Economy, 18, 331-363. https://doi.org/10.3846/20294913.2012.676996Suder, A., Kahraman, C. (2018). Multiattribute evaluation of organic and inorganic agricultural food investments using fuzzy TOPSIS. Technological and Economic Development of Economy, 24, 844-858. https://doi.org/10.3846/20294913.2016.1216905Tilstra, A.H., Backlund, P.B., Seepersad, C.C., Wood, K.L. (2015). Principles for designing products with flexibility for future evolution. International Journal of Mass Customisation, 5, 22-54. https://doi.org/10.1504/IJMASSC.2015.069597Tsaur, R.C. (2011) Decision risk analysis for an interval TOPSIS method. Applied Mathematics and Computation, 218, 4295-4304. https://doi.org/10.1016/j.amc.2011.10.001Turskis, Z., Zavadskas, E.K. (2010) A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method. Informatica, 21, 597-610. https://doi.org/10.15388/Informatica.2010.307Wang, Y.M., Luo, Y. (2009) On rank reversal in decision analysis. Mathematical and Computer Modelling, 49, 1221-1229. https://doi.org/10.1016/j.mcm.2008.06.019Ye, J. (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. Journal of Intelligent & Fuzzy Systems, 28, 247-255. https://doi.org/10.3233/IFS-141295Yue, Z. (2013) Group decision making with multi-attribute interval data. Information Fusion, 14, 551-561. https://doi.org/10.1016/j.inffus.2013.01.00

VIKOR Technique:A Systematic Review of the State of the Art Literature on Methodologies and Applications

The main objective of this paper is to present a systematic review of the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method in several application areas such as sustainability and renewable energy. This study reviewed a total of 176 papers, published in 2004 to 2015, from 83 high-ranking journals; most of which were related to Operational Research, Management Sciences, decision making, sustainability and renewable energy and were extracted from the “Web of Science and Scopus” databases. Papers were classified into 15 main application areas. Furthermore, papers were categorized based on the nationalities of authors, dates of publications, techniques and methods, type of studies, the names of the journals and studies purposes. The results of this study indicated that more papers on VIKOR technique were published in 2013 than in any other year. In addition, 13 papers were published about sustainability and renewable energy fields. Furthermore, VIKOR and fuzzy VIKOR methods, had the first rank in use. Additionally, the Journal of Expert Systems with Applications was the most significant journal in this study, with 27 publications on the topic. Finally, Taiwan had the first rank from 22 nationalities which used VIKOR technique

Revisiting the interval and fuzzy topsis methods: Is euclidean distance a suitable tool to measure the differences between fuzzy numbers?

Euclidean distance (ED) calculates the distance between n-coordinate points that n equals the dimension of the space these points are located. Some studies extended its application to measure the difference between fuzzy numbers (FNs).This study shows that this extension is not logical because although an n-coordinate point and an FN are denoted the same, they are conceptually different. An FN is defined by n components; however, n is not equal to the dimension of the space where the FN is located. This study illustrates this misapplication and shows that the ED between FNs does not necessarily reflect their difference. We also revisit triangular and trapezoidal fuzzy TOPSIS methods to avoid this misapplication. For this purpose, we first defuzzify the FNs using the center of gravity (COG) method and then apply the ED to measure the difference between crisp values. We use an example to illustrate that the existing fuzzy TOPSIS methods assign inaccurate weights to alternatives and may even rank them incorrectly

International entrepreneurial startups' location under uncertainty through a heterogeneous multi-layer decision-making approach:Evidence and application of an emerging economy

Purpose: Science and technology parks (STPs) have a limited capacity, which can create challenging conditions for applicants. This makes the location selection a multi-criteria decision-making (MCDM) problem to find and apply for the most appropriate STP with the highest accordance with the startup's requirements. This research aims to select the most appropriate STP to locate an international entrepreneurial pharmaceutical startup under uncertainty. Since drugs are generally produced domestically in developing countries such as Iran, the access of pharmaceutical startups to the resources provided by STPs can lead to overcoming competitors and improving the country's health system. Design/methodology/approach: In this research, the factors or attributes effective on startup location were extracted through a two-round Delphi method, which was performed among 15 experts within three groups. Subsequently, the determining factors were used to select the location of a pharmaceutical startup among possible STPs. In this regard, decision-makers were allowed to use different types of numbers to transfer their opinion. Afterward, the heterogeneous weighted aggregated sum product assessment (HWASPAS) method was applied to calculate the score of each alternative and rank them to place the studied startup successfully. Findings: The results indicated that Tehran STP stands in the first place; however, if the decision was made based on single criterion like cost, some other STPs could be preferable, and many managers would lose this choice. Furthermore, the results of the proposed method were close to other popular heterogeneous MCDM approaches. Originality/value: A heterogeneous WASPAS is developed in this article for the first time to enable international entrepreneurs to imply their opinion with various values and linguistic variables to reduce the emphasis on accurate data in an uncertain environment