Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

On the fixed point theory of soft metric spaces

[EN] The aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results. We also present some examples to validate and illustrate our approach.Salvador Romaguera thanks the support of Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Abbas, M.; Murtaza, G.; Romaguera Bonilla, S. (2016). On the fixed point theory of soft metric spaces. Fixed Point Theory and Applications. 2016(17):1-11. https://doi.org/10.1186/s13663-016-0502-yS111201617Zadeh, LA: Fuzzy sets. Inf. Control 8, 103-112 (1965)Molodtsov, D: Soft set theory - first results. Comput. Math. Appl. 37, 19-31 (1999)Aktaş, H, Çağman, N: Soft sets and soft groups. Inf. Sci. 177, 2726-2735 (2007)Ali, MI, Feng, F, Liu, X, Min, WK, Shabir, M: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547-1553 (2009)Feng, F, Liu, X, Leoreanu-Fotea, V, Jun, YB: Soft sets and soft rough sets. Inf. Sci. 181, 1125-1137 (2011)Jiang, Y, Tang, Y, Chen, Q, Wang, J, Tang, S: Extending soft sets with description logics. Comput. Math. Appl. 59, 2087-2096 (2009)Jun, YB: Soft BCK/BCI-algebras. Comput. Math. Appl. 56, 1408-1413 (2008)Jun, YB, Lee, KJ, Khan, A: Soft ordered semigroups. Math. Log. Q. 56, 42-50 (2010)Jun, YB, Lee, KJ, Park, CH: Soft set theory applied to ideals in d-algebras. Comput. Math. Appl. 57, 367-378 (2009)Jun, YB, Park, CH: Applications of soft sets in ideal theory of BCK/BCI-algebras. Inf. Sci. 178, 2466-2475 (2008)Kong, Z, Gao, L, Wang, L, Li, S: The normal parameter reduction of soft sets and its algorithm. Comput. Math. Appl. 56, 3029-3037 (2008)Majumdar, P, Samanta, SK: Generalized fuzzy soft sets. Comput. Math. Appl. 59, 1425-1432 (2010)Li, F: Notes on the soft operations. ARPN J. Syst. Softw. 1, 205-208 (2011)Maji, PK, Roy, AR, Biswas, R: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077-1083 (2002)Qin, K, Hong, Z: On soft equality. J. Comput. Appl. Math. 234, 1347-1355 (2010)Xiao, Z, Gong, K, Xia, S, Zou, Y: Exclusive disjunctive soft sets. Comput. Math. Appl. 59, 2128-2137 (2009)Xiao, Z, Gong, K, Zou, Y: A combined forecasting approach based on fuzzy soft sets. J. Comput. Appl. Math. 228, 326-333 (2009)Xu, W, Ma, J, Wang, S, Hao, G: Vague soft sets and their properties. Comput. Math. Appl. 59, 787-794 (2010)Yang, CF: A note on soft set theory. Comput. Math. Appl. 56, 1899-1900 (2008)Yang, X, Lin, TY, Yang, J, Li, Y, Yu, D: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58, 521-527 (2009)Zhu, P, Wen, Q: Operations on soft sets revisited (2012). arXiv:1205.2857v1Feng, F, Jun, YB, Liu, XY, Li, LF: An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234, 10-20 (2009)Feng, F, Jun, YB, Zhao, X: Soft semirings. Comput. Math. Appl. 56, 2621-2628 (2008)Feng, F, Liu, X: Soft rough sets with applications to demand analysis. In: Int. Workshop Intell. Syst. Appl. (ISA 2009), pp. 1-4. (2009)Herawan, T, Deris, MM: On multi-soft sets construction in information systems. In: Emerging Intelligent Computing Technology and Applications with Aspects of Artificial Intelligence, pp. 101-110. Springer, Berlin (2009)Herawan, T, Rose, ANM, Deris, MM: Soft set theoretic approach for dimensionality reduction. In: Database Theory and Application, pp. 171-178. Springer, Berlin (2009)Kim, YK, Min, WK: Full soft sets and full soft decision systems. J. Intell. Fuzzy Syst. 26, 925-933 (2014). doi: 10.3233/IFS-130783Mushrif, MM, Sengupta, S, Ray, AK: Texture classification using a novel, soft-set theory based classification algorithm. Lect. Notes Comput. Sci. 3851, 246-254 (2006)Roy, AR, Maji, PK: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 412-418 (2007)Zhu, P, Wen, Q: Probabilistic soft sets. In: IEEE Conference on Granular Computing (GrC 2010), pp. 635-638 (2010)Zou, Y, Xiao, Z: Data analysis approaches of soft sets under incomplete information. Knowl.-Based Syst. 21, 941-945 (2008)Cagman, N, Karatas, S, Enginoglu, S: Soft topology. Comput. Math. Appl. 62, 351-358 (2011)Das, S, Samanta, SK: Soft real sets, soft real numbers and their properties. J. Fuzzy Math. 20, 551-576 (2012)Das, S, Samanta, SK: Soft metric. Ann. Fuzzy Math. Inform. 6, 77-94 (2013)Abbas, M, Murtaza, G, Romaguera, S: Soft contraction theorem. J. Nonlinear Convex Anal. 16, 423-435 (2015)Chen, CM, Lin, IJ: Fixed point theory of the soft Meir-Keeler type contractive mappings on a complete soft metric space. Fixed Point Theory Appl. 2015, 184 (2015)Feng, F, Li, CX, Davvaz, B, Ali, MI: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 8999-9911 (2010)Maji, PK, Biswas, R, Roy, AR: Soft set theory. Comput. Math. Appl. 45, 555-562 (2003)Wardowski, D: On a soft mapping and its fixed points. Fixed Point Theory Appl. 2013, 182 (2013)Kannan, R: Some results on fixed points II. Am. Math. Mon. 76, 405-408 (1969)Meir, A, Keeler, E: A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326-329 (1969)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed-point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976

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-

Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods