A “Journey” from Traditional to Fuzzy Methods of Decision-Making
Subject Areas : Transactions on Fuzzy Sets and Systems
Michael Gr.
Voskoglou
1
(Department of Mathematical Sciences, Graduate Technological Educational Institute of Western Greece, Meg. Alexandrou 1, 263 34 Patras, Greece.)
Keywords: Decision-making (DM), Fuzzy set (FS), Intuitionistic FS (IFS), Neutrosophic set (NS), Grey number (GN), Soft set (SS).,
Abstract :
Decision-making (DM) is one of the most important components of human cognition. Starting with a review of the traditional criteria for DM, this work presents also a method for the verification of a decision, a step of the DM process which, due to its special interest, is usually examined separately from its other steps. Frequently in everyday life, however, the data of a DM problem are vague and characterized by uncertainty. In such cases the traditional techniques for DM, which are based on principles of the bivalent logic (yes-no), cannot help effectively in making the right decision. The first who introduced principles of the fuzzy sets theory in DM were Bellman and Zadeh in 1970 and an example is given here illustrating their fuzzy criterion for DM. Also, among the several fuzzy methods proposed later by other researchers for a more effective DM, a hybrid method is developed here for parametric multiple-criteria DM using soft sets and grey numbers (or intuitionistic fuzzy sets, or neutrosophic sets) as tools, which improves an earlier method proposed by Maji et al. in 2002. All the DM approaches presented in this paper are illustrated with everyday practical examples.
[1] Alazemi FKAOH, Ariffin MKABM, Mustapha FB, Supeni EEB. A comprehensive fuzzy decision-making method for minimizing completion time in manufacturing process in supply chains. Mathematics. 2021; 9(22): 2919. DOI: https://doi.org/10.3390/math9222919
[2] Alcantud JCR. Fuzzy Techniques for Decision Making. Switzerland: Symmetry Publishing; 2018.
[3] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20(1): 87-96. DOI: http://dx.doi.org/10.1016/S0165-0114(86)80034-3
[4] Barker RC. The Power of Decision. 2011. LA: Penguin Publishing Group; 2011.
[5] Bellman RA, Zadeh LA. Decision making in fuzzy environment. Management Science. 1970; 17(4): 141-164. DOI: http://dx.doi.org/10.1287/mnsc.17.4.B141
[6] Berger JO. Statistical Decision Theory: Foundations, Concepts and Methods. New York: Springer Verlag; 1980.
[7] Chiclana F, Herrera F, Herrera-Viedma E. Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems. 1998; 97(1): 33-48. DOI: https://doi.org/10.1016/S0165-0114(96)00339-9
[8] Deng J. Control problems of grey systems. Systems and Control Letters. 1982; 288-294. DOI: http://dx.doi.org/10.1016/S0167-6911(82)80025-X
[9] Ekel P. Methods of decision making in fuzzy environment and their applications. Nonlinear Analysis: Theory, Methods & Applications. 2001; 47(2): 979-990.
[10] Ekel P. Fuzzy sets and models of decision making. Computers & Mathematics with Applications. 2002; 44(7): 863-875. DOI: https://doi.org/10.1016/S0898-1221(02)00199-2
[11] Ekel P, Kokshenev I, Parreiras R, Pedrycz W, Pereira JrJ. Multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications. Information Sciences. 2016; 361: 100-119. DOI: https://doi.org/10.1016/j.ins.2016.04.030
[12] Heath C, Heath D. Decisive: How to Make Better Choices in Life and Work. 2013.
[13] Khan A, Yang M-S, Haq M, Shah AA, Arif M. A new approach for normal parameter reduction using σ-algebraic soft sets and its application in multi-attribute decision making. Mathematics. 2022; 10(8): 1297. DOI: https://doi.org/10.3390/math10081297
[14] Maji PK, Roy AR, Biswas R. An application of soft sets in a decision making problem. Computers and Mathematics with Applications. 2002; 44: 1077-1083. DOI: https://doi.org/10.1016/S0898-1221(02)00216-X
[15] Molodtsov D. Soft set theory-First results. Computers and Mathematics with Applications. 1999; 37(4-5): 19-31. DOI: https://doi.org/10.1016/S0898-1221(99)00056-5
[16] Moore RA, Kearfort RB, Clood MJ. Introduction to Interval Analysis. 1995.
[17] Smarandache F. Neutrosophy / Neutrosophic Probability, Set, and Logic. 1998.
[18] Voskoglou MGr. Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities. 2017.
[19] Voskoglou MGr. A hybrid model for decision making utilizing TFNs and soft sets as tools. Equations. 2022; 2: 65-69. DOI: https://doi.org/10.37394/232021.2022.2.11
[20] Voskoglou MGr. A combined use of soft sets and grey numbers in decision making. Journal of Computational and Cognitive Engineering. 2023; 2(1): 1-4. DOI: https://doi.org/10.47852/bonviewJCCE2202237
[21] Voskoglou MGr. An application of neutrosophic sets to decision making. Neutrosophic Sets and Systems. 2023; 53: 1-9. https://digitalrepository.unm.edu/nss journal/vol53/iss1/1
[22] Voskoglou, M.Gr. and Broumi, S. Applications of intuitionistic fuzzy sets to assessment, and decision making. Journal of Fuzzy Extensions and Applications. 2023; 4(4): 299-309. DOI: https://doi.org/10.22105/jfea.2023.425520.1326
[23] Wang H, Smarandanche F, Zhang Y, Sunderraman R. Single valued neutrosophic sets. Review of the Air Force Academy (Brasov). 2010; 1(16): 10-14.
https://www.afahc.ro/ro/revista/NR 1 2010/Nr 1 2010.pdf
[24] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[25] Zhu B, Ren P. Type-2 fuzzy numbers made simple in decision making. Fuzzy Optimization and Decision Making. 2022; 175-195. DOI: https://doi.org/10.1007/s10700-021-09363-y