Grey Multiple-Criteria Decision-Making
DOI:
https://doi.org/10.52812/ijgs.88Keywords:
Grey Number, Soft Set, Tabular Representation, Decision-making, Multiple Criteria Decision Analysis, Nonparametric Mathemathical Method, Grey System, Intelligent System, Fuzzy logicAbstract
Decision Making (DM) is one of the most important components of human cognition. In particular, the Multiple-Criteria DM (MCDM), is a composite form of DM evaluating options with conflicting goals and choosing the best solution among the existing ones. Following the fuzzy DM criterion of Bellman and Zadeh in 1970, several other methods have been developed by other researchers for DM in fuzzy environments. Here we present a parametric, MCDM method utilizing grey numbers as tools. This method improves an earlier approach of Maji and colleagues in 2002, who used the tabular representation of a soft set as a tool for parametric MCDM in a fuzzy environment. The method is also extended to cover cases of weighted DM and suitable examples are presented illustrating our results.
References
Alazemi, F. K. A., Ariffin, M. K. A. B. M., Mustapha, F. B., & Supeni, E. E. B. (2021). A comprehensive fuzzy decision-making method for minimizing completion time in manufacturing process in supply chains. Mathematics, 9(22), 2919. https://doi.org/10.3390/math9222919
Alcantud, J. C. R. (2018). Fuzzy techniques for decision making. Symmetry, 10(1), 6. https://doi.org/10.3390/sym10010006
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141. https://doi.org/10.1287/mnsc.17.4.B141
Berger J. O. (1980). Statistical Decision Theory: Foundations, Concepts and Methods. Springer- Verlag, New York. https://doi.org/10.1007/978-1-4757-1727-3
Chiclana, F., Herrera, F., & Herrera-Viedma, E. (1998). Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems, 97(1), 33-48. https://doi.org/10.1016/S0165-0114(96)00339-9
Deng, J. (1982). Control problems of grey systems. Systems & Control Letters, 1(5), 288-294. https://doi.org/10.1016/S0167-6911(82)80025-X
Ekel, P. Y. (2001). Methods of decision making in fuzzy environment and their applications. Nonlinear Analysis: Theory, Methods & Applications, 47(2), 979-990. https://doi.org/10.1016/S0362-546X(01)00239-5
Ekel, P. Y. (2002). Fuzzy sets and models of decision making. Computers & Mathematics with Applications, 44(7), 863-875. https://doi.org/10.1016/S0898-1221(02)00199-2
Ekel, P., Kokshenev, I., Parreiras, R., Pedrycz, W., & Pereira Jr, J. (2016). Multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications. Information Sciences, 361, 100-119. https://doi.org/10.1016/j.ins.2016.04.030
Khan, A., Yang, M. S., Haq, M., Shah, A. A., & Arif, M. (2022). A new approach for normal parameter reduction using σ-algebraic soft sets and its application in multi-attribute decision making. Mathematics, 10(8), 1297. https://doi.org/10.3390/math10081297
Liu, S., & Lin, Y. (Eds.). (2010). Advances in Grey System Research. Springer, Berlin – Heidelberg, Germany. https://doi.org/10.1007/978-3-642-13938-3
Maji, P. K., Roy, A. R., & Biswas, R. (2002). An application of soft sets in a decision making problem. Computers & Mathematics with Applications, 44(8-9), 1077-1083.
Molodtsov, D. (1999). Soft set theory – first results. Computers and Mathematics with Applications, 37(4-5), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
Moore, R.A., Kearfort, R. B., & Clood, M.J. (1995). Introduction to Interval Analysis (2nd Printing). SIAM, Philadelphia, USA.
Taherdoost, H., & Madanchian, M. (2023). Multi-criteria decision making (MCDM) methods and concepts. Encyclopedia, 3(1), 77-87. https://doi.org/10.3390/encyclopedia3010006
Voskoglou, M.Gr. (2014). Probability and Fuzziness in Decision Making. Egyptian Computer Science Journal, 38(3), 86-99. http://www.ecsjournal.org/Archive/Volume38/Issue3/9.pdf
Voskoglou, M.Gr. (2019a). Generalizations of Fuzzy Sets and Related Theories, in M. Voskoglou (Ed.), An Essential Guide to Fuzzy Systems, Commentary, 345-352, Nova Publishers, N.Y.
Voskoglou, M.Gr. (2019b). Methods for Assessing Human-Machine Performance under Fuzzy Conditions. Mathematics, 7, 230. https://doi.org/10.3390/math7030230
Voskoglou, M.Gr. (2023a). A Combined Use of Soft Sets and Grey Numbers in Decision Making. Journal of Computational and Cognitive Engineering, 2(1), 1-4. https://doi.org/10.47852/bonviewJCCE2202237
Voskoglou, M.Gr. (2023b). Applications of Intuitionistic Fuzzy Sets to Assessment, and Decision Making. Journal of Fuzzy Extensions and Applications, 4(4), 299-309. https://doi.org/10.59400/jam.v1i4.325
Voskoglou, M.Gr. (2023c). An Application of Neutrosophic Sets to Decision Making. Neutrosophic Sets and Systems, 53, 1-9.
Zadeh, LA. (1965). Fuzzy Sets. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhu, B. & Ren, P. (2022). Type-2 fuzzy numbers made simple in decision making. Fuzzy Optimization and Decision Making, 21, 175-195. https://doi.org/10.1007/s10700-021-09363-y
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