Fuzzy Utility Theory and Its Role in Multi-Criteria Decision Making

Fuzzy utility theory, as a generalization of classical utility theory, enables decision-making modeling under conditions of uncertainty and ambiguity. This paper provides a comprehensive review of the mathematical foundations, advanced concepts, and practical applications of this theory. First, the theoretical foundations including fuzzy preference relations, axioms, and Billot's existence theorem for fuzzy utility functions are explained. Then, supplementary concepts such as the fuzzy Archimedean principle, independence axiom, choice coherence, fuzzy lotteries, fuzzy expected utility, and risk aversion criteria are elucidated with numerical examples. Also, a real-world case study on selecting the optimal location for constructing a water quality monitoring station is analyzed using fuzzy data and multi-criteria decision-making methods, and the stability of results is examined through sensitivity analysis. The results show that the fuzzy approach can effectively model the uncertainties present in real-world data and provide stable and reliable rankings.

کلیدواژه ها:

Fuzzy utility ، Fuzzy preference relation ، multi-criteria decision making ، Fuzzy lottery ، Fuzzy risk aversion ، Fuzzy value of information