Fuzzy Sets and Decision Analysis

Abstract

The applicability of fuzzy set theory to decision analysis (DA) is examined. It extends the ideas of an earlier paper "Fuzzy decision analysis," by Watson et al. [33]. Particular emphasis is placed on justifying the use of Zadeh's fuzzy calculus to model impression, and an axiomatic system is suggested towards this end. This is seen as an attempt at extending Savage's axioms of subjective probability to produce "approximate probabilities." It is argued that the method proposed by Watson et al. for comparing decision options is unsatisfactory, and several alternative methods are developed. Some computational anomalies are pointed out which severely limit the potential of this methodology. It is suggested that, for individual decisionmaking, fuzzy decision analysis should be viewed as an automatic sensitivity analysis, but that fuzzy sets may be useful with another interpretation for group decisionmaking. The conclusions are that the methodology has too many limitations to be of use for isolated decisions but that it may have a value for often repeated generic decisions.