A fuzzy set approach to case-based decision

This paper is an attempt at providing a fuzzy set-based approach to case-based decision. Case-based decision consists in selecting an action to be applied to a current problem on the basis of a set of cases storing the results of various actions applied to similar, previously encountered, problems. Recently, Gilboa and Schmeidler have presented an axiomatic justification of a counterpart of the expected utility used in decision under uncertainty, where similarity degrees play a role somewhat analogous to probability, and have proposed to apply it to case-based decision. This proposal resembles Sugeno's approach to fuzzy control. The relation between the two approaches is investigated. Besides, another approach, based on possibility and necessity measures, is presented and discussed. The idea is to favor actions which have never given bad results in problems similar to the current problem. A much more permissive view considers all the actions which have given good results (at least one time) in a similar problem.