A FORMULATION OF FUZZY DECISION PROBLEMS AND ITS APPLICATION TO AN INVESTMENT PROBLEM

Abstract

Although the decision‐making problem at the lower level is generally well‐defined, the decision‐making problem at the higher level would not contain the detail. Much of decision‐making at the higher level might take place in a fuzzy environment, so that it is only necessary to decide roughly what actions, what states and what parameters should be considered. This paper deals with the higher level problem in which we can regard the elements‐states of nature, feasible actions and available information‐as fuzzy objects. Since the uncertainty of meaning of objects is represented by the fuzzy sets and the uncertainty of occurrence of objects is defined by the probability, a specific formulation of the higher level decision problem can be defined by the probability of fuzzy events. From the same aspect, the definitions of worth, entropy and quantity concerning fuzzy information are given in this paper, and we have tried to extend some of the statistical decision theory to the fuzzy decision problem. To explain our formulation, an investment problem is presented as an example.