Minimizing unconstrained fuzzy functions

In this paper we introduce a definition for a fuzzy function as a possibility distribution over the set of all functions with certain properties. We then examine some of the implications of this definition. In particular, we show that the image of a fuzzy function is a fuzzy vector (as defined herein). We also show that the set of values at which a real-valued fuzzy function achieves its minimum is a fuzzy number and if the fuzzy function is convex, in a particular sense, then the set of vectors for which the function achieves the minimum values is connected. Lastly, we discuss minimization of an unconstrained fuzzy function and how one might proceed to defuzzify the solution. (C) 1999 Elsevier Science B.V. All rights reserved.