Minimizing unconstrained fuzzy functions

✍ Scribed by K.David Jamison; Weldon A. Lodwick

• Book ID: 104292517
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 613 KB
• Volume: 103
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00183-8

✦ Synopsis

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 nneonstrained fuzzy function and how one might proceed to defuzzify the solution.