Solving Fuzzy Equations

Authors: James J Buckley Leonard J Jowers

Publish Date: 2007

Volume: , Issue: , Pages: 89-115

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Abstract

We start in the next Section 102 with looking at possible solutions to the simple fuzzy linear equation overlineA cdot overlineX + overlineB = overlineC We discuss three different types of solution which we have studied before in solving fuzzy equations Then we present a fourth type of solution based on our fuzzy Monte Carlo method in Section 1022 This new solution is based on random fuzzy numbers In Section 103 we look at only “classical” solutions to the fuzzy quadratic equation and apply our fuzzy Monte Carlo method to obtain new solutions Then in Section 104 we consider the fuzzy matrix equation overlineA cdot overlineX=overlineB and a number of solution types for overlineX and then another solution based on fuzzy Monte Carlo techniques The last section contains a brief summary and our conclusionsIn this chapter overline M ≤ overline N will mean that overline M is a fuzzy subset of overline N Section 223 and not that overline M is less than or equal to overline N Solving fuzzy equations has always been an active area of research Some recent references on this topic are 1416182122

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