Approximate Solutions of Fuzzy Relation Equations
In the previous Chs. we have discussed various problems concerning solutions of fuzzy relation equations. Obviously an underlying assumption is that there exists a nonempty set of solutions. A situation, may occurr, and indeed it is quite common, in which no solution exists. Nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution. This stream of investigations is particularly interesting for applicational purposes. Contrary to the topics already discussed in the previous Chs., this is a field of research which has not been developed enough so far. It concerns studies on solvability properties of fuzzy relation equations. In this Ch., we shall try to answer, by using several techniques, the following basic question: how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property?
KeywordsApproximate Solution Membership Function Fuzzy Relation Prob Ability Fuzzy Data
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