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Sets of solution-set-invariant coefficient matrices of simple fuzzy relation equations. (English) Zbl 0649.04003
Let x, b be two fuzzy sets and A, A’ be two fuzzy relations such that the finite fuzzy equations \(x\circ A=b\) and \(x\circ A'=b\) hold, where “\(\circ ''\) denotes the max-min composition, A, A’ are assigned and x is unknown. If the membership values of b are ordered in strictly decreasing sense, then the above equations are called simple. Let X and X’, respectively, be the sets of the solutions of the above equations. Using results of Wang Peizhuang, S. Sessa, the reviewer, and W. Pedrycz [Busefal 18, 67-74 (1984; Zbl 0581.04001)], the authors give an iff condition in order to have \(X=X'\). Further results on the number of the distinct elements of X are established.
Reviewer: A.Di Nola

MSC:
03E99 Set theory
03B52 Fuzzy logic; logic of vagueness
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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