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Solution of fuzzy equations with extended operations. (English) Zbl 0556.04001
For a general binary operation *:X$$\times Y\to Z$$, where X, Y, Z are (crisp) sets, an algorithm for solving the fuzzy equation $$A*B=C$$ (or A*B$$\subseteq C)$$ is given; here A, B, C are fuzzy subsets of X, Y, Z, respectively and A (or B) and C are fixed. The methods constructed in the paper may be applied for the fuzzy arithmetic operations (when * stands for $$+$$, -, $$\times$$, $$\div$$, extended for fuzzy numbers, i.e., fuzzy subsets of the set of real numbers $${\mathbb{R}})$$. Existence conditions for the solvability of a given equation are formulated.
Reviewer: Vl.Topencharov

##### MSC:
 3e+20 Other classical set theory (including functions, relations, and set algebra) 3e+72 Theory of fuzzy sets, etc.
##### Keywords:
fuzzy equation; fuzzy arithmetic
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