Solution of fuzzy equations with extended operations (Q761455)

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.