Abstract
This paper deals with algebraic equations involving generalized fuzzy numbers with continuous membership functions. The generalized fuzzy number defined in this paper is a general name for fuzzy numbers, fuzzy intervals, crisp numbers, and interval numbers. Three important properties of the generalized fuzzy numbers with continuous membership functions are introduced as the basis for deriving the solvability criterion. The sufficient and necessary condition for solving A ± X = C is derived. The sufficient and necessary condition for solving A × X = C and A ÷ X = C when A and C are nonzero generalized fuzzy numbers is also derived in this paper. Instead of the inverse operation method, which fails for fuzzy sets, inverse operations on the boundary points of α-level set intervals for continuous membership functions are used when the derived criteria of solvability are satisfied. A unique solution rather than a solution set is obtained.
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