Abstract
Recently, many scholars studied approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators. In fact, these approximations may not exist for some linear operators. The purpose of this paper is to study necessary and sufficient conditions of linear operators which are preserved by interval, triangular, symmetric triangular, trapezoidal, or symmetric trapezoidal approximations of fuzzy numbers. In addition, an effective method for solving such problems is proposed.
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