On fuzzy number calculus

The commonly accepted theory of fuzzy numbers (Czogala and Pedrycz, 1985) is that set up by Dubois and Prade (1978), who proposed a restricted class of membership functions, called (L,R)–numbers with shape functions L and R. However, approximations of fuzzy functions and operations are needed if one wants to follow Zadeh’s (Zadeh 1975; 1983) extension principle. It leads to some drawbacks that concern properties of fuzzy algebraic operations, as well as to unexpected and uncontrollable results of repeatedly applied operations (Wagenknecht, 2001; Wagenknecht et al., 2001).

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