Bell-shaped fuzzy numbers associated with the normal curve

Abstract

Statisticians often focus on fuzzy numbers with triangular or trapezoidal membership functions because they are very easy to apply. Although they offer a good approximation of a fuzzy variable, several doubts arise about the appropriateness of these kind of shapes. As known, fuzzy sets are useful for interval data when the “degree of truth” of the values varies within this range. In particular, they are desirable for translating human language into numbers. In this paper, we propose an alternative membership function that appears more appropriate to deal with linguistic variables. We refer to this function as “bell-shaped fuzzy number associated with the normal curve”. In particular, we highlight the specific properties of the proposed fuzzy number and illustrate the utility of linking this function with the normal distribution.