Arithmetic operations on piecewise linear fuzzy number

Abstract

Many types of fuzzy numbers were studied in the literature and applied in many mathematical fields. Three of these types, the triangular, the trapezoidal and the hexagonal fuzzy number are used widely, especially in mathematical programming. A piecewise linear fuzzy number (PLFN), which generalizes these three types, is introduced in this paper. Based on the definition of the ranking function with total integral value, a ranking function for this piecewise linear fuzzy number is proposed. Arithmetic operations with their properties are introduced on the trapezoidal fuzzy number as a special case, then a generalization of these operations on the PLFN is given. It is also shown that the proposed operations on the PLFN are accepted generalizations of the conventional arithmetic operations on real numbers.