Soft computing algorithm for arithmetic multiplication of fuzzy sets based on universal analytic models

Abstract

This paper deals with the investigations of increasing dependability of computing operations for fuzzy numbers with triangular and bell-shape membership functions (MFs). Special attention is paid to the synthesis of analytic models of the MFs for the results of fuzzy arithmetic operations. New analytical models of the result’s MFs with the description of synthesis procedures for the multiplication operation with triangular fuzzy numbers in R+ and R are presented in a universal style. The general analytic models for determination of α-cuts parameters (direct and inverse approaches) for result fuzzy sets are given. Modeling results confirm the efficiency of the proposed models and fuzzy arithmetic algorithms for fuzzy information processing.