New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers

Abstract

This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied for the first time in this paper for the present analysis. Using single parametric form, the n × n fully fuzzy system of linear equations have been converted to a 2n × 2n crisp system of linear equations. On the other hand, double parametric form of fuzzy numbers converts the n × n fully fuzzy system of linear equations to a crisp system of same order. Triangular and trapezoidal convex normalized fuzzy sets are used for the present analysis. Known example problems are solved to illustrate the efficacy and reliability of the proposed methods.