New concepts on the fuzzy linear systems and an ‎application

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint and radius functions for a fuzzy number, midpoint and radius vectors for a fuzzy number vector and midpoint and radius systems for a fuzzy linear system. All these new definitions are defined based on the parametric form of fuzzy numbers. Then, by these new concepts, we propose a simple method to solve a fuzzy linear system and obtain it's algebraic solution. Also, we present a sufficient condition for the obtained solution vector to be always a fuzzy vector. Finally, several numerical examples are given to show the efficiency and capability of the proposed ‎method.‎

Keywords:

Fuzzy linear system , Midpoint function , Radius function , Midpoint vector , Radius vector , Midpoint system , Radius ‎system‎