Fuzzy Set and Its Extension

6Fuzzy Linear Equations

6.1 Introduction

Many real‐time engineering systems are too complex to be defined in precise terms and imprecision is often involved. Linear system of equations with uncertainty parameters plays a significant role in the areas of economics, finance, engineering, control system, and so on. To analyze such situation, fuzzy information is required. Fuzzifying either parameters or variables or both in these systems has been one of the research areas, since these kinds of systems are encountered in many applications.

This chapter deals in solving fuzzy system of linear equations. There are many non‐fuzzy classical methods to solve linear equations but in this chapter, solving fuzzy linear equation is discussed. A general model for solving a fuzzy linear system of equations where coefficient matrix is crisp and the right‐hand‐side column is a fuzzy vector was first proposed by Friedman et al. [1], and later with his colleagues, they replaced the original fuzzy linear system by a crisp linear system and solved it.

Then, Dehgan et al. [2] considered all parameters in a fuzzy linear system as fuzzy numbers and is called fully fuzzy linear system. The method is used in computing inverse of a matrix in fuzzy case that employs a linear equation system and identity matrix.

A matrix equation is represented as , where is a fuzzy matrix of size (n × n) and and are ...