# Solutions of Fuzzy System of Linear Equations

Laxminarayan Sahoo (Raniganj Girls' College, India)
DOI: 10.4018/978-1-7998-0190-0.ch002
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## Abstract

This chapter deals with solution methodology of fuzzy system of linear equations (FSLEs). In fuzzy set theory, finding solutions of FLSEs has long been a well-known problem to the researchers. In this chapter, the fuzzy number has been converted into interval number, and the authors have solved the interval system of linear equation for finding the fuzzy valued solution. Here, a fuzzy valued linear system has been introduced and a numerical example has been solved and presented for illustration of purpose.
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## 2 Some Mathematical Background

In this section some definitions and basic concepts related to fuzzy sets, fuzzy numbers and interval numbers used in this chapter are described briefly.

### 2.1 Preliminary Definitions About Fuzzy Set

A fuzzy set is defined by a membership function, which corresponds to each element x in X to a real number in the interval 0≤x≤1. The function represents the grade of membership of x in.

Definition 2.1 The α-cut (Zimmermann, 2001) of a fuzzy set is a crisp subset of X and is denoted by , where is the membership function of and 0≤α≤1.

Definition 2.2 A fuzzy set is called a normal fuzzy set if there exists at least one xX such that .

Definition 2.3 A fuzzy set is called convex iff for every pair of x1,x2X, the membership function of satisfies , where 0≤λ≤1.

Definition 2.4 A fuzzy number is a fuzzy set which is both convex and normal.

Definition 2.5 The triangular fuzzy number (TFN) is a normal fuzzy number denoted as =(a1,a2,a3) where a1a2a3 and its membership function is defined by

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