Some Methods for Solving Fully Fuzzy Linear System of Equations

Abstract

System of simultaneous linear equations plays a major role in various areas such as mathematics, physics, statistics, engineering and social sciences. These are important for studying and solving a large proportion of the problems in many topics in applied mathematics. Usually in many applications all the system’s parameters are represented by fuzzy rather than crisp numbers, and hence it is important to develop mathematical models and numerical procedures that would appropriately treat general fully fuzzy linear system and solve them. This thesis is devoted to some methods for solving fully fuzzy linear systems (system of linear equations in which all the parameters are represented by fuzzy numbers). The chapter-wise summary of the thesis is as follows Chapter 1 is introductory in nature. This chapter includes the basic concepts used throughout the work.

Chapter 2 presents brief review of the work done in the area of fuzzy linear system of equations.

In Chapter 3, matrix inversion method, Cramer’s rule and LU decomposition method to solve the fully fuzzy linear systems are presented. To illustrate all the presented methods numerical examples are solved.

In Chapter 4, LU decomposition method, presented in chapter 3, is modified to show the advantages of the modified method. The numerical example, solved in chapter 3, is solved by the modified LU decomposition method and it is shown that the results obtained by both the methods are same while it is easy and less time