Fuzzy Linear Equations

This chapter presents a method for fuzzy linear systems with fuzzy coefficients that involves fuzzy variables. Fuzzy linear equation has been solved using both direct method and Cramer's rule method. It is useful in analysis of physical systems and other topics in real engineering problems, where uncertainty aspects are present. When one wants to find the inverse of square and non-singular matrices, whose values are real numbers, then a linear equation is formed that is composed of product of two matrices – n × n coefficients matrix and n × n unknown matrix. This system is equated with identity matrix and is solved. The chapter discusses a method for computing the inverse of a fuzzy matrix using LR-type fuzzy numbers. It also explains fuzzy identity matrix, fuzzy one number, and fuzzy zero number as these are required in computing the inverse of fuzzy matrix with LR-type fuzzy numbers.