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LU Decomposition Method for Solving Fully Fuzzy Linear System with Trapezoidal Fuzzy Numbers

System of simultaneous linear equations plays a vital role in mathematics, Operations Research, Statistics, Physics, Engineering and Social Sciences etc. In many applications at least some of the system's parameters and measurements are represented by fuzzy numbers rather than crisp numbers. Therefore it is imperative to develop mathematical models and numerical procedures to solve such a fuzzy linear system. The general model of a fuzzy linear system whose coefficient matrix is crisp and the right hand side column is an arbitrary fuzzy vector. In the fully fuzzy linear system all the parameters are considered to be fuzzy numbers. Since triangular fuzzy numbers is a special case of trapezoidal fuzzy numbers, hence in this paper we considered fully fuzzy linear system with trapezoidal fuzzy numbers. LU decomposition method for a crisp matrix is well known in solving linear system of equations. We discuss LU decomposition of the coefficient matrix of the fully fuzzy linear system, in which the coefficients are trapezoidal fuzzy numbers.