Fuzzy system of linear equations with crisp coefficients

Authors:
S. Chakraverty;Diptiranjan Behera
Affiliations:
Department of Mathematics, National Institute of Technology, Rourkela, Odisha, India;Department of Mathematics, National Institute of Technology, Rourkela, Odisha, India
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

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Abstract

This paper proposed a new and simple solution approach to solve a general fuzzy system of linear equations. In the original system, the coefficient matrix is considered as real crisp whereas the unknown variable vector and right hand side vector are considered as fuzzy. Here, three different types of fuzzy numbers viz. triangular, trapezoidal and Gaussian fuzzy numbers are taken into consideration. First the system is solved in term of fuzzy centre then this solution is used with width to get the final solution of the original system. Solution theorems are stated and proved related to the proposed method. The method is also used to solve some known example problems found in the references and the results are compared to show the efficacy of the proposed method.