The general algebraic solution of fuzzy linear systems based on a block representation of {1}-inverses

Document Type : Research Paper

Authors

1 Innovation Center, School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

2 Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

3 School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

Abstract

A new method for solving a fuzzy linear system (FLS), $A\tilde X=\tilde Y$, where the coefficient matrix $A$ is an arbitrary real matrix is obtained. A necessary and sufficient condition for the ${\cal R}$-consistency of the associated system of linear equations is obtained, related to its
representative solutions.  Moreover, the general form of representative solutions of such linear systems is presented. The straightforward method for solving $m\times n$ FLS based on an arbitrary $\{1\}$-inverse of $A$ is introduced. This method is illustrated by interesting examples.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 20, Issue 3
May and June 2023
Pages 115-126

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