Abstract
The fuzzy symmetric solution of fuzzy matrix equationAX˜=B˜, in whichAis a crispm×mnonsingular matrix andB˜is anm×nfuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method.
Highlights
Linear systems always have important applications in many branches of science and engineering
We propose a general model for solving the fuzzy matrix equation AX = B where A is crisp m × m nonsingular matrix and B is an m × n fuzzy numbers matrix with nonzero spreads
The model is proposed in this way, that is, we first convert the fuzzy matrix equation to a fuzzy system of linear equations based on the Kronecker product of matrices and obtain three types of fuzzy symmetric solutions of the fuzzy matrix equation by solving the fuzzy linear systems
Summary
Linear systems always have important applications in many branches of science and engineering. Since Friedman et al [8, 9] proposed a general model for solving an n × n fuzzy linear systems whose coefficients matrix is crisp and the right-hand side is an arbitrary fuzzy numbers vector by an embedding approach in 1998, many works have been done about how to deal with some fuzzy linear systems with more advanced forms such as dual fuzzy linear systems (DFLSs), general fuzzy linear systems (GFLSs), fully fuzzy linear systems (FFLSs), dual full fuzzy linear systems (DFFLSs), and general dual fuzzy linear systems (GDFLSs).
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