Abstract
The fuzzy matrix equationsA~⊗X~⊗B~=C~in whichA~,B~, andC~arem×m,n×n, andm×nnonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition, the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to illustrate the proposed method.
Highlights
Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process
The model is proposed in this way; that is, we extend the fuzzy linear matrix system into a system of linear matrix equations according to arithmetic operations of LR fuzzy numbers
In this work we presented a model for solving fuzzy linear matrix equations à ⊗ X ⊗ B = Cin which à and Bare m × m and n × n fuzzy matrices, respectively, and Cis an m × n arbitrary LR fuzzy numbers matrix
Summary
Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. [18,19,20,21], Wang and Zheng [22, 23], and Dehghan et al [24, 25] The general method they applied is the fuzzy linear equations were converted to a crisp function system of linear equations with high order according to the embedding principles and algebraic operations of fuzzy numbers. In this paper we propose a general model for solving the fuzzy linear matrix equation à ⊗X ⊗B = C, where Ã, B, and Care m × m, n × n, and m × n nonnegative LR fuzzy numbers matrices, respectively. The LR fuzzy solution of the original matrix equation is derived from solving crisp systems of linear matrix equations.
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