A new metric for \(L\)-\(R\) fuzzy numbers and its application in fuzzy linear systems. (English) Zbl 1277.15002
Linear systems with crisp \(n\times n\) matrix and fuzzy right-hand sides were introduced by M. Friedman, M. Ma and A. Kandel [Fuzzy Sets Syst. 96, No. 2, 201–209 (1998; Zbl 0929.15004); comment and reply ibid. 140, 559–561 (2003)] and solved for triangular fuzzy numbers. This solution was generalized for trapezoidal fuzzy numbers by S. H. Nasseri and M. Gholami [“Linear system of equations with trapezoidal fuzzy numbers”, J. Math. Comput. Sci. 3, No. 1, 71–79 (2011)]. A consideration of linear systems with \(L\)-\(R\) fuzzy numbers leads to nonlinear calculations connected with shapes. In this paper, the authors use fixed shape functions \(L\), \(R\) common for all considered fuzzy numbers. The paper brings algorithms for exact and approximate solutions of such fuzzy linear systems with examples of applications. The metric used in the approximation is based on the support and core of fuzzy numbers (and is independent of \(L\), \(R\)).
Reviewer: Józef Drewniak (Rzeszów)
MSC:
| 15A06 | Linear equations (linear algebraic aspects) |
| 26E50 | Fuzzy real analysis |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
| 90C30 | Nonlinear programming |
Keywords:
fuzzy number; fuzzy vector; fuzzy linear system; fuzzy solution; approximate solution; algorithmCitations:
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