Duality in fuzzy linear systems. (English) Zbl 0945.15002

Ma, Ming; Friedman, M.; Kandel, A.

Fuzzy Sets Syst. 109, No. 1, 55-58 (2000).

As the authors say in their announced paper [see M. Friedman, M. Ma and A. Kandel, Fuzzy linear systems, Fuzzy Sets Syst. (to appear)] they investigate a general model for solving an \(n{\times}n\) fuzzy linear system whose coefficient matrix is crisp and the right-hand side column is an arbitrary fuzzy vector. They use the parametric form of fuzzy numbers and replace the original system by a \((2n){\times}(2n)\) representation. This enables them to treat this problem using the theory of positive matrices.
In the paper under review they apply the same approach to solve dual fuzzy linear systems and give two necessary and sufficient conditions for the existence of solutions.

Reviewer: Nikolai I.Osetinski (Moskva)

MSC:

15A06	Linear equations (linear algebraic aspects)
03E72	Theory of fuzzy sets, etc.
15B33	Matrices over special rings (quaternions, finite fields, etc.)

Keywords:

fuzzy linear equation system; duality; embedding method; nonnegative matrix