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A constructive proof for Farkas lemma with trapezoidal fuzzy numbers

S. H. Nasseri, M. Arab


Farkas’ lemma deals with two linear systems of equations and inequalities, exactly one of which has a solution in any instance. In this paper, we consider a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the linear programming problems with fuzzy variables and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. We shall prove these results by using the duality results on linear programming problems with fuzzy variables.


Fuzzy Farkas lemma, linear programming with fuzzy variables, duality results, ranking functions.

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