Linear programming problem with generalized interval-valued fuzzy numbers

Document Type: Original Article


1 Department of Mathematics, Kashan Branch, Islamic Azad University, Kashan, Iran

2 Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran


In this paper, we concentrate on linear programming problems in which the cost vector, the technological coefficients and the right-hand side values are interval-valued generalized trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method described in the literature to find the optimal solution of the linear programming problems with interval-valued generalized trapezoidal fuzzy numbers. We apply the signed distance for defuzzification of this problem. The crisp problem obtained after the defuzzification is solved by the linear programming methods. Finally, we give an illustrative example and its numerical solutions.


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