(2201-7210) A bilevel linear programming model with interval type-2 triangular fuzzy numbers

Document Type : Research Paper

Authors

Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

In the real world, the parameters of a problem may not be the crisp values. The fuzzy theory among the theories in which uncertainty plays a crucial role. Type-2 fuzzy sets generalize fuzzy sets. We consider a special type of such sets here.
In this paper, we consider two issues. First, we review the method proposed by Javanmard and Mishmast Nehi for solving an interval type-2 triangular fuzzy linear programming problem, and improve it.
Then, we express a bilevel linear programming problem, that, to the best of our knowledge, has not been investigated so far.
We consider the bilevel linear programming problem with uncertainty where all the coefficients in the problem are interval type-2 triangular fuzzy numbers.
We convert an interval type-2 triangular fuzzy bilevel linear programming problem into an interval bilevel linear programming problem using Grzegorzewski's nearest interval approximation method.
Finally, we obtain five problems, and by solving them, we achieve the solution of interval type-2 triangular fuzzy bilevel linear programming problem as an interval type-2 triangular fuzzy number.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 20, Issue 5
September and October 2023
Pages 47-69

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