An Interval-Valued Method For Solving Fuzzy Multi-LevelMultiObjective Integer Fractional Programming Problem
Journal Title: International Journal of engineering Research and Applications - Year 2018, Vol 8, Issue 10
Abstract
This paper presents an interval-valued method to solve fuzzy multi-level multi-objective integer fractional programming problem (F-MMIFP). The problem under consideration involves fuzzy parameters in the objective functions, in the left-hand side and in the right-hand side of the constraints. The suggested method depends on the concept of the α-level set of the fuzzy numbers. The 𝛂-MMIFP problem can be converted to interval-valued multi-level multi-objective integer fractional programming problem (IV-MMIFP), which can be transformed to interval-valued multilevel single objective integer fractional programming problem (IV-MSIFP) by using the nonnegative weighting sum approach. Then, this resulting problem can be rewritten in the form of real-valued multi-level single objective integer fractional programming problem (RV-MSIFP) using the interval-valued optimization technique together with the convex linear combination of the first and least point of the intervals in the constraints. Finally, a non-dominated solution of the problem of concern (F-MMIFP) is obtained. In addition, an algorithm is described in finite steps to solve problem (F-MMIFP). An illustrative numerical example is included to demonstrate the proposed solution algorithm.
Authors and Affiliations
Omar M. Saad, Mervat M. Elshafei, Marwa M. Sleem
Keywords
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