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Approaches for Solving Fully Fuzzy Rough Multi-Objective Nonlinear Programming Problems

E. Ammar and A. Al-Asfar
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E. Ammar: Department of Mathematics, Faculty of Science, Tanta University, Egypt
A. Al-Asfar: Department of Mathematics, Faculty of Science, Tanta University, Egypt

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 2, 113-128

Abstract: Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers. The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems. The second proposed method for solving FFRMONLP problems is ?-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by ?-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

Date: 2021
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