Enhancing Possibilistic Fuzzy Goal Programming Approach for Solving Multi Objective Minimum Cost Flow Problems Coefficients

Hamiden  Abd El- Wahed Khalifa; Seyed  Ahmad Edalatanah

doi:10.22105/tqfb.v1i1.22

Authors

Hamiden Abd El- Wahed Khalifa * Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951 Saudi Arabia; ‎
Seyed Ahmad Edalatanah Department of Applied Mathematics, AyendangInstitute of Higher Education, Tonkabon, Iran

https://doi.org/10.22105/tqfb.v1i1.22

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Abstract

This study investigates a multi-objective minimum cost flow with probabilistic objective function coefficients (Poss- MOMCF). Under using the cut set of the possibilistic variables, the Poss-MOMCF problem is converted into the corresponding ( -MOMCF) and hence into the ( -MOMCF) problem. A necessary and sufficient condition for investigating the possibly optimal solution is established. A fuzzy goal programming approach is applied to obtain the parametric optimal compromise solution. The stability set of the first kid under the concept of possibly optimal solution is characterized and analyzed without differentiability. Finally, a numerical example is given in the sake of the paper to clarify the methodology.

Keywords

Optimization problem‎ Minimum cost flow Multi-objective optimization‎ Possibilistic variables‎ Fuzzy goal programming approach‎ α-possibly optimal solution Goal programming Decision maker Compromise solution Parametric analysis

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