Title: Interactive fuzzy goal programming approach for solving possibilistic multi-objective minimum cost flow problems

Authors: Hamiden Abd El-Wahed Khalifa; A. Akilbasha; Tarishi Baranwal

Addresses: Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia; Faculty of Graduate Studies for Statistical Research, Department of Operations and Management Research, Cairo University, Giza, 12613, Egypt ' Department of Mathematics and Statistics, Dr. Vishwanath Karad MIT World Peace University, Pune, 411 038, Maharashtra, India ' Department of Mathematics and Statistics, Dr. Vishwanath Karad MIT World Peace University, Pune, 411 038, Maharashtra, India

Abstract: In this study, a multi-objective minimal cost flow with possibilistic objective function coefficients (Poss-MOMCF) is studied. Under using the α-cut set of the possibilistic variables, the Poss-MOMCF problem is converted into the corresponding (α-MOMCF) and hence into the (P-MOMCF) problem. A necessary and sufficient condition for investigating the α-possibly optimal solution is established. The α-parametric optimal compromise solution is obtained via an interactive fuzzy goal programming approach. The stability set of the first kind under the concept of α-possibly optimal solution is characterised and analysed without differentiability. The methodology is finally illustrated using a numerical example for the sake of the study.

Keywords: optimisation problem; minimum cost flow; multi-objective optimisation; possibilistic variables; fuzzy sets; fuzzy goal programming approach; α-possibly optimal solution; decision making and costs; compromise solution; parametric analysis.

DOI: 10.1504/IJBPSCM.2024.140042

International Journal of Business Performance and Supply Chain Modelling, 2024 Vol.15 No.1, pp.91 - 108

Received: 13 Jun 2023
Accepted: 27 May 2024
Published online: 15 Jul 2024 *

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