Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness

Pavan Kumar () and Hamiden Abd El-Wahed Khalifa
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Pavan Kumar: School of Advanced Science and Languages, VIT Bhopal University, Sehore 466116, India
Hamiden Abd El-Wahed Khalifa: Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia

Mathematics, 2023, vol. 11, issue 14, 1-16

Abstract: In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α -pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same α -pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided.

Keywords: optimization; multi-objective dynamic programming; fuzzy sets; piecewise quadratic fuzzy numbers; close interval approximation; optimization algorithm; DP approach; GAMS computer package; ? -pareto optimal solution; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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