Journal Article

Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers

Chatterjee, Subhashish, Bhowmick, Aliviya, Chakraverty, Snehashish

2024

Overview

This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.

• Publisher: MDPI AG
• Subject: Decision making / double parametric form / fully fuzzy linear programming / Fuzzy algorithms / Fuzzy logic / Fuzzy sets / Fuzzy systems / Inequality / Linear equations / Linear programming / Mathematical optimization / mathematical programming / Mathematical research / Methods / Numbers / Optimization / Parameter uncertainty / single parametric form / triangular fuzzy number