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

Aliviya Bhowmick (), Snehashish Chakraverty and Subhashish Chatterjee
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Aliviya Bhowmick: Department of Mathematics & Computing, IIT(ISM) Dhanbad, Dhanbad 826004, Jharkhand, India
Snehashish Chakraverty: Department of Mathematics, NIT Rourkela, Rourkela 769008, Odisha, India
Subhashish Chatterjee: Department of Mathematics & Computing, IIT(ISM) Dhanbad, Dhanbad 826004, Jharkhand, India

Mathematics, 2024, vol. 12, issue 19, 1-18

Abstract: 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.

Keywords: mathematical programming; fully fuzzy linear programming; single parametric form; double parametric form; triangular fuzzy number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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