Title: A mathematical approach to solve multi-objective pentagonal fuzzy linear plus linear fractional programming problems

Authors: Sujit Maharana; Suvasis Nayak

Addresses: Department of Mathematics, School of Applied Sciences, KIIT (Deemed to be University), Bhubaneswar 751024, Odisha, India ' Department of Mathematics, School of Applied Sciences, KIIT (Deemed to be University), Bhubaneswar 751024, Odisha, India

Abstract: Optimisation algorithms efficiently deal with many real life problems. In numerous practical circumstances, the concept of fuzziness can be utilised for the problems with uncertainty. This paper deals with a computationally simple and efficient solution approach to solve a mathematical model of fuzzy multi-objective linear plus linear fractional programming problem which is designed in an environment of pentagonal fuzzy numbers. In this model, fuzzy cuts are used in the objective functions to transform the fuzzy valued functions into crisp interval-valued forms and the concept of ranking function is used in the constraints to convert the fuzzy valued inequalities into deterministic expressions. First order Taylor's series approximation is used as the linearisation process. Furthermore, the weighting sum method with analytic hierarchy process is applied to tackle the multi-objective optimisation. To justify and validate the feasibility of the proposed methodology, two existing numerical examples are solved and also the computational results are comparatively studied.

Keywords: linear plus linear fractional programming; multi-objective optimisation; pentagonal fuzzy numbers; interval valued functions.

DOI: 10.1504/IJMOR.2026.156084

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.4, pp.451 - 475

Received: 08 Feb 2024
Accepted: 23 Sep 2024
Published online: 03 Sep 2026 *

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