Generating compromise solution of bi-level multi-objective intuitionistic fuzzy fractional programming problem

Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar 751024, Odisha, India

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Received: 3 March 2025
Accepted: 10 February 2026

Abstract

The real world optimization problems in hierarchical decision making systems, often encounter multiple functions in fractional forms with uncertain parameters. To tackle such situation of uncertainty, this paper proposes a novel methodology to find a compromise solution of a bi-level multi-objective linear fractional programming problem which is designed in a fuzzy environment with its parameters expressed as intuitionistic triangular fuzzy numbers. Based on the concept of intuitionistic fuzzy (α, β)-cuts and some theoretical aspects, the bi-level intuitionistic fuzzy model is formulated into an equivalent bi-level optimization with multiple interval valued fractional functions. The method proposed by Chakraborty and Gupta, is utilized to compute the individual compromise solution of each interval valued fractional objective function. Subsequently, the upper and lower level compromise solutions are computed to ascertain the aspiration values of the multiple interval valued fractional functions and the decision variables controlled at the upper level. Goal programming approach using a proposed modified linearization technique for fractional functions, is implemented to derive the compromise solution of the bi-level fuzzy optimization model. An existing numerical example, a practical problem in production sector are solved and the comparative discussion on result analysis is incorporated to demonstrate the feasibility and efficiency of the proposed approach.