On fully intuitionistic fuzzy linear fractional programming via novel parameterized membership functions with application in portfolio optimization

Department of Mathematics, Punjab Engineering College (Deemed to be University), Chandigarh 160012, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 3 October 2024
Accepted: 6 February 2026

Abstract

Fractional programming is an extensively used technique to simultaneously deal with two conflicting objectives, by optimizing their ratio. This paper focuses on fully intuitionistic fuzzy fractional programming to address real-world problems. Firstly, the intuitionistic fuzzy model is converted into a crisp multi-objective problem with fractional objectives. Subsequently, a novel intuitionistic fuzzy programming approach is proposed, offering an insightful method for selecting least acceptable values. The existing literature on intuitionistic fuzzy programming employs linear, exponential, hyperbolic, or parabolic membership and non-membership functions. This article presents that these functions result in a highly restrictive feasibility region. Thus, a family of parameterized membership and non-membership functions is introduced, which overcomes the limitations of conventionally used functions and effectively captures both the acceptance as well as rejection degrees. In this article, theoretical foundations are established for the proposed technique through several theorems which have been constructed and proved. Additionally, the proposed technique is illustrated through a numerical example and applied to a real-life portfolio optimization problem, demonstrating its effectiveness. Finally, a comparative analysis with prevalent studies is also conducted to emphasize the versatile nature of the proposed functions.