Modeling Portfolio Selection Under Intuitionistic Fuzzy Environments

Tusan Derya (), Mehveş Güliz Kelce and Kumru Didem Atalay
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Tusan Derya: Department of Industrial Engineering, Baskent University, 06790 Ankara, Turkey
Mehveş Güliz Kelce: Department of Industrial Engineering, Baskent University, 06790 Ankara, Turkey
Kumru Didem Atalay: Department of Industrial Engineering, Baskent University, 06790 Ankara, Turkey

Mathematics, 2025, vol. 13, issue 20, 1-22

Abstract: Portfolio optimization is a multifaceted process aimed at achieving a balance between investors’ risk tolerance and expected returns. However, the inherent uncertainty and unpredictability of financial markets significantly hinder the attainment of this balance. Therefore, there is an increasing need for models capable of representing these uncertainties in a more realistic manner. In this study, novel intuitionistic fuzzy mathematical models are proposed to provide alternative portfolio options that align with diverse investor expectations and risk perceptions. By utilizing mathematical programming formulations incorporating intuitionistic fuzzy parameters, the study contributes to the theoretical framework and enables the analysis of portfolio structures that vary in response to imprecisely defined return levels. The intuitionistic fuzzy parameters are modeled using appropriate membership and non-membership functions, and mean absolute deviation is employed as the risk measure within the proposed models. Various alternative solutions are generated by considering different lower and upper bound constraints, thereby allowing for the construction of flexible investment strategies suitable for different investor profiles. The practical applicability of the proposed models is demonstrated using real-world stock data obtained from Borsa Istanbul. The empirical results reveal that the models provide solutions that are sensitive to individual risk preferences and adaptable to changing market conditions. Accordingly, the developed intuitionistic fuzzy models serve as effective tools for determining optimal portfolio allocations and developing resilient investment strategies.

Keywords: portfolio optimization; intuitionistic fuzzy mathematical programming; mean absolute deviation; risk management; uncertainty modeling; Borsa İstanbul (BIST) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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