A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets

Murat Kirisci

A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets

Abstract

Based on criteria derived from environmental, social, and governance (ESG) sub-criteria, this study presents a decision support system to aid in selecting the optimal green finance investment plan. For interval-valued Pythagorean fuzzy sets, a scoring function, distance measure, similarity measure, and entropy measure are introduced as a set of new mathematical tools for decision-making under uncertainty. The Interval-Valued Pythagorean Fuzzy Sets framework is employed to evaluate seven popular sustainable investment strategies: Impact Investing, Environmental, Social, and Governance (ESG) Integration, Green Bonds, Sustainable Agriculture Funds, Shareholder Engagement, Renewable Energy Funds, and Thematic Investing. This work primarily utilizes a score function and distance metric for interval-valued Pythagorean fuzzy numbers to address specific comparative challenges. We used an entropy measure based on an interval-valued Pythagorean fuzzy set to calculate the objective weights. We then used the weighted distance-based approximation approach. The best option may be close to the negative-ideal solution (AIP-worst plan) and far from the positive-ideal solution (PIS-best plan), according to the weighted distance-based approximation technique.

Keywords

References

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 343–349.
Du, Y., Hou, F., Zafar, W., Yu, Q., & Zhai, Y. (2017). A novel method for multi-attribute decision making with interval-valued Pythagorean fuzzy linguistic information. International Journal of Intelligent Systems, 32(10), 1085–1112.
Gandotra, N., Kizielewicz, B., Anand, A., Baczkiewicz, A., Shekhovtsov, A., Watrobski, J., Rezai, A., & Salabun, W. (2021). New Pythagorean entropy measure with application in multi-criteria decision analysis. Entropy, 23(12), 1600.
Garg, H., Dutta, D., Dutta, P., & Gohain, B. (2024a). An extended group decision-making algorithm with intuitionistic fuzzy set information distance measures and their applications. Computers & Industrial Engineering, 197, 110537.
Garg, H., Waqas, M., Ali, Z., & Emam, W. (2024b). EDAS method for circular Pythagorean fuzzy with improved Dombi power aggregation operators and their application in policy analysis and decision support systems. Alexandria Engineering Journal, 106, 172–193.
Hao, Z., Xu, Z., Zhao, H., & Fujita, H. (2018). A dynamic weight determination approach based on the intuitionistic fuzzy Bayesian network and its application to emergency decision making. IEEE Transactions on Fuzzy Systems, 26(4), 1893–1907.
Kirişci, M. (2019a). Fibonacci statistical convergence on intuitionistic fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems, 4, 1–14.

Kirişci, M. (2019b). Comparison of the medical decision-making with intuitionistic fuzzy parameterized fuzzy soft set and Riesz summability. New Mathematics and Natural Computation, 15, 351–359.
Kirişci, M. (2024). Measures of distance and entropy based on the Fermatean fuzzy-type soft sets approach. Universal Journal of Mathematics and Applications, 7, 12–29.
Kirişci, M. (2025a). Risk assessment for breast cancer with integrated group decision-making method. Fundamentals of Contemporary Mathematical Sciences, 6(1), 1–18.
Kirişci, M. (2025b). An integrated decision-making process for risk analysis of decentralized finance. Neural Computing and Applications, 37, 6021–6051.
Mohammed, S. Y., Oleiwi, A. K., Kh Asman, T., Saleh, H. M., Mahmood, A. M., & Avci, I. (2023). A survey of MCDM-based software engineering method. Babylonian Journal of Mathematics, 13–18.
Peng, X. D., & Garg, H. (2018). Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with a new information measure. Computers & Industrial Engineering, 119, 439–452.
Peng, X., & Li, W. (2019). Algorithms for interval-valued Pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA. IEEE Access, 7, 7419–7441.
Rao, R. V., & Singh, D. (2012). Weighted Euclidean distance based approach as a multiple attribute decision making method for plant or facility layout design selection. International Journal of Industrial Engineering Computations, 3, 365–382.
Riaz, M., Qamar, F., Tariq, S., & Alsager, K. (2024). AI-driven LOPCOW-AROMAN framework and topological data analysis using circular intuitionistic fuzzy information: Healthcare supply chain innovation. Mathematics, 12, 3593.
Yager, R. R. (2013). Pythagorean fuzzy subsets. Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting.
Zadeh, L. A. (1965). Fuzzy sets. Information and Computation, 8, 338–353.
Zhang, X. L. (2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent Systems, 31, 593–611.

Details

Primary Language

English

Subjects

Financial Mathematics, Operations Research İn Mathematics

Journal Section

Research Article

Authors

Murat Kirisci ^*
0000-0003-4938-5207
Türkiye

Publication Date

December 31, 2025

Submission Date

December 10, 2025

Acceptance Date

December 31, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

IZ

https://izlik.org/JA35DU77DN

Cite

RIS / Bibtex

APA

Kirisci, M. (2025). A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets. Türkiye Mathematical Sciences, 2(2), 11-30. https://izlik.org/JA35DU77DN

AMA

1.Kirisci M. A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets. TMS. 2025;2(2):11-30. https://izlik.org/JA35DU77DN

Chicago

Kirisci, Murat. 2025. “A New Decision-Making Approach for the Green Finance Investment Strategies With Interval-Valued Pythagorean Fuzzy Sets”. Türkiye Mathematical Sciences 2 (2): 11-30. https://izlik.org/JA35DU77DN.

EndNote

Kirisci M (December 1, 2025) A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets. Türkiye Mathematical Sciences 2 2 11–30.

IEEE

[1]M. Kirisci, “A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets”, TMS, vol. 2, no. 2, pp. 11–30, Dec. 2025, [Online]. Available: https://izlik.org/JA35DU77DN

ISNAD

Kirisci, Murat. “A New Decision-Making Approach for the Green Finance Investment Strategies With Interval-Valued Pythagorean Fuzzy Sets”. Türkiye Mathematical Sciences 2/2 (December 1, 2025): 11-30. https://izlik.org/JA35DU77DN.

JAMA

1.Kirisci M. A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets. TMS. 2025;2:11–30.

MLA

Kirisci, Murat. “A New Decision-Making Approach for the Green Finance Investment Strategies With Interval-Valued Pythagorean Fuzzy Sets”. Türkiye Mathematical Sciences, vol. 2, no. 2, Dec. 2025, pp. 11-30, https://izlik.org/JA35DU77DN.

Vancouver

1.Murat Kirisci. A new decision-making approach for the green finance investment strategies with interval-valued Pythagorean fuzzy sets. TMS [Internet]. 2025 Dec. 1;2(2):11-30. Available from: https://izlik.org/JA35DU77DN