Solving Pythagorean Fuzzy Assignment Problems in Management: A Framework Based on Spherical Distance Measures
DOI:
https://doi.org/10.31181/msa31202636Keywords:
Pythagorean Fuzzy Set, Spherical Distance Measure, Exponential Score Function, Assignment ProblemAbstract
In practical scenarios, uncertainty often arises from measurement limitations or incomplete information, making it impossible to obtain exact values for key variables. Additionally, decision-makers may struggle to articulate precise judgments under constraints such as time or limited knowledge. To better capture this ambiguity, fuzzy-based frameworks allow individuals to express their assessments in more flexible terms. Among these, the Pythagorean fuzzy set offers a broader descriptive range than intuitionistic fuzzy sets for representing degrees of membership and non-membership. This paper introduces two approaches based on positive and negative ideal solutions to solve assignment problems under Pythagorean fuzzy conditions by applying a spherical distance measure and a new scoring method. The effectiveness of the proposed technique is illustrated through numerical examples.
Downloads
References
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
Atanassov, K. (1984). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
Yager, R. R. (2013). Pythagorean membership grades in multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 DOI: https://doi.org/10.1109/TFUZZ.2013.2278989
Tahir, M., Kfueit, K., Rasheed, M., Hanan, A., & Shahid, M. I. (2025). Pythagorean soft sets and hypersoft sets: A comprehensive framework for advanced uncertainty modeling in decision making. Spectrum of Decision Making and Applications, 4(1), 1–26. https://doi.org/10.31181/sdmap41202761 DOI: https://doi.org/10.31181/sdmap41202761
Adak, A. K., & Kumar, D. (2023). Spherical distance measurement method for solving mcdm problems under pythagorean fuzzy environment. Journal of Fuzzy Extension and Applications, 4(1), 28–39. https://doi.org/10.22105/jfea.2022.351677.1224
Adak, A. K., & Nilkamal. (2025). Pythagorean fuzzy sets for credit risk assessment: A novel approach to predicting loan default. Control and Optimization in Applied Mathematics (COAM), 10(1), 175–191. https://doi.org/10.30473/coam.2025.73505.1287
Asif, M., Ishtiaq, U., & Argyros, I. K. (2025). Hamacher aggregation operators for pythagorean fuzzy set and its application in multi-attribute decision-making problem. Spectrum of Operational Research, 2(1), 27–40. https://doi.org/10.31181/sor2120258 DOI: https://doi.org/10.31181/sor2120258
Chanas, S., Kolodziejczyk, W., & Machaj, A. (1984). A fuzzy approach to the transportation problem. Fuzzy Sets and Systems, 13(3), 211–221. https://doi.org/10.1016/0165-0114(84)90057-5 DOI: https://doi.org/10.1016/0165-0114(84)90057-5
Ejegwa, P. A. (2019). Pythagorean fuzzy set and its application in career placements based on academic performance using max-min-max composition. Complex & Intelligent Systems, 5(2), 165–175. https://doi.org/10.1007/s40747-019-0091-6 DOI: https://doi.org/10.1007/s40747-019-0091-6
Hassan, K., Shaheen, T., Ali, W., Haq, I. U., Bibi, N., & Adak, A. K. (2024). Decision-making techniques based on aggregation operators and similarity measures under q-rung orthopair hesitant fuzzy connection numbers and their application. Decision Making and Analysis, 2(1), 58–72. https://doi.org/10.55976/dma.22024127458-72 DOI: https://doi.org/10.55976/dma.22024127458-72
Zhang, X., & Xu, Z. (2014). Extension of topsis to multiple criteria decision making with pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676 DOI: https://doi.org/10.1002/int.21676
Gurukumaresan, D., Duraisamy, C., Srinivasan, R., & Vijayan, V. (2020). Optimal solution of fuzzy assignment problem with centroid methods. Materials Today: Proceedings, 37, 553–555. https://doi.org/10.1016/j.matpr.2020.05.582 DOI: https://doi.org/10.1016/j.matpr.2020.05.582
Kumar, A., & Gupta, A. (2011). Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions. Fuzzy Information and Engineering, 3(1), 3–21. https://doi.org/10.1007/s12543-011-0062-0 DOI: https://doi.org/10.1007/s12543-011-0062-0
Thakre, T. A., Chaudhari, O. K., & Dhawade, N. R. (2018). Placement of staff in lic using fuzzy assignment problem. International Journal of Mathematics Trends and Technology, 53(4), 259–266. https://doi.org/10.14445/22315373/IJMTT-V53P532 DOI: https://doi.org/10.14445/22315373/IJMTT-V53P532
Roseline, S., & Amirtharaj, H. (2015). Methods to find the solution for the intuitionistic fuzzy assignment problem with ranking of intuitionistic fuzzy numbers. International Journal of Innovative Research in Science, Engineering and Technology, 4(7), 10008–10014. https://doi.org/10.15680/IJIRSET.2015.0410045
Mukherjee, S., & Basu, K. (2012). Solution of a class of intuitionistic fuzzy assignment problem by using similarity measures. Knowledge-Based Systems, 27, 170–179. https://doi.org/10.1016/j.knosys.2011.09.007 DOI: https://doi.org/10.1016/j.knosys.2011.09.007
Kumar, G., & Bajaj, R. K. (2014). On solution of interval valued intuitionistic fuzzy assignment problem using similarity measure and score function. International Journal of Mathematical and Computational Sciences, 8(4), 715–720.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Amal Adak, Dragan Pramucar, Wajid Ali (Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.









