Research on the Redefined Square Root Interval-valued Normal Pythagorean Fuzzy Multi-Attribute Decision-Making Model Based on Aggregation Operators

Murugan Palanikumar; Nasreen Kausar

doi:10.31181/sor58

Authors

Murugan Palanikumar Department of Mathematics, SRM Valliammai Engineering College, Kattankulathur-603203, India Author https://orcid.org/0009-0005-4354-933X
Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, 10145 Balikesir, Turkey Author https://orcid.org/0000-0002-8659-0747

DOI:

https://doi.org/10.31181/sor58

Keywords:

Multiple attributes decision-making, Aggregating operations, Normal fuzzy set, Weighted vector, Weighted averaging, Weighted geometric

Abstract

In this communication, we construct new multiple attribute decision-making (MADM) problems using the redefined square root interval-valued normal Pythagorean fuzzy set (RSIVNPFS). The interval-valued Pythagorean fuzzy sets (IVPFSs) and square root PFSs are extended by the square RSIVNPFS. We introduce RSIVNPF weighted averaging (RSIVNPFWA), RSIVNPF weighted geometric (RSIVNPFWG), generalized RSIVNPFWA (RSGIVNPFWA), and generalized RSIVNPFWG (RSGIVNPFWG). Idempotence, boundedness, commutativity, and monotonicity in algebraic operations are all satisfied by RSIVNPFSs. We develop an algorithm for dealing with MADM problems using the aggregation operators (AOs). The applications of the Euclidean distance (ED) and the Hamming distance (HD) are described using examples from everyday scenarios. We also compare several suggested and current models to show the validity and applicability of the models. Our objective is to compare expert opinions with the criteria in order to determine the best option and to demonstrate the superiority and validity of the suggested AOs.

Downloads

Download data is not yet available.

References

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

Gorzalczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1), 1–17. https://doi.org/10.1016/0165-0114(87)90148-5

Biswas, R. (2006). Vague groups. International Journal of Computational Cognition, 4(2), 20–23.

Peng, X., & Yang, Y. (2015). Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. International Journal of Intelligent Systems, 31(5), 444–487. https://doi.org/10.1002/int.21790

Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989

Akram, M., Dudek, W. A., & Ilyas, F. (2019). Group decision making based on Pythagorean fuzzy TOPSIS method. International Journal of Intelligent Systems, 34(7), 1455–1475. https://doi.org/10.1002/int.22103

Rahman, K., Ali, A., Abdullah, S., & Amin, F. (2018). Approaches to multi-attribute group decision-making based on induced interval-valued Pythagorean fuzzy Einstein aggregation operator. New Mathematics and Natural Computation, 14(3), 343–361. https://doi.org/10.1142/S1793005718500217

Yang, Z., & Chang, J. (2020). Interval-valued Pythagorean normal fuzzy information aggregation operators for multiple attribute decision making approach. IEEE Access, 8, 51295–51314. https://doi.org/10.1109/ACCESS.2020.2978976

Al-shami, T. M., Ibrahim, H. Z., Azzam, A. A., & El-Maghrabi, A. I. (2022). Square root-fuzzy sets and their weighted aggregated operators in application to decision-making. Journal of Function Spaces, 2022, 1–14. https://doi.org/10.1155/2022/3653225

Ejegwa, P. A. (2020). Distance and similarity measures for Pythagorean fuzzy sets. Granular Computing, 5(1), 225–238. https://doi.org/10.1007/s41066-018-00149-z

Palanikumar, M., Arulmozhi, K., & Jana, C. (2022). Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued aggregation operators. Computational and Applied Mathematics, 41(90), 1–27. https://doi.org/10.1007/s40314-022-01791-9

Zhou, Q., Mo, H., & Deng, Y. (2020). A new divergence measure of Pythagorean fuzzy sets based on belief function and its application in medical diagnosis. Mathematics, 8(1), 142. https://doi.org/10.3390/math8010142

Oztaysi, B., Onar, S. C., & Kahraman, C. (2020). Social open innovation platform design for science teaching by using Pythagorean fuzzy analytic hierarchy process. Journal of Intelligent & Fuzzy Systems, 38(1), 809–819. https://doi.org/10.3233/JIFS-179450

Song, P., Li, L., Huang, D., Wei, Q., & Chen, X. (2020). Loan risk assessment based on Pythagorean fuzzy analytic hierarchy process. Journal of Physics: Conference Series, 1437(1), 012101. https://doi.org/10.1088/1742-6596/1437/1/012101

Liu, P., & Wang, P. (2018). Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems, 33(2), 259–280. https://doi.org/10.1002/int.21927

Akram, M., & Arshad, M. (2019). A novel trapezoidal bipolar fuzzy TOPSIS method for group decision making. Group Decision and Negotiation, 28(3), 565–584. https://doi.org/10.1007/s10726-018-9606-6

Adeel, A., Akram, M., & Koam, A. A. (2019). Group decision-making based on m-polar fuzzy linguistic TOPSIS method. Symmetry, 11(6), 735. https://doi.org/10.3390/sym11060735

Ullah, K., Mahmood, T., Ali, Z., & Jan, N. (2020). On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex & Intelligent Systems, 6(1), 15–27. https://doi.org/10.1007/s40747-019-0103-6