Multi-Attribute Decision-Making for T-Spherical Fuzzy Information Utilizing Schweizer-Sklar Prioritized Aggregation Operators for Recycled Water
DOI:
https://doi.org/10.31181/dma21202425Keywords:
T-spherical fuzzy sets, Schweizer and Sklar norms, Hamacher norms, Lukasiewicz norms, Aggregation operators, Multi Attribute Decision-MakingAbstract
To handle problematic and ambiguous data, Schweizer and Sklar added a parameter p in 1960, which helped to develop the theory of SS t-norm (SSTN) and t-conorm (SSTCN). The parameter p=-1.1 can be used to easily derive the information of the Hamacher and Lukasiewicz t-norms. Furthermore, prioritized aggregation operators (PAOs) choose which data will be collected into a singleton set. The main contribution of this work is the construction of new aggregation operators for T-spherical fuzzy (T-SF) information based on SS t-norm and t-conorm. Moreover, the fundamental characteristics of the operators are identified. Further, we developed MADM (Multi-Attribute Decision-Making) models and deduced several useful properties from the operators T-SFSSPA, T-SFSSWPA, T-SFSSPG, and T-SFSSWPG. Finally, using an actual case study, we were able to draw the conclusion that, in comparison to the ground-breaking and current methods to enhance the value and capability of the diagnosed operators, the proposed MADM algorithm performs noticeably better than the operators in place for resolving the water recycling problem in a way that is easy to understand.
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
Mahmood, T., & Ali, Z. (2022). Fuzzy superior mandelbrot sets. Soft Computing, 26(18), 9011-9020. https://doi.org/10.1007/s00500-022-07254-x
Orazbayeva, B., & Plewa, C. (2022). Academic motivations to engage in university-business cooperation: a fuzzy set analysis. Studies in Higher Education, 47(3), 486-498. https://doi.org/10.1080/03075079.2020.1761784
De, S. K., Roy, B., & Bhattacharya, K. (2022). Solving an EPQ model with doubt fuzzy set: a robust intelligent decision-making approach. Knowledge-Based Systems, 235, 107666. https://doi.org/10.1016/j.knosys.2021.107666
Tang, G., & Wang, F. (2022). What contributes to the sustainability of self-organized non-profit collaboration in disaster relief? A fuzzy-set qualitative comparative analysis. Public Management Review, 24(3), 466-488. https://doi.org/10.1080/14719037.2020.1834608
Boukezzoula, R., Jaulin, L., & Coquin, D. (2022). A new methodology for solving fuzzy systems of equations: Thick fuzzy sets based approach. Fuzzy Sets and Systems, 435, 107-128. https://doi.org/10.1016/j.fss.2021.06.003
Cassar, V., Bezzina, F., & Fabri, S. (2022). A fuzzy-set approach to re-exploring work-related stress-outcome relationships: implications for research methods, theory and practice. Electronic Journal of Business Research Methods, 20(2), pp63-74. https://doi.org/10.34190/ejbrm.20.2.2207
Ghasemi, F., Ghasemi, A., & Kalatpour, O. (2022). Prediction of human error probability during the hydrocarbon road tanker loading operation using a hybrid technique of fuzzy sets, Bayesian network and CREAM. International Journal of Occupational Safety and Ergonomics, 28(3), 1342-1352. https://doi.org/10.1080/10803548.2021.1889877
Libório, M. P., Ekel, P. Y., Martinuci, O. D. S., Figueiredo, L. R., Hadad, R. M., Lyrio, R. D. M., & Bernardes, P. (2022). Fuzzy set based intra-urban inequality indicator. Quality & Quantity, 56(2), 667-687. https://doi.org/10.1007/s11135-021-01142-6
Deveci, M., Simic, V., Karagoz, S., & Antucheviciene, J. (2022). An interval type-2 fuzzy sets based Delphi approach to evaluate site selection indicators of sustainable vehicle shredding facilities. Applied Soft Computing, 118, 108465. https://doi.org/10.1016/j.asoc.2022.108465
Saridou, B., Rose, J. R., Shiaeles, S., & Papadopoulos, B. (2022). SAGMAD—A Signature Agnostic Malware Detection System Based on Binary Visualisation and Fuzzy Sets. Electronics, 11(7), 1044. https://doi.org/10.3390/electronics11071044
Atanassov, K.T. (1999). Intuitionistic Fuzzy Sets. In: Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 35. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1870-3_1
Garg, H., & Rani, D. (2022). Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications. Expert Systems with Applications, 191, 116228. https://doi.org/10.1016/j.eswa.2021.116228
Garg, H., Ali, Z., Mahmood, T., Ali, M. R., & Alburaikan, A. (2023). Schweizer-Sklar prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision-making. Alexandria Engineering Journal, 67, 229-240. https://doi.org/10.1016/j.aej.2022.12.049
Jia, X., & Wang, Y. (2022). Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making. Expert Systems with Applications, 191, 116242. https://doi.org/10.1016/j.eswa.2021.116242
Bal, M., Ahmad, K. D., Hajjari, A. A., & Ali, R. (2022). A short note on the kernel subgroup of intuitionistic fuzzy groups. Journal of Neutrosophic and Fuzzy Systems, 2(1), 14-20. https://doi.org/10.54216/JNFS.020102
Panda, R. R., & Nagwani, N. K. (2022). Topic modeling and intuitionistic fuzzy set-based approach for efficient software bug triaging. Knowledge and Information Systems, 64(11), 3081-3111. https://doi.org/10.1007/s10115-022-01735-z
Gu, X. B., Ma, Y., Wu, Q. H., Ji, X. J., & Bai, H. (2021). The risk assessment of landslide hazards in Shiwangmiao based on intuitionistic fuzzy sets-Topsis model. Natural Hazards, 1-21. https://doi.org/10.1007/s11069-021-05053-5
Liang, Z., & Zhang, L. (2022). Intuitionistic fuzzy twin support vector machines with the insensitive pinball loss. Applied Soft Computing, 115, 108231. https://doi.org/10.1016/j.asoc.2021.108231
Gohain, B., Chutia, R., & Dutta, P. (2022). Distance measure on intuitionistic fuzzy sets and its application in decision‐making, pattern recognition, and clustering problems. International Journal of Intelligent Systems, 37(3), 2458-2501. https://doi.org/10.1002/int.22780
Anwar, M. Z., Al-Kenani, A. N., Bashir, S., & Shabir, M. (2022). Pessimistic multigranulation rough set of intuitionistic fuzzy sets based on soft relations. Mathematics, 10(5), 685. https://doi.org/10.3390/math10050685
Yang, J., Yao, Y., & Zhang, X. (2022). A model of three-way approximation of intuitionistic fuzzy sets. International Journal of Machine Learning and Cybernetics, 13, 163-174. https://doi.org/10.1007/s13042-021-01380-y
Yager, R. R. (2013, June). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
Cường, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409-409. https://doi.org/10.15625/1813-9663/30/4/5032
Cuong, B. C., & Pham, V. H. (2015). Some fuzzy logic operators for picture fuzzy sets. In 2015 seventh international conference on knowledge and systems engineering (KSE) (pp. 132-137). IEEE. https://doi.org/10.1109/KSE.2015.20
Mahmood, T., Ullah, K., Khan, Q., & Jan, N. (2019). An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Computing and Applications, 31, 7041-7053. https://doi.org/10.1007/s00521-018-3521-2
Munir, M., Kalsoom, H., Ullah, K., Mahmood, T., & Chu, Y. M. (2020). T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems. Symmetry, 12(3), 365. https://doi.org/10.3390/sym12030365
Zeng, S., Munir, M., Mahmood, T., & Naeem, M. (2020). Some T-spherical fuzzy Einstein interactive aggregation operators and their application to selection of photovoltaic cells. Mathematical Problems in Engineering, 2020, 1-16. https://doi.org/10.1155/2020/1904362
Liu, P., Wang, D., Zhang, H., Yan, L., Li, Y., & Rong, L. (2021). Multi-attribute decision-making method based on normal T-spherical fuzzy aggregation operator. Journal of Intelligent & Fuzzy Systems, 40(5), 9543-9565. https://doi.org/10.3233/JIFS-202000
Khan, Q., Gwak, J., Shahzad, M., & Alam, M. K. (2021). A novel approached based on T-spherical fuzzy Schweizer-Sklar power Heronian mean operator for evaluating water reuse applications under uncertainty. Sustainability, 13(13), 7108. https://doi.org/10.3390/su13137108
Ullah, K., Mahmood, T., & Garg, H. (2020). Evaluation of the performance of search and rescue robots using T-spherical fuzzy Hamacher aggregation operators. International Journal of Fuzzy Systems, 22(2), 570-582. https://doi.org/10.1007/s40815-020-00803-2
Gou, X., Xiao, P., Huang, D., & Deng, F. (2021). Probabilistic double hierarchy linguistic alternative queuing method for real economy development evaluation under the perspective of economic financialization. Economic research-Ekonomska istraživanja, 34(1), 3225-3244. https://doi.org/10.1080/1331677X.2020.1870520
Gou, X., Xu, Z., Liao, H., & Herrera, F. (2021). Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society, 72(12), 2611-2630. https://doi.org/10.1080/01605682.2020.1806741
Gou, X., Xu, Z., Zhou, W., & Herrera-Viedma, E. (2021). The risk assessment of construction project investment based on prospect theory with linguistic preference orderings. Economic research-Ekonomska istraživanja, 34(1), 709-731. https://doi.org/10.1080/1331677X.2020.1868324
Al-Quran, A. (2023). T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making. AIMS Mathematics, 8(5), 12257-12286. https://doi.org/10.3934/math.2023618
Garg, H., Munir, M., Ullah, K., Mahmood, T., & Jan, N. (2018). Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators. Symmetry, 10(12), 670. https://doi.org/10.3390/sym10120670
Ali, Z., Mahmood, T., & Yang, M. S. (2020). Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry, 12(8), 1311. https://doi.org/10.3390/sym12081311
Liu, P., Wang, D., Zhang, H., Yan, L., Li, Y., & Rong, L. (2021). Multi-attribute decision-making method based on normal T-spherical fuzzy aggregation operator. Journal of Intelligent & Fuzzy Systems, 40(5), 9543-9565. https://doi.org/10.3233/JIFS-202000
Ullah, K., Mahmood, T., & Jan, N. (2018). Similarity measures for T-spherical fuzzy sets with applications in pattern recognition. Symmetry, 10(6), 193. https://doi.org/10.3390/sym10060193
Garg, H., Ullah, K., Mahmood, T., Hassan, N., & Jan, N. (2021). T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making. Journal of ambient intelligence and humanized computing, 1-14. https://doi.org/10.1007/s12652-020-02600-z
Wang, H., & Ullah, K. (2023). T-spherical uncertain linguistic MARCOS method based on generalized distance and Heronian mean for multi-attribute group decision-making with unknown weight information. Complex & Intelligent Systems, 9(2), 1837-1869. https://doi.org/10.1007/s40747-022-00862-y
de Souza, R. M., & De Carvalho, F. D. A. (2004). Clustering of interval data based on city–block distances. Pattern Recognition Letters, 25(3), 353-365. https://doi.org/10.1016/j.patrec.2003.10.016
Deschrijver, G., & Kerre, E. E. (2002). A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms. Notes on Intuitionistic Fuzzy Sets, 8(1), 19-27.
Khan, Q., Khattak, H., AlZubi, A. A., & Alanazi, J. M. (2022). Multiple attribute group decision-making based on intuitionistic fuzzy schweizer-sklar generalized power aggregation operators. Mathematical Problems in Engineering, 2022. https://doi.org/10.1155/2022/4634411
Wang, P., & Liu, P. (2019). Some Maclaurin symmetric mean aggregation operators based on Schweizer-Sklar operations for intuitionistic fuzzy numbers and their application to decision making. Journal of Intelligent & Fuzzy Systems, 36(4), 3801-3824. https://doi.org/10.3233/JIFS-18801
Yu, X., & Xu, Z. (2013). Prioritized intuitionistic fuzzy aggregation operators. Information Fusion, 14(1), 108-116. https://doi.org/10.1016/j.inffus.2012.01.011
Yager, R. R. (2008). Prioritized aggregation operators. International Journal of Approximate Reasoning, 48(1), 263-274. https://doi.org/10.1016/j.ijar.2007.08.009
Jana, C., Senapati, T., Pal, M., & Yager, R. R. (2019). Picture fuzzy Dombi aggregation operators: Application to MADM process. Applied Soft Computing, 74, 99-109. https://doi.org/10.1016/j.asoc.2018.10.021
Garg, H., Ali, Z., Mahmood, T., Ali, M. R., & Alburaikan, A. (2023). Schweizer-Sklar prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision-making. Alexandria Engineering Journal, 67, 229-240. https://doi.org/10.1016/j.aej.2022.12.049
Fan, J., Han, D., & Wu, M. (2022). T-spherical fuzzy COPRAS method for multi-criteria decision-making problem. Journal of Intelligent & Fuzzy Systems, 43(3), 2789-2801. https://doi.org/10.3233/JIFS-213227
Sarfraz, M., Ullah, K., Akram, M., Pamucar, D., & Božanić, D. (2022). Prioritized aggregation operators for intuitionistic fuzzy information based on Aczel–Alsina T-norm and T-conorm and their applications in group decision-making. Symmetry, 14(12), 2655. https://doi.org/10.3390/sym14122655
Ejegwa, P. A., & Agbetayo, J. M. (2023). Similarity-distance decision-making technique and its applications via intuitionistic fuzzy pairs. Journal of Computational and Cognitive Engineering, 2(1), 68-74. http://ojs.bonviewpress.com/index.php/JCCE/article/view/136
Liu, P., Wang, P., & Pedrycz, W. (2020). Consistency-and consensus-based group decision-making method with incomplete probabilistic linguistic preference relations. IEEE Transactions on Fuzzy Systems, 29(9), 2565-2579. https://doi.org/10.1109/TFUZZ.2020.3003501
Liu, P., Li, Y., & Wang, P. (2022). Opinion dynamics and minimum adjustment-driven consensus model for multi-criteria large-scale group decision making under a novel social trust propagation mechanism. IEEE Transactions on Fuzzy Systems, 31(1), 307-321. https://doi.org/10.1109/TFUZZ.2022.3186172
Liu, P., Zhang, K., Wang, P., & Wang, F. (2022). A clustering-and maximum consensus-based model for social network large-scale group decision making with linguistic distribution. Information Sciences, 602, 269-297. https://doi.org/10.1016/j.ins.2022.04.038
Ayub, S., Shabir, M., Riaz, M., Karaaslan, F., Marinkovic, D., & Vranjes, D. (2022). Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis. Axioms, 11(12), 686. https://www.mdpi.com/2075-1680/11/12/686
Wang, P., Liu, P., & Chiclana, F. (2021). Multi-stage consistency optimization algorithm for decision making with incomplete probabilistic linguistic preference relation. Information Sciences, 556, 361-388. https://doi.org/10.1016/j.ins.2020.10.004
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Scientific Oasis

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