An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws
DOI:
https://doi.org/10.31181/jdaic10006062023aKeywords:
The intuitionistic fuzzy soft set (IFSS), Aczel–Alsina aggregation operators, Multi-attribute decision-making (MADM)Abstract
The intuitionistic fuzzy soft set (IFSS) is a vital technique for tackling uncertainty while the collection of information with the help of the membership function having values from unit interval. Moreover, the Aczel-Alsina t-norm (AATNRM) and Aczel-Alsina t-conorm (AATCRM) are the most generalized and flexible operational laws to operate the information which is the part of the unit intervals. The purpose of this article is to provide a number of aggregation operations (AOs) for information represented by intuitionistic fuzzy soft values (IFSVs) based on AATRM and AATCRM. Therefore, some new operational laws are developed by using on the AATRM and AATCRM for the development of the sum and product laws for IFSVs. Then, intuitionistic fuzzy soft Aczel-Alsina weighted averaging (IFSAAWA) and geometric (IFSAAWG) operators are purposed based on these operational laws. Additionally, some of their characteristics are examined, and the difference of the proposed and existing operators is investigated. Moreover, the proposed approach is applied to the problem of multi-attribute decision-making (MADM) for significance.
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Aczél, J., & Alsina, C. (1982). Characterizations of Some Classes of Quasilinear Functions with Applications to Triangular Norms and to Synthesizing Judgements. Aequationes mathematicae, 25, 313–315.
Akram, M., & Bibi, R. (2023). Multi-Criteria Group Decision-Making Based on an Integrated PROMETHEE Approach with 2-Tuple Linguistic Fermatean Fuzzy Sets. Granular Computing, https://doi.org/10.1007/s41066-022-00359-6.
Akram, M., Peng, X., & Sattar, A. (2021). A New Decision-Making Model Using Complex Intuitionistic Fuzzy Hamacher Aggregation Operators. Soft Computing, 25, 7059–7086.
Albaity, M., Mahmood, T., & Ali, Z. (2023). Impact of Machine Learning and Artificial Intelligence in Business Based on Intuitionistic Fuzzy Soft WASPAS Method. Mathematics, 11, 1453.
Ali, Z., Mahmood, T., Aslam, M., & Chinram, R. (2021a). Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making. Mathematics, 9(16), 1922.
Ali, Z., Mahmood, T., Ullah, K., Pamucar, D., & Cirovic, G. (2021b). Power Aggregation Operators Based on T-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making. Symmetry, 13, 1986.
Arora, R. (2020). Intuitionistic Fuzzy Soft Aggregation Operator Based on Einstein Norms and Its Applications in Decision-Making. In Abraham, A., Cherukuri, A.K., Melin, P., & Gandhi, N. (Eds), Proceedings of the Intelligent Systems Design and Applications (pp. 998-1008). Cham: Springer International Publishing.
Arora, R., & Garg, H. (2017). Prioritized Averaging/Geometric Aggregation Operators under the Intuitionistic Fuzzy Soft Set Environment. Scientia Iranica, 25(1), 466-482.
Atanassov, K. (1986). Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87–96.
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, 19–27.
Farahbod, F., & Eftekhari, M. (2012). Comparison of Different T-Norm Operators in Classification Problems. International Journal of Fuzzy Logic Systems, 2, 33–39.
Frank, M.J. (1979). On the Simultaneous Associativity of F (x, y) And x+ y- F (x, y). Aequationes mathematicae, 19, 194–226.
Gao, H. (2018). Pythagorean Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making. Journal of Intelligent & Fuzzy Systems, 35, 2229–2245.
Garg, H., & Arora, R. (2018). Novel Scaled Prioritized Intuitionistic Fuzzy Soft Interaction Averaging Aggregation Operators and Their Application to Multi Criteria Decision Making. Engineering Applications of Artificial Intelligence, 71, 100–112.
Garg, H., & Kumar, K. (2018). Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and Its Application to Group Decision-Making Process Using the Set Pair Analysis. Arabian Journal for Science and Engineering, 43, 3213–3227.
Garg, H., & Rani, D. (2019a). Some Generalized Complex Intuitionistic Fuzzy Aggregation Operators and Their Application to Multicriteria Decision-Making Process. Arabian Journal for Science and Engineering, 44, 2679–2698.
Garg, H., & Rani, D. (2019b). Novel Aggregation Operators and Ranking Method for Complex Intuitionistic Fuzzy Sets and Their Applications to Decision-Making Process. Artificial Intelligence Review, 53, 3595-3620.
Hayat, K., Tariq, Z., Lughofer, E., & Aslam, M.F. (2021). New Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets. Soft Computing, 25, 13353–13364.
Huang, J.-Y. (2014). Intuitionistic Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making. Journal of Intelligent & Fuzzy Systems, 27, 505–513.
Hussain, A., Ullah, K., Alshahrani, M.N., Yang, M.-S., & Pamucar, D. (2022). Novel Aczel–Alsina Operators for Pythagorean Fuzzy Sets with Application in Multi-Attribute Decision Making. Symmetry, 14, 940.
Khan, M.J., Kumam, P., & Kumam, W. (2021). Theoretical Justifications for the Empirically Successful VIKOR Approach to Multi-Criteria Decision Making. Soft Computing, 25, 7761–7767.
Liu, P., Wang, P., & Pedrycz, W. (2021). Consistency- and Consensus-Based Group Decision-Making Method With Incomplete Probabilistic Linguistic Preference Relations. IEEE Transactions on Fuzzy Systems, 29, 2565–2579.
Liu, P., Li, Y., & Wang, P. (2023). 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, 307–321.
Liu, P., Zhang, K., Dong, X., & Wang, P. (2022a). A Big Data-Kano and SNA-CRP Based QFD Model: Application to Product Design Under Chinese New E-Commerce Model. IEEE Transactions on Engineering Management, 1–15, doi:10.1109/TEM.2022.3227094.
Liu, P., Zhang, K., Wang, P., & Wang, F. (2022b). A Clustering- and Maximum Consensus-Based Model for Social Network Large-Scale Group Decision Making with Linguistic Distribution. Information Sciences, 602, 269–297.
Lu, J., Wei, C., Wu, J., & Wei, G. (2019). TOPSIS Method for Probabilistic Linguistic MAGDM with Entropy Weight and Its Application to Supplier Selection of New Agricultural Machinery Products. Entropy, 21, 953.
Mahmood, T., & Ali, Z. (2023). Multi-Attribute Decision-Making Methods Based on Aczel–Alsina Power Aggregation Operators for Managing Complex Intuitionistic Fuzzy Sets. Computational and Applied Mathematics, 42, 87.
Mahmood, T. (2022). Multi-Attribute Decision-Making Method Based on Bipolar Complex Fuzzy Maclaurin Symmetric Mean Operators. Computational and Applied Mathematics, 41, 1–25.
Mahmood, T. & Ur Rehman, U. (2022). A Novel Approach towards Bipolar Complex Fuzzy Sets and Their Applications in Generalized Similarity Measures. International Journal of Intelligent Systems, 37, 535–567.
Maji, P.K., Biswas, R. & Roy, A.R. (2001). Intuitionistic Fuzzy Soft Sets. Journal of fuzzy mathematics, 9, 677–692.
Molodtsov, D. (1999). Soft Set Theory—First Results. Computers & Mathematics with Applications, 37, 19–31.
Riaz, M. & Farid, H.M.A. (2022). Picture Fuzzy Aggregation Approach with Application to Third-Party Logistic Provider Selection Process. Reports in Mechanical Engineering, 3, 318–327.
Riaz, M., & Hashmi, M.R. (2019). Linear Diophantine Fuzzy Set and Its Applications towards Multi-Attribute Decision-Making Problems. Journal of Intelligent & Fuzzy Systems, 37, 5417–5439.
Schweizer, B., & Sklar, A. (1960). Statistical Metric Spaces. Pacific Journal of Mathematics, 10, 313–334.
Seikh, M.R., & Mandal, U. (2021). Intuitionistic Fuzzy Dombi Aggregation Operators and Their Application to Multiple Attribute Decision-Making. Granular Computing, 6, 473–488.
Senapati, T., Chen, G., Mesiar, R., & Yager, R.R. (2022). Novel Aczel–Alsina Operations-Based Interval-Valued Intuitionistic Fuzzy Aggregation Operators and Their Applications in Multiple Attribute Decision-Making Process. International Journal of Intelligent Systems, 37(8), 5059–5081.
Wang, W., & Liu, X. (2012). Intuitionistic Fuzzy Information Aggregation Using Einstein Operations. IEEE Transactions on Fuzzy Systems, 20, 923–938.
Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8, 338–353.
Zhao, M., Wei, G., Wei, C., & Wu, J. (2021). Improved TODIM Method for Intuitionistic Fuzzy MAGDM Based on Cumulative Prospect Theory and Its Application on Stock Investment Selection. International Journal of Machine Learning and Cybernetics, 12, 891–901.
Zhao, X., & Wei, G. (2013). Some Intuitionistic Fuzzy Einstein Hybrid Aggregation Operators and Their Application to Multiple Attribute Decision Making. Knowledge-Based Systems, 37, 472–479.
