Hybridizations of Archimedean copula and generalized MSM operators and their applications in interactive decision-making with q-rung probabilistic dual hesitant fuzzy environment

Gogineni  Anusha; Paladugu Venkata  Ramana; Rupak  Sarkar

doi:10.31181/dmame0329102022a

Authors

Gogineni Anusha Department of Engg. Mathematics, College of Engg., Koneru Lakshmaiah Education Foundation, Vaddeswaram-522032, Andhra Pradesh, India https://orcid.org/0000-0002-0948-7498
Paladugu Venkata Ramana Department of Basic Science & Humanities, Vignan's Lara Institute of Technology and Sciences, Vadlamudi-522213, Andhra Pradesh, India
Rupak Sarkar Department of Mathematics, Women’s Polytechnic, Hapania, Tripura, India

DOI:

https://doi.org/10.31181/dmame0329102022a

Keywords:

q-Rung probabilistic dual hesitant fuzzy set, Archimedean Copula, generalized Maclaurin symmetric mean operators, group decision-making

Abstract

The q-rung probabilistic dual hesitant fuzzy sets (qRPDHFSs), which outperform dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets, and probabilistic dual hesitant Pythagorean fuzzy sets, are used in this research to develop an interactive group decision-making approach. We first suggest the Archimedean Copula-based operations on q-rung probabilistic dual hesitant fuzzy (qRPDHF) components and investigate their key features before constructing the approach. We then create some new aggregation operators (AOs) in light of these operations, including the qRPDHF generalized Maclaurin symmetric mean (MSM) operator, qRPDHF geometric generalized MSM operator, qRPDHF weighted generalized MSM operator, and qRPDHF weighted generalized geometric generalized MSM operator. These aggregation operators are better than current operators on qRPDHF because they can take into account the interactions between a large number of criteria and probability distributions. The evaluation findings are distorted since the present methodologies do not take expert involvement into account in order to achieve the required consistency level. We employ the idea of interaction, consistency, resemblance, and consensus-building among the decision-makers in our method to get around this. We create an optimization model based on the cross-entropy of the qRPDHF components to estimate the weights of the criterion. We provide contextual research on the choice of open-source software LMS in order to demonstrate the relevance of the recommended AOs. Likewise, we ran a sensitivity test on the weights of the criterion to make sure that our model is consistent. The comparison investigation has demonstrated that the suggested approach can overcome the challenges of previous works.

Downloads

Download data is not yet available.

References

Bacigal, T., Mesiar, R., & Najjari, V. (2015). Generators of Copulas and aggregation. Information Sciences, 306, 81-87.

Bashiri, M., & Badri, H. (2011). A group decision making procedure for fuzzy interactive linear assignment programming. Expert Systems with Application, 38 (5), 5561–5568.

Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: a guide for practitioners, In Kacprzyk, editors. Studies in fuzziness and soft computing. Berlin: Springer.

Bonferroni, C. (1950). Sulle medie multiple di potenze. Bolletino dell Unione Matematica Italiana, 5 (3), 267-270.

Cheng, X., Gu, J., & Xu, Z.S. (2018). Venture capital group decision-making with interaction under probabilistic linguistic environment. Knowledge Based Systems, 140, 82-91.

Garg, H., & Kaur, G. (2018a). A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications. Neural Computing and Applications, https://doi.org/10.1007/s00521-019-04362-y.

Garg, H., & Kaur, G. (2018). Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision making based on aggregation operators with new distance measures. Mathematics, 6(12), 280 (https://doi. org/10. 3390/math6120280).

Gou, X.J., Liao, H.C., Xu, Z.S., Min, R., & Herrera, F. (2019). Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: Consistency based measures, index and repairing algorithms and decision model. Information Sciences, 489, 93-112.

Grabisch, M., Maricha, J. L., Mesiar, R. & Pap, E. (2011). Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes. Information Sciences, 181, 23-43.

Han, B., Tao, Z., Chen, H., Zhou, L., & Liu, J. (2020). A new computational model based on Archimedean copula for probabilistic unbalanced linguistic term set and its application to multi-attribute group decision-making. Computers and Industrial Engineering, 140, 106264.

Han, X. L., & Li, S.R. (1994). The priority method in view of consistency harmonious weight index. System Engineering, Theory and Methodology, 3(1), 41-45.

Hao, Z., Xu , Z., Zhao, H., & Su, Z (2017). Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowledge Based Systems, 127, 16–28.

Hara, T., Uchiyama, M., & Takahasi, S.E. (1998). A refinement of various mean inequalities. Journal of In-equalities and Applications, 2(4), 387-395.

Hezam, I.M., Mishra, A. R., Rani, P., Saha, A., Pamucar, D., & Smarandache, F. (2023). An integrated decision support framework using single-valued neutrosophic- MASWIP-COPRAS for sustainability assessment of bio-energy production technologies. Expert System with Applications, 211, 118674.

Ji, C., Zhang, R., & Wang, j. (2021). Probabilistic dual‑hesitant Pythagorean fuzzy sets and their application in multi-attribute group decision-making. Cognitive Computation, 13, 919–935.

Krishankumar, R., Sivagami, R., Saha, A., P. Rani, Ravichandran, K. S., & Arun, K. (2022). Cloud vendor selection for the health-care industry using a big data driven decision model with probabilistic linguistic information. Applied Intelligence, http://doi.org/10.1007/s10489-021-02913-2.

Li, L., Lei, H., & Wang, J. (2020). q-Rung probabilistic dual hesitant fuzzy sets and their application in multi-attribute decision-making. Mathematics, 8, 1574 (doi:10.3390/math8091574).

Maclaurin, C. (1729). A second letter to Martin Folkes, Esq concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans Roy Soc London Ser A 36, 59-96.

Mishra, A. R., Rani, P., Pamucar, D., Hezam, I.M., & Saha, A. (2022b). Entropy and discrimination measures based q-rung orthopair fuzzy MULTIMOORA framework for selecting solid waste disposal method. Environmental Science and Pollution Research, https://link.springer.com/article/10.1007/s11356-022-22734-1.

Mishra, A. R., Rani, P., Saha, A., Hezam, I.M., & Pamucar, D. (2022c). Fermatean fuzzy copula aggregation operators and similarity measures-based complex proportional assessment approach for renewable energy source selection. Complex and Intelligent Systems. http://doi.org/10.1007/s40747-022-00743-4.

Mishra, A. R., Saha, A., Rani, P., Hezam, I.M., Shrivastava, R., & Smarandache, F. (2022d). An integrated decision support framework using single-valued MEREC-MULTIMOORA for low carbon tourism strategy assessment. IEEE Access, 10, 24411-24432.

Mishra, A. R., Saha, A., Rani, P., Pamucar, D., Dutta, D., & Hezam, I.M. (2022a). Sustainable supplier selection using HF-DEA-FOCUM-MABAC technique: A case study in the auto making industry. Soft Computing, http://doi.org/10.1007/s00500-022-07192-8.

Nather, W. (2010). Copulas and t-norms: Mathematical tools for combining probabilistic and fuzzy information with application to error propagation and interaction. Structural Safety, 32, 366-371.

Nelsen, R.B. (2013). An introduction to Copula, Springer Science and Business Media.

Poswal, P., Chauhan, A., Rajoria, Y. K., Boadh, R., & Goel, A. (2022). Fuzzy optimization model of two parameter weibull deteriorating rate with quadratic demand and variable holding cost under allowable shortages. Yugoslav Journal of Operations Research, 32(4), 453-470.

Rani, P., Mishra, A. R., Saha, A. (2021). Fermatean fuzzy Heronian mean operators and MEREC based additive ratio assessment method for food waste treatment technology selection. International Journal of Intelligent Systems, 37 (3), 2612-2647.

Ren, Z., Xu, Z., & Wang, H. (2017). An extended TODIM method under probabilistic dual hesitant fuzzy information and its application on enterprise strategic assessment. In: 2017 IEEE international conference on industrial engineering and engineering management (IEEM). 1464–1468.

Ren, Z., Xu, Z., & Wang, H. (2019). The strategy selection problem on artificial intelligence with an integrated VIKOR and AHP method under probabilistic dual hesitant fuzzy information. IEEE Access, 7, 103979– 103999.

Reverberi, P., & Talamo, M. (1999). A probabilistic model for interactive decision-making. Decision Support Systems, 25 (4), 289–308.

Saha, A., , & Yager, R. R. (2021a). Hybridizations of generalized Dombi operators and Bonferroni mean operators under dual probabilistic linguistic environment for group decision-making. International Journal of Intelligent Systems, 36(11), 6645-6679,

Saha, A., Dutta, D., Kar, S. (2021b). Some new hybrid hesitant fuzzy weighted aggregation operators based on Archimedean and Dombi operations for multi-attribute decision making. Neural Computing and Applications, 33 (14), 8753-8776.

Saha, A., Ecer, F., Chatterjee, P., Senapati, T., & Zavadskas, E. K. (2022b). q-Rung orthopair fuzzy improved power weighted operators for solving group decision-making issues. INFORMATICA (https://www.informatica.vu.lt/journal/INFORMATICA/article/1271/read).

Saha, A., Garg, H., & Dutta, D. (2021c). Generalized Dombi and Bonferroni mean operators based group decision-making under probabilistic linguistic q-rung orthopair fuzzy environment. International Journal of Intelligent System, 36 (12), 7770-7804.

Saha, A., Pamucar, D., Gorcun, O. F., & Mishra, A. R. (2023). Warehouse site selection for the automotive industry using a Fermatean fuzzy based decision-making approach. Expert System With Applications, 211, 118497.

Saha, A., Simic, V., Senapati, T., Dabic-Miletic, S., & Ala, A. (2022a). A dual hesitant fuzzy sets-based methodology for advantage prioritization of zero-emission last-mile delivery solutions for sustainable city logistics. IEEE Transactions on Fuzzy Systems, https://doi.org/10.1109/TFUZZ.2022.3164053.

Sakawa, M., & Yano, H. (1986). Interactive fuzzy decision making for multi-objective nonlinear programming using augmented minimax problems. Fuzzy Sets and Systems, 20(1), 31–43.

Senapati, T. (2022). Approaches to multi-attribute decision making based on picture fuzzy Aczel-Alsina average aggregation operators. Computational & Applied Mathematics, 41(40), 1-28. https://doi.org/10.1007/s40314-021-01742-w.

Senapati, T., Chen, G., Mesiar, R., Yager, R.R., & Saha, A. (2022). Novel Aczel-Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment. International Journal of General Systems, 51(5), 511-546.

Shi, X., & Xia, H. (1997). Interactive bi-level multi-objective decision making. Operations Research, 48 (9), 943-949.

Sklar, M. (1959). Fonctions de repartition a n dimensions et leurs marges. Universite Paris, 8, 229-231.

Tao, Z., Han, B., & Chen, H. (2018). On Intuitionistic fuzzy Copula aggregation operators in multiple-attribute decision-making. Cognitive Computation (http: //doi.org/10.1007/s12559-018-9545-1).

Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539.

Wang, J.Q., Yang, Y., & Li, L. (2018). Multi criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Computing and Applications, 30 (5), 1529-1547.

Watson, W.E., Michaelsen, L.K., & Sharp, W. (1991). Member competence, group interaction, and group decision making: a longitudinal study. Journal of Applied Psychology, 76 (6), 803–809.

Xu, Z., & Zhou, W. (2017). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16(4), 481–503.

Xu, Z.S., & Chen, J. (2007). An interactive method for fuzzy multiple attribute group decision making. Information Science, 177 (1), 248–263.

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

Zhu, B., Xu, Z., Xia, M. (2012). Dual hesitant fuzzy sets. Journal of Applied Mathematics, https://doi.org/10.1155/2012/879629.