Novel decision-making framework based on complex q-rung orthopair fuzzy information

Document Type : Article

Authors

1 Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

2 Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan

3 Department of Mathematics, Minhaj University, Lahore, Pakistan

Abstract

The q-rung orthopair fuzzy sets (q-ROFSs) are increasingly valuable to express fuzzy and vague
information, as the generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets
(PFSs). In this paper, we propose complex $q$-rung orthopair fuzzy sets (C$q$-ROFSs) as a new tool to deal with vagueness, uncertainty and fuzziness by extending the range of membership and non-membership function of $q$-ROFS from real to complex number with the unit disc.
We develop some new complex $q$-rung orthopair fuzzy Hamacher operations and complex $q$-rung orthopair fuzzy Hamacher aggregation operators, i.e., the complex $q$-rung orthopair fuzzy Hamacher weighted average (C$q$-ROFHWA) operator, and the complex $q$-rung orthopair fuzzy Hamacher weighted geometric (C$q$-ROFHWG) operator. Subsequently, we introduce the innovative concept of a complex $q$-rung orthopair fuzzy graphs based on Hamacher operator called complex $q$-rung orthopair fuzzy Hamacher graphs (C$q$-ROFHGs) and determine its energy and Randi'{c} energy.
In particular, we present the energy of a splitting C$q$-ROFHG and shadow C$q$-ROFHG. Further, we describe the notions of complex $q$-rung orthopair fuzzy Hamacher digraphs (C$q$-ROFHDGs).
Finally, a numerical instance related to the facade clothing systems selection is presented to demonstrate the validity of the proposed concepts in decision making (DM).

Keywords

References

References:
1. Zhang, K., Zhan, J., and Wu, W.Z. "On multi-criteria decision-making method based on a fuzzy rough set model with fuzzy a-neighborhoods", IEEE Transactions on Fuzzy Systems, (2020). DOI: 10.1109/TFUZZ.2020.3001670.
2. Ye, J., Zhan, J., Ding, W., et al. "A novel fuzzy rough set model with fuzzy neighborhood operators", Information Sciences, 544, pp. 266-297 (2021).
3. Wang, J., Ma, X., Xu, Z., et al. "Three-way multiattribute decision making under hesitant fuzzy environments", Information Sciences, 552, pp. 328-351 (2021).
4. Zhan, J., Jiang, H., and Yao, Y. "Three-way multiattribute decision-making based on outranking relations", IEEE Transactions on Fuzzy Systems, (2020). DOI: 10.1109/TFUZZ.2020.3007423.
5. Ye, J., Zhan, J., and Xu, Z. "A novel decisionmaking approach based on three-way decisions in fuzzy information systems", Information Sciences , 541, pp. 362-390 (2020).
6. Zadeh, L.A. "Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965).
7. Atanassov, K.T. "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986).
8. Yager, R.R. "Pythagorean membership grades in multi-criteria decision making", IEEE Transactions on Fuzzy Systems, 22(4), pp. 958-965 (2014).
9. Senapati, T. and Yager, R.R. "Fermatean fuzzy sets", Journal of Ambient Intelligence and Humanized Computing, 11(2), pp. 663-674 (2020).
10. Yager, R.R. "Generalized orthopair fuzzy sets", IEEE Transactions on Fuzzy Systems, 25(5), pp. 1222-1230 (2016).
11. Ramot, D., Milo, R., Friedman, M., et al. "Complex fuzzy sets", IEEE Transactions on Fuzzy Systems, 10(2), pp. 171-186 (2002).
12. Alkouri, A. and Salleh, A. "Complex atanassov's intuitionistic fuzzy relation", In Abstract and Applied Analysis, pp. 1-18 (2013).
13. Alkouri, A. and Salleh, A.R. "Complex intuitionistic fuzzy sets", In AIP Conference Proceedings, 1482(1), pp. 464-470 (2012).
14. Garg, H. and Rani, D. "Robust averaging-geometric aggregation operators for complex intuitionistic fuzzy sets and their applications to MCDM process", Arabian Journal for Science and Engineering, 45(3), pp. 2017-2033 (2020).
15. Rani, D. and H. Garg, "Distance measures between the complex intuitionistic fuzzy sets and their applications to the decision-making process", International Journal for Uncertainty Quantification, 7(5), pp. 423-439 (2017).
16. Garg, H. and Rani, D., "New generalised Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm", Journal of Experimental & Theoretical Artificial Intelligence, 32(1), pp. 81-109 (2020).
17. Garg, H. and Rani, D. "Exponential, logarithmic and compensative generalized aggregation operators under complex intuitionistic fuzzy environment", Group Decision and Negotiation, 28(5), pp. 991-1050 (2019).
18. Rani, D. and Garg, H. "Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making", Expert Systems, 35(6), 12325 (2018).
19. Liu, P., Mahmood, T., and Ali, Z. "Complex q-rung orthopair fuzzy aggregation operators and their applications in multi-attribute group decision-making", Information, 11(1), 5 (2020).
20. Garg, H., Gwak, J., Mahmood, T., et al. "Power aggregation operators and VIKOR methods for complex q-rung orthopair fuzzy sets and their applications", Mathematics, 8(4), p. 538 (2020).
21. Liu, P., Ali, Z., and Mahmood, T., "A method to multi-attribute group decision-making problem with complex q-rung orthopair linguistic information based on Heronian mean operators", International Journal of Computational Intelligence Systems, 12(2), pp. 1465- 1496 (2019).
22. Gutman, I. "The energy of a graph: old and new results", In Algebraic Combinatorics and Applications, Springer Berlin Heidelberg, pp. 196-211 (2001).
23. Vaidya, S.K. and Popat, K.M. "Some new results on energy of graphs", MATCH Commun. Math. Comput. Chem, 77, pp. 589-594 (2017) .
24. Rosenfeld, A. "Fuzzy graphs, fuzzy sets and their applications" (L.A. Zadeh, K.S. Fu, M. Shimura, Eds.) Academic Press, New York, pp. 77-95 (1975).
25. Anjali, N. and Mathew, S. "Energy of a fuzzy graph", Annals of Fuzzy Mathematics and Informatics, 6, pp. 455-465 (2013).
26. Akram, M. and Naz, S. "Energy of Pythagorean fuzzy graphs with applications", Mathematics, 6(8), p. 136 (2018).
27. Akram, M., Naz, S., and Davvaz, B. "Simplified interval-valued Pythagorean fuzzy graphs with application", Complex and Intelligent Systems, 5(2), pp. 229-253 (2019).
28. Naz, S. and Akram, M. "Novel decision-making approach based on hesitant fuzzy sets and graph theory", Computational and Applied Mathematics, 38(1), p. 7 (2019).
29. Thirunavukarasu, P., Suresh, R., and Viswanathan, K.K. "Energy of a complex fuzzy graph", International Journal of Mathematical Sciences and Engineering Applications, 10(1), pp. 243-248 (2016).
30. Luqman, A., Akram, M., Al-Kenani, A.N., et al. "A study on hypergraph representations of complex fuzzy information", Symmetry, 11(11), p. 1381 (2019).
31. Luqman, A., Akram, M., and Smarandache, F. "Complex neutrosophic hypergraphs: new social network models", Algorithms, 12(11), pp. 234-261 (2019).
32. Naz, S., Ashraf, S., and Akram, M. "A novel approach to decision-making with Pythagorean fuzzy information", Mathematics, 6(6), pp. 95-122 (2018).
33. Akram, M. and Naz, S. "A novel decision-making approach under complex pythagorean fuzzy environment", Mathematical and Computational Applications, 24(3), pp. 73-105 (2019).
34. Habib, A., Akram, M., and Farooq, A. "q-Rung orthopair fuzzy competition graphs with application in the soil ecosystem", Mathematics, 7(1), p. 91 (2019).
35. Yin, S., Li, H., and Yang, Y. "Product operations on q-rung orthopair fuzzy graphs", Symmetry, 11(4), pp. 588-610 (2019).
36. Akram, M., Alsulami, S., Karaaslan, F., et al. "q-rung orthopair fuzzy graphs under Hamacher operators", Journal of Intelligent and Fuzzy Systems, 40(1), pp. 1367-1390 (2021).
37. Guleria, A. and Bajaj, R.K. "T-spherical fuzzy graphs: operations and applications in various selection processes", Arabian Journal for Science and Engineering, 45(3), pp. 2177-2193 (2020).
38. Akram, M., Naz, S., Shahzadi, S., et al.  Geometricarithmetic energy and atom bond connectivity energy of dual hesitant q-rung orthopair fuzzy graphs", Journal of Intelligent and Fuzzy Systems, 40, pp. 1287- 1307 (2021).
39. Naz, S., Akram, M., Alsulami, S., et al. "Decisionmaking analysis under interval-valued q-rung orthopair dual hesitant fuzzy environment", International Journal of Computational Intelligence Systems, 14(1), pp. 332-357 (2021).
40. Hamacher, H. "Uber logische verknupfungen unscharfer aussagen und deren zugehrige bewertungsfunktionen", Progress in Cybernetics and Systems Research, 3, pp. 276-288 (1978).
41. Liu, P., Mahmood, T., and Ali, Z. "Complex q-rung orthopair fuzzy aggregation operators and their applications in multi-attribute group decision-making", Information, 11(1), pp. 5-31 (2020).
42. Garg, H., Gwak, J., Mahmood, T., et al. "Power aggregation operators and VIKOR methods for complex q-rung orthopair fuzzy sets and their applications", Mathematics, 8(4), pp. 538-571 (2020).
Scientia Iranica
Volume 30, Issue 4 - Serial Number 4
Transactions on Industrial Engineering (E)
July and August 2023
Pages 1450-1479

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