The algebraic structures of complex intuitionistic fuzzy soft sets associated with groups and subgroups

Document Type : Article

Authors

1 aA-Level Academy, UCSI College KL Campus, Lot 12734, Jalan Choo Lip Kung Taman Taynton View, 56000 Cheras,Kuala Lumpur, MALAYSIA

2 Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur, MALAYSIA

3 Department of Mathematics, Yazd University, Yazd, Iran

4 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, West Bengal, India.

Abstract

In recent years, the theory of complex fuzzy sets has captured the attention of many researchers, and research in this area has intensified in the past five years. However, almost all of the researchers in this area have focused on the development of various complex fuzzy based models as well as constructing decision making processes using current decision making approaches and tools. In this spirit, this paper focuses on developing the algebraic structures pertaining to groups and subgroups for the complex intuitionistic fuzzy soft set model. This paper was constructed based on the complex intuitionistic fuzzy soft set model which is characterized by a membership and a non-membership structure for both the amplitude and phase terms of the elements. This model was chosen due to its dual-membership structure that is better able to handle the uncertainties and partial ignorance that exists in most complex data, whilst retaining all the characteristics and advantages of complex fuzzy sets. Besides examining the properties and structural characteristics of the algebraic structures, the relationship between the algebraic structures introduced here and the corresponding algebraic structures in fuzzy group theory and classical group theory were also discussed and verified.

Keywords

References

References:
1. Zadeh, L.A. "Fuzzy sets", Information and Control, 8, pp. 338-353 (1965).
2. Atanassov, K.T. "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986).
3. Molodtsov, D. "Soft set theory - First results", Computers and Mathematics with Applications, 37(4-5), pp. 19-31 (1999).
4. Maji, P.K., Biswas, R., and Roy, A.R. "Fuzzy soft sets", Journal of Fuzzy Mathematics, 3(9), pp. 589-602 (2001).
5. Maji, P.K., Biswas, R., and Roy, A.R. "Intuitionistic fuzzy soft sets", Journal of Fuzzy Mathematics, 9(3), pp. 677-692 (2001).
6. Yang, X., Lin, T.Y., Yang, J., Li, Y., and Yu, D. "Combination of interval-valued fuzzy set and soft set", Computers and Mathematics with Applications, 58, pp. 521-527 (2009).
7. Jiang, Y., Tang, Y., Chen, Q., Liu, H., and Tang, J. "Interval-valued intuitionistic fuzzy soft sets and their properties", Computers and Mathematics with Applications, 60, pp. 906-918 (2010).
8. Xu, W., Ma, J.,Wang, S., and Hao, G. "Vague soft sets and their properties", Computers and Mathematics with Applications, 59, pp. 787-794 (2010).
9. Ramot, D., Milo, R., Friedman, M., and Kandel, A. "Complex fuzzy sets", IEEE Transactions on Fuzzy Systems, 10(2), pp. 171-186 (2002).
10. Kumar, T. and Bajaj, R.K. "On complex intuitionistic fuzzy soft sets with distance measures and entropies", Journal of Mathematics, 2014, pp. 1-12 (2014).
11. Feng, F., Young, B.J., and Zhao, X. "Soft semirings", Computers and Mathematics with Applications, 56, pp. 2621-2628 (2008).
12. Greenfield, S., Chiclana, F., and Dick, S. "Intervalvalued complex fuzzy logic", IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, pp. 2014-2019 (2016).
13. Alkouri, A.U.M. and Salleh, A.R. "Complex intuitionistic fuzzy sets", AIP Conference Proceedings, 1482, pp. 464-470 (2012).
14. Selvachandran, G., Maji, P.K., Abed, I.E., and Salleh, A.R. "Complex vague soft sets and its distance measures", Journal of Intelligent and Fuzzy Systems, 31, pp. 55-68 (2016).
15. Selvachandran, G., Maji, P.K., Abed, I.E., and Salleh, A.R. "Relations between complex vague soft sets", Applied Soft Computing, 47, pp. 438-448 (2016).
16. Ramot, D., Friedman, M., Langholz, G., and Kandel, A. "Complex fuzzy logic", IEEE Transactions on Fuzzy Systems, 11(4), pp. 450-461 (2003).
17. Dick, S. "Toward complex fuzzy logic", IEEE Transactions on Fuzzy Systems, 13(3), pp. 405-414 (2005).
18. Zhang, G., Dillon, T.S., Cai, K.Y., Ma, J., and Lu, J. "Operation properties and equalities of complex fuzzy sets", International Journal of Approximate Reasoning, 50, pp. 1227-1249 (2009).
19. Aktas, H. and Cagman, N. "Soft sets and soft groups", Information Science, 177(13), pp. 2726-2735 (2007).
20. Aygunoglu, A. and Aygun, H. "Introduction to fuzzy soft groups", Computers and Mathematics with Applications, 58, pp. 1279-1286 (2009).
21. Acar, U., Koyuncu, F., and Tanay, B. "Soft sets and soft rings", Computers and Mathematics with Applications, 59(11), pp. 3458-3463 (2010).
22. Inan, E. and Ozturk, M.A. "Fuzzy soft rings and fuzzy soft ideals", Neural Computing and Applications, 21(1), pp. 1-8 (2011).
23. Ghosh, J., Dinda, B., and Samanata, T.K. "Fuzzy soft rings and fuzzy soft ideals", International Journal of Pure and Applied Sciences and Technology, 2(2), pp. 66-74 (2011).
24. Zhu, K.Y. "Novel soft fuzzy rough rings (ideals) of rings and their application in decision making", Soft Computing - A Fusion of Foundations, Methodologies & Applications, 23(9), pp. 3167-3189 (2019).
25. Vimala, J., Arockia Reeta, J., and Barathi, P. "Algebraic applications on I-fuzzy soft group", International Journal of Soft Computing, 12(5-6), pp. 322-328 (2017).
26. Zhan, J., Dudek, W.A., and Neggers, J. "A new soft union set: Characterizations of hemirings", International Journal of Machine Learning and Cybernetics, 8(2), pp. 525-535 (2017).
27. Bera, T. and Mahapatra, N.K. "On neutrosophic normal soft groups", International Journal of Applied and Computational Mathematics, 3(4), pp. 3047-3066 (2017).
28. Yamak, S., Kazanci, O., and Davvaz, B. "Soft hyperstructures", Computers and Mathematics with Applications, 62, pp. 797-803 (2011).
29. Leoreanu-Fotea, V., Feng, F., and Zhan, J. "Fuzzy soft hypergroups", International Journal of Computer Mathematics, 89(8), pp. 963-974 (2012).
30. Selvachandran, G. "Introduction to the theory of soft hyperrings and soft hyperring homomorphism", JP Journal of Algebra, Number Theory and Applications, 36(3), pp. 279-294 (2015).
31. Selvachandran, G. and Salleh, A.R. "Hypergroup theory applied to fuzzy soft sets", Global Journal of Pure and Applied Mathematics, 11(2), pp. 825-834 (2015).
32. Selvachandran, G. and Salleh, A.R. "Fuzzy soft hyperrings and fuzzy soft hyperideals", Global Journal of Pure and Applied Mathematics, 11(2), pp. 807-823 (2015).
33. Selvachandran, G. and Salleh, A.R. "Vague soft hypergroups and vague soft hypergroup homomorphism", Advances in Fuzzy Systems, 2014, pp. 1-10 (2014).
34. Selvachandran, G. and Salleh, A.R. "Algebraic hyperstructures of vague soft sets associated with hyperrings and hyperideals", The Scientific World Journal, 2015, pp. 1-12 (2015).
35. Khan, A., Farooq, M., and Davvaz, B. "On (M, N) intersectional soft interior hyperideals of ordered semihypergroups", Journal of Intelligent and Fuzzy Systems, 33(6), pp. 3895-3904 (2017).
36. Ma, X., Zhan, J., and Leoreanu-Fotea, V. "Rough soft hyperrings and corresponding decision making", Journal of Intelligent and Fuzzy Systems, 33(3), pp. 1479-1489 (2017).
37. Al-Husban, R., Salleh, A.R., and Ahmad, A.G. "Complex intuitionistic fuzzy subrings", AIP Conference Proceedings, 1784, pp. 1-7 (2016).
38. Al-Husban, R., Salleh, A.R., and Ahmad, A.G. "Complex intuitionistic fuzzy subrings", AIP Conference Proceedings, 1739, pp. 1-7 (2016).
39. Al-Husban, A. and Salleh, A.R. "Complex fuzzy group based on complex fuzzy space", Global Journal of Pure and Applied Mathematics, 12(2), pp. 1433-1450 (2016).
40. Alsarahead, M.O. and Ahmad, A.G. "Complex fuzzy subgroups", Applied Mathematical Sciences, 11(41), pp. 2011-2021 (2017).
41. Alsarahead, M.O. and Ahmad, A.G. "Complex fuzzy soft group", Journal of Quality Management and Analysis, 13(2), pp. 17-28 (2017).
42. Rosenfeld, A. "Fuzzy groups", Journal of Mathematical Analysis and Applications, 35, pp. 512-517 (1971).
Scientia Iranica
Volume 26, Issue 3
Transactions on Industrial Engineering (E)
May and June 2019
Pages 1898-1912

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History

  • Receive Date: 19 December 2017
  • Revise Date: 27 February 2018
  • Accept Date: 23 April 2018

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