T -spherical fuzzy soft sets and its aggregation operators with application in decision-making

Document Type : Article

Authors

Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, Pin-173 234, Himachal Pradesh, India

Abstract

In the present manuscript, we introduce a novel concept of T-spherical fuzzy soft set with various important operations and properties. In the field of information theory, an aggregation operator is a structured mathematical function which aggregates all the information received as input and provides a single output entity, which are found to be applicable for various important decision making applications. Some averaging aggregation operators and geometric aggregation operators (weighted, ordered and hybrid) for T-spherical fuzzy soft numbers have been proposed with their various properties. Further, utilizing the proposed aggregation operators of various types along with the properly defined score function/accuracy function, an algorithm for solving a decision making problem has been provided. The proposed methodology has also been well illustrated with the help of a numerical example. Some comparative remarks and advantages of the introduced notion of T-spherical fuzzy soft set and the proposed methodology have been listed for a better motivation and readability.

Keywords

Main Subjects


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. Atanassov, K.T., and Vassilev, P. \On the intuitionistic
fuzzy sets of n-th type", Advances in Data Analysis
with Computational Intelligence Methods, Studies in
Computational Intelligence, 738, pp. 265{274 (2018).
4. Yager, R.R. \Pythagorean fuzzy subsets", In Proceedings
of Joint IFSA World Congress and NAFIPS Annual
Meeting, Edmonton, Canada, pp. 57{61 (2013).
5. Cuong, B. \Picture fuzzy sets- rst results Part 1",
Seminar on Neuro{Fuzzy Systems with Applications,
Institute of Mathematics, Hanoi (2013).
6. Mahmood, T., Kifayat, U., Khan, Q., and Jan, N.
\An approach toward decision making and medical
diagnosis problems using the concept of spherical fuzzy
sets", Neural Computing and Applications, 31(11), pp.
7041{7053 (2019).
7. Kifayat, U., Mahmood, T., and Jan, N. \Similarity
measures for T-spherical fuzzy sets with applications in
pattern recognition", Symmetry, 10(6), p. 193 (2018).
8. Garg, H., Munir, M., Ullah, K., Mahmood, T.,
and Jan, N. \Algorithm for T-spherical fuzzy multiattribute
decision making based on improved interactive
aggregation operators", Symmetry, 10, p. 670
(2018).
9. Arora, R. and Garg, H. \Robust aggregation operators
for multi-criteria decision-making with intuitionistic
fuzzy soft set environment", Scientia Iranica, 25(2),
pp. 931{942 (2018).
10. Garg, H., Agarwal, N., and Tripathi, A. \Some
improved interactive aggregation operators under
interval-valued intuitionistic fuzzy environment and
its application to decision making process", Scientia
Iranica, 24(5), pp. 2581{2604 (2017).
11. Xu, Z.S. and Yager, R.R. \Some geometric aggregation
operators based on intuitionistic fuzzy sets", International
Journal of General System, 35(4), pp. 417{433
(2006).
12. Yager, R.R. \Prioritized aggregation operators", International
Journal of Approximate Reasoning, 48(1),
pp. 263{274 (2008).
13. Xu, Z. and Yager, R.R. \Power-geometric operators
and their use in group decision making", IEEE Transactions
on Fuzzy Systems, 18(1), pp. 94{105 (2010).
14. Yu, D. \Intuitionistic fuzzy prioritized operators and
their application in multi criteria group decision making",
Technological and Economic Development of
Economy, 19(1), pp. 1{21 (2013).
15. Yager, R.R. \On generalized Bonferroni mean operators
for multi criteria aggregation", International
Journal of Approximate Reasoning, 50(8), pp. 1279{
1286 (2009).
16. Xu, Z.S. and Yager, R.R. \Intuitionistic fuzzy bonferroni
means", IEEE Transaction on Systems, Man and
Cybernetics, 41(2), pp. 568{578 (2011).
17. Liu, P. and Li, H. \Interval valued intuitionistic
fuzzy power Bonferroni aggregation operators and
their application to group decision making", Cognitive
Computation, 9(4), pp. 494{512 (2017).
18. Wang, W. and Liu, X. \Intuitionistic fuzzy information
aggregation using Einstein operations", IEEE Transactions
on Fuzzy Systems, 20(5), pp. 923{938 (2012).
19. Tao, Z., Han, B., and Chen, H. \On intuitionistic fuzzy
copula aggregation operators in multiple attribute
1028 A. Guleria and R.K. Bajaj/Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 1014{1029
decision making", Cognitive Computation, 10(4), pp.
610{624 (2018).
20. Garg, H. \Generalized pythagorean fuzzy geometric
aggregation operators using t{norm and t{conorm for
multi criteria decision making", International Journal
of Intelligent Systems, 32(6), pp. 597{630 (2017).
21. Molodstov, D.A. \Soft set theory rst result", Computers
and Mathematics with Application, 27, pp. 19{31
(1999).
22. Maji, P.K., Biswas, R., and Roy, A.R. \Intuitionistic
fuzzy soft sets", Journal of Fuzzy Mathematics, 9, pp.
677{692 (2001).
23. Kalaichelvi, A. and Haritha, M.P. \Application of
fuzzy soft sets to investment decision making problem",
International Journal of Mathematical Sciences
and Applications, 1(3), pp. 1583{1586 (2011).
24. Ozgur, N.Y., and Tas, N. \A note on application of
fuzzy soft sets to investment decision making problem",
Journal of New Theory, 7, pp. 1{10 (2015).
25. Irkin, R., Ozgur, N.Y., and Tas, N. \Optimization of
lactic acid bacteria viability using fuzzy soft set modelling",
International Journal of Optimization Control:
Theories & Applications, 8(2), pp. 266{275 (2018).
26. Karaca, F. and Tas, N. \Decision making problem
for life and non-life insurances", Journal of BAUN,
Institute of Science and Technology, 20(1), pp. 572{
588 (2018).
27. Maji, P.K., Biswas, R., and Roy, A.R. \An application
of soft sets in a decision making problem", Computers
and Mathematics with Applications, 44, pp. 1077{1083
(2002).
28. Maji, P.K., Biswas, R., and Roy, A.R. \Soft set theory",
Computers and Mathematics with Applications,
45, pp. 555{562 (2003).
29. Peng, X., Yang, Y., Song, J., and Jiang, Y.
\Pythagorean fuzzy soft set and its application", Computer
Engineering, 41, pp. 224{229 (2015).
30. Peng, X. and Yang, Y. \Algorithms for interval valued
fuzzy soft sets in stochastic multi-criteria decision
making based on regret theory and prospect theory
with combined weight", Applied Soft Computing, 54,
pp. 415{430 (2017).
31. Peng, X. and Garg, H. \Algorithms for interval valued
fuzzy soft sets in emergency decision making based on
WDBA and CODAS with new information measure",
Computers & Industrial Engineering, 119, pp. 439{452
(2018).
32. Peng, X. and Liu, C. \Algorithms for neutrosophic
soft decision making based on EDAS, new similarity
measure and level soft set", Journal of Intelligent and
Fuzzy Systems, 32, pp. 955{968 (2017).
33. Peng, X. and Li, W. \Algorithms for hesitant fuzzy
soft decision making based on revised aggregation
operators, WDBA and CODAS", Journal of Intelligent
and Fuzzy Systems, pre-press, pp. 1{17 (2019).
34. Wei, G. \Picture fuzzy aggregation opertors and their
application to multiple attribute decision making",
Journal of Intelligent and Fuzzy Systems, 33, pp. 713{
724 (2017).
35. Liu, P. and Zhang, X. \A novel picture fuzzy linguistic
aggregation operator and its application to group
decision making", Cognitive Computation, 10(2), pp.
242{259 (2018).
36. Atanassov, K.T. \Geometrical interpretation of the
elements of the intuitionistic fuzzy objects", Preprint
IMMFAIS1{89, So a, 1989. Reprinted: Int. J. Bioautomation,
20(1), pp. S27{S42 (2016).
37. Maji, P.K., Biswas, R., and Roy, A.R. \Fuzzy soft
sets", Journal of Fuzzy Mathematics, 9(3), pp. 589{
602 (2001).
38. Chetia, B. and Das, P.K. \Some results of intuitionistic
fuzzy soft matrix theory", Advances in Applied Science
Research, 3, pp. 412{423 (2012).
39. Naim, C. and Serdar, E. \Soft matrix theory and its
decision making", Computers and Mathematics with
Applications, 59, pp. 3308{3314 (2010).
40. Yong, Y. and Chenli, J. \Fuzzy soft matrices and their
applications", Lecture Notes in Computer Science,
LNAI7002, pp. 618{627 (2011).
41. Tas, N., Ozgur, N.Y., and Demir, P. \An application
of soft set and fuzzy soft set theories to stock
management", Suleyman Demirel University, Journal
of Natural and Applied Sciences, 21(3), pp. 791{796
(2017).
42. Guleria, A. and Bajaj, R.K. \On Pythagorean fuzzy
soft matrices, operations and their applications in decision
making and medical diagnosis", Soft Computing,
23(17), pp. 7889-7900 (2019).
43. Bajaj, R.K. and Guleria, A. \Dimensionality reduction
technique in decision making using pythagorean fuzzy
soft matrices", Recent Patents on Computer Science,
12, pp. 1{8 (2019).
44. Kumar, T. and Bajaj, R.K. \On complex intuitionistic
fuzzy soft sets with distance measures and entropies",
Journal of Mathematics, 2014, Article ID{972198, 12
pages (2014).
45. Thirunavukarasu, P., Suresh, R., and Ashokkumar V.
\Theory of complex fuzzy soft set and its applications",
International Journal for Innovative Research in Science
and Technology, 3(10), pp. 13{18 (2017).