Neutrosophic Extension of N-soft Set and Similarity-Based Decision-Making

Abstract

In this paper, the extension of N-soft sets, which is a very important mathematical model in non-binary evaluations to overcome uncertainty, under neutrosophic logic are studied and neutrosophic N-soft sets are introduced and are motivated. This new mathematical model, which deals with neutrosophic logic and N-soft set, which have been studied extensively in recent years to overcome uncertainty, aims to express the uncertainty situations encountered in the best way and thus approach the ideal in decision making. Moreover, some fundamental properties, products and useful operations are given for this new mathematical model. Then, we defined distance measures between two neutrosophic N-soft sets and expressed similarity measures based on decision making problem. Finally, an application is given that illustrates how uncertainty situations can be expressed in a decision-making problem by using the suggested similarity measures.

Keywords

• Neutrosophic N-soft set
• Distance measures
• Similarity measures
• decision making

References

1. [1] Abu Qamar, M., Hassan, N., An approach toward a Q-neutrosophic soft set and its application in decision making, Symmetry, 11(2)(2019), 139.
2. [2] Akram, M., Adeel, A., Alcantud, J.C.R., Fuzzy N-soft sets: a novel model with applications, Journal of Intelligent and Fuzzy Systems, 35(4)(2018), 4757–4771.
3. [3] Akram, M., Adeel, A., Alcantud, J.C.R., Group decision-making methods based on hesitant N-soft sets, Expert Systems with Applications, 115(2019), 95–105.
4. [4] Akram, M., Adeel, A., Alcantud, J.C.R., Hesitant fuzzy N-soft sets: A new model with applications in decision-making, Journal of Intelligent and Fuzzy Systems, 36(6)(2019), 6113–6127.
5. [5] Akram, M., Adeel, A., TOPSIS approach for MAGDM based on interval-valued hesitant fuzzy N-soft environment, International Journal of Fuzzy Systems, 21(3)(2019), 993–1009.
6. [6] Akram, M., Ali, G., Alcantud, J. C. R., New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets, Soft Computing, 23(20)(2019), 9853–9868.
7. [7] Ali, M. I., Feng, F., Liu, X., Min, W.K., Shabir, M., On some new operations in soft set theory, Computers and Mathematics with Applications, 57(2007), 1547–1553.
8. [8] Alkhazaleh, S., Salleh, A.R., Hassan, N., Fuzzy parameterized interval-valued fuzzy soft set, Applied Mathematical Sciences, 5(2011), 3335–3346.

9. [9] Alkhazaleh, S., Salleh, A.R., Soft expert sets, Advances in Decision Sciences, 15(2011), 757868-1.
10. [10] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets Systems, 20(1986), 87–96.
11. [11] Atanassov, K., Gargov, G., Interval valued intuitionistic fuzzy sets, Fuzzy Set Systems, 31(1989), 343–349.
12. [12] Broumi, S., Generalized neutrosophic soft set, International Journal of Computer Science, Engineering and Information Technology, 3(2)(2013), 17–30.
13. [13] Broumi, S., Smarandache, F., Intuitionistic neutrosophic soft set, Journal of Information and Computing Science, 8(2)(2013), 130–140.
14. [14] Broumi, S., Deli, I., Smarandache, F., N-valued interval neutrosophic sets and their application in medical diagnosis, Critical Review, Center for Mathematics of Uncertainty, Creighton University, USA, 10(2015), 46–69.
15. [15] Broumi, S., Deli, I., Correlation measure for neutrosophic refined sets and its application in medical diagnosi, Palestine Journal of Mathematics, 5(1)(2016), 135–143.
16. [16] Chen, D.G., Tsang, E.C.C., Yeung, D.S., Xizhao, W., The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49(2005), 757–763.
17. [17] Çagman, N., Enginoglu, S., Soft set theory and uni-int decision making, European Journal of Operational Research, 207(2010), 848–855.
18. [18] Dalkılıç, O., Demirtas N., Bipolar soft filter, Journal of Universal Mathematics, 3(1)(2020), 21–27.
19. [19] Dalkılıç, O., Demirtaş, N., VFP-soft sets and its application on decision making problems, Journal of Polytechnic, (2021), https://doi.org/10.2339/politeknik.685634.
20. [20] Dalkılıç, O., An application of VFPFSS’s in decision making problems, Journal of Polytechnic, (2021), https://doi.org/10.2339/politeknik.758474.
21. [21] Das, S., Kar, D.S., Group decision making in medical system: an intuitionistic fuzzy soft set approach, Applied Soft Computing, 24(2014), 196–211.
22. [22] Deli, I., Interval-valued neutrosophic soft sets and its decision making, International Journal of Machine Learning and Cybernetics, 8(2)(2017), 665–676.
23. [23] Deli, I., Subas, Y., A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems, International Journal of Machine Learning and Cybernetics, 8(4)(2017), 1309–1322.
24. [24] Demirtaş, N., Dalkılıç, O., An application in the diagnosis of prostate cancer with the help of bipolar soft rough sets, on Mathematics and Mathematics Education (ICMME 2019), KONYA, (2019), 283.
25. [25] Demirtas, N., Hussaın, S., Dalkılıç, O., New approaches of inverse soft rough sets and their applications in a decision making problem, Journal of Applied Mathematics and Informatics, 38(3-4)(2020), 335–349.
26. [26] Demirtaş, N., Dalkılıç, O., Decompositions of soft $\alpha$-continuity and soft A-continuity, Journal of New Theory, 31(2020), 86–94.
27. [27] Fatimah, F., Rosadi, D., Hakim, R.B.F., Alcantud, J.C.R., N-soft sets and their decision-making algoritms, Soft Computing, 22(2018), 3829–3842.
28. [28] Feng, F., Jun, Y.B., Liu, X., Li, L., An adjustable approach to fuzzy soft sets based decision making, Journal of Computational and Applied Mathematics, 234(2010), 10–20.
29. [29] Feng, F., Li, C., Davvaz, B., Irfan Ali, M., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing, 14(2010), 899–911.
30. [30] Grattan-Guiness, I., Fuzzy membership mapped onto interval and many-valued quantities, Z Math Logic Grundlagen Mathematics, 22(1975), 149–160.
31. [31] Jahn, K.U., Intervall-wertige Mengen, Mathematische Nachrichten, 68(1975), 115–132.
32. [32] Jiang, Y., Tang, Y., Chen, Q., An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling, 35(2011), 824–836.
33. [33] Kamal, N.L.A.M., Abdullah, L., Abdullah, I., Alkhazaleh, S., Karaaslan, F., Multivalued interval neutrosophic soft set: formulation and theory, Neutrosophic Sets and Systems, 30(1)(2019), 12.
34. [34] Kong, Z., Gao, L.Q., Wang, L.F., Li, S., The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications, 56(2008), 3029–3037.
35. [35] Maji, P.K., Biswas, R., Roy, A.R., Fuzzy soft set theory, Journal of Fuzzy Mathematics, 9(3)(2001), 589–602.
36. [36] Maji, P.K., Roy, A.R., Biswas, R., An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(2002), 1077–1083.
37. [37] Maji, P.K., Roy, A.R., Biswas, R., Soft set theory, Computers and Mathematics with Applications, 24(2003), 555–562.
38. [38] Maji, P.K., Roy, A.R., Biswas, R., On intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 12(3)(2004), 669–683.
39. [39] Maji, P.K., A neutrosophic soft set approach to a decision making problem, Annals of Fuzzy Mathematics and Informatics, 3(2)(2012), 313–319.
40. [40] Maji, P.K., Neutrosophic soft set, Computers and Mathematics with Applications, 45(2013), 555–562.
41. [41] Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37(1999), 19–31.
42. [42] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11(1982), 341–356.
43. [43] Qin, K., Hong, Z., On soft equality, J. Computers and Mathematics with Applications, 234(5)(2010), 1347–1355.
44. [44] Riaz, M., C¸ agman, N., Zareef, I., Aslam, M., N-soft topology and its applications to multi-criteria group decision making,Journal of Intelligent and Fuzzy Systems, 36(6)(2019), 6521–6536.
45. [45] Saha, A., Broumi, S., Parameter reduction of neutrosophic soft sets and their applications, Neutrosophic Sets and Systems, 32(1)(2020), 1.
46. [46] Sambuc, R., Fonctions ’-floues: Application l’aide au diagnostic en pathologie thyroidienne. Ph. D. Thesis Univ. Marseille, France, (1975).
47. [47] Smarandache, F., A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, 1999.
48. [48] Smarandache, F., Neutrosophy a new branch of philosophy, Multi. Val. Logic-Special Issue: Neutrosophy and Neutrosophic Logic, 8(2002), 297–384.
49. [49] Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Indian Journal of Pure and Applied Mathematics, 24(2005), 287–297.
50. [50] Uluçay, V., Sahin, M., Hassan, N., Generalized neutrosophic soft expert set for multiple-criteria decision-making, Symmetry, 10(10)(2018), 437.
51. [51] Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R., Single valued neutrosophic sets, Multispace Multistruct, 4(2010), 410–413.
52. [52] Zadeh, L.A., Fuzzy sets, Information and Control, 8(1965), 338–353.
53. [53] Zadeh, L., The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8(1975), 199–249.