On properties of fuzzy soft locally connected spaces

Abstract

The main aim of this paper is to continue investigate the further properties of fuzzy soft connected spaces defined in [26]. We also initiate and explore the concept of fuzzy soft locally connected spaces. We observe that every fuzzy soft locally connected space need not be fuzzy soft connected space. Moreover, we discuss its properties in general as well as with respect to fuzzy soft components. Examples are also provided to clarify and validate the defined notions. We believe that the findings in this paper will be the inspiration for many researchers and will yield more natural results towards applications in information science, decision making and medical diagnosis problems.

Keywords

• Fuzzy soft sets,Fuzzy soft topology,Fuzzy soft open(closed),Fuzzy soft classes,Fuzzy soft connected,Fuzzy soft locally connected,Fuzzy soft components

References

1. B. Ahmad, A. Kharal: Mappings on fuzzy soft classes, Advances in Fuzzy Systems, (2009), Article ID 407890, 6 Pages.
2. B. Ahmad, S. Hussain: On some structures of soft topology, Mathematical Sciences, 6(64) (2012), 7 Pages.
3. H. Aktas, N. Cagman: Soft sets and soft groups, Information Science, 177 (2007), 2726 2735.
4. C. L. Chang: Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1)(1968), 182190.
5. B. Chen: Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics Information Sciences, 7(1)(2013), 287294.
6. B. Chen: Soft local properties of soft semi-open sets, Discrete Dynamics in Nature and Society, Vol. 2013, Article ID 298032, 6 pages.
7. S. Du, Q. Qin, Q. Wang, and B. Li: Fuzzy description of topological relations I: a unied fuzzy 9-intersection model, Proceedings of the 1st International Conference on Advances in Natural Computation (ICNC 05), vol. 3612 of Lecture Notes in Computer Science, pp. 12611273, Changsha, China, August 2005.
8. F. Feng, Y. M. Li: Soft subsets and soft product operations, Information Sciences, 232(2013), 4457.

9. F. Feng, Y. M. Li, N. Cagman: Generalized uni-int decision making scheme based on choice value soft sets, Europeon Journal of Operaion Research, 220(2012), 162170.
10. F. Feng, M. Akram, B. Davvaz, V. Leoreanu-Fotea: Attribute analysis of information systems based on elementry soft implications, Knowledge Based Systems, 70(2014),281 292.
11. F. Feng, W. Pedrycz: On scalar products and decomposition theorems of fuzzy soft sets, Journal of Multi-valued Logic and Soft Computing, 25(2015), 4580.
12. F. Feng, Y. B. Jun, X. Y. Liu, L. F. Li: An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234(2009), 1020.
13. F. Feng, X. Y. Liu: Soft rough sets with applications to demand analysis, Int. Workshop Intell. Syst. Appl. (ISA 2009), (2009), pp. 14.
14. C. Gundaz, S. Bayramov: Some results on fuzzy soft topological spaces, Mathematical Problems in Engineering, (2013), Article ID 935308, 10 Pages.
15. T. Herawan, M. M. Deris: On multi-soft sets construction in information systems. In: Emerging Intelligent Computing Technology and Applications with Aspects of Articial In- telligence, pp. 101-110. Springer, Berlin (2009).
16. T. Herawan, A. N. M. Rose, M. M. Deris: Soft set theoretic approach for dimensionality reduction. In: Database Theory and Application, pp. 171-178. Springer, Berlin (2009).
17. S. Hussain, B. Ahmad : Some properties of soft topological spaces, Computers and Mathe- matics with Applications, 62(11) (2011) 40584067.
18. S. Hussain, B. Ahmad : Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3) (2015), 559568.
19. S. Hussain: A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1) (2015), 611.
20. S. Hussain: On some soft functions, Mathematical Science Letters, 4(1) (2015), 5561.
21. S. Hussain: Properties of soft semi-open and soft semi-closed sets, Pensee Journal, 76(2)(2014), 133143.
22. S. Hussain: On some generalized structures in fuzzy soft topological spaces, Information Science Letters, 4(3)(2015), 107115.
23. S. Hussain: On some generalized soft mappings, Hacettepe Journal of Mathematics and Statistics, 45(3)(2016), 743754.
24. S. Hussain: On weak and strong forms of fuzzy soft open sets, Fuzzy Information and Engineering, (8)(2016), 451463.
25. S. Hussain: On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings, Hacettepe Journal of Mathematics and Statistics, 46(5)(2017), 851863.
26. S. Karatas, B. Kilic, M. Tellioglu: On fuzzy soft connected topological spaces, Journal of Linear and Topological Algebra, 4(3)(2015), 229240.
27. A. Z. Khameneh, A. Kilicman and A. R. Salleh: Fuzzy soft boundary, Annals of Fuzzy Mathematics and Informatics, 8(5)(2014), 687703.
28. Y. K. Kim, W. K. Min: Full soft sets and full soft decision systems, J. Intell. Fuzzy Syst., 26(2014), 925933.
29. Z. Kong, L. Q. Gao, L. F. Wong: Comment on a fuzzy soft set theoretic approach to decision making problems, J. Comp. Appl. Math., 223 (2009), 540542.
30. Z. Kong, L. Q. Gao, L. F. Wong, S. Li: The normal parameter reduction of soft sets and its algorithm,Comput. Math. Appl., 56 (2008), 30293037.
31. P. K. Maji, R. Biswas, A. R. Roy: Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003), 555562.
32. P. K. Maji, R. Biswas, A. R. Roy: Fuzzy Soft sets, J. Fuzzy Maths., 9(3) (2001), 589602.
33. J. Mahanta, P. K. Das: Results on fuzzy soft topological spaces, Arxiv: 1203.0634v1 [math.GM] 3 Mar. 2012.
34. D. Molodtsov: Soft set theory rst results, Computers and Mathematics with Applications, 37(4-5) (1999), 1931.
35. D. Molodtsov, V. Y. Leonov, D. V. Kovkov: Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 9(1)(2006), 2839.
36. M. Mushrif, S. Sengupta, A. K. Ray: Texture classication using a novel soft set theory based classication algorithm, Springer Berlin, Heidelberg , 254264(2006).
37. G. J. Nazaro: Fuzzy topological polysystems, Journal of Mathematical Analysis and Ap- plications, 41(1973),734742.
38. D. Pie, D. Miao: From soft sets to information systems, X. Hu, Q. Liu, A. Skowron, Y. Y. Lin, R. R. Yager, B. Zhang(Eds.) Proceedings of Granular Computing Vol. 2, IEEE(2005), 2005, 617621.
39. A. R. Roy, P. K. Maji: A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203(2007), 412418.
40. M. Shabir, M. Naz: On soft topological spaces, Computers and Mathematics with Applica- tions, 61(7)(2011), 17861799.
41. B. Tanay and M. B. Kandemir: Topological structure of fuzzy soft sets, Computers and Mathematics with Applications, 61(10)(2011), 29522957.
42. B. P. Varol and H. Aygun: Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41(3)(2012), 407419.
43. Z. Xiao, K. Gong, S. Xia, Y. Zou: Exclusive disjunctive soft sets, Comput. Math. Appl., 59(2009), 21282137.
44. Z. Xiao, K. Gong, Y. Zou: A combined forecasting approach based on fuzzy soft sets. J. Comput. Appl. Math., 228(2009), 326333.
45. X. Yang, T.Y. Lin, J. Yang, Y. Li, D. Yu: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58(2009), 521527.
46. L. A. Zadeh: Fuzzy sets, Information and Control, 8(1996),338353.
47. Y. Zou, Z. Xiao: Data analysis approaches of soft sets under incomplete information Knowl- edge Based Syst., 21(2008), 941945.