Year 2018,
Volume: 47 Issue: 3, 589 - 599, 01.06.2018
Sabir Hussain
References
- B. Ahmad, A. Kharal: Mappings on fuzzy soft classes, Advances in Fuzzy Systems, (2009),
Article ID 407890, 6 Pages.
- B. Ahmad, S. Hussain: On some structures of soft topology, Mathematical Sciences, 6(64)
(2012), 7 Pages.
- H. Aktas, N. Cagman: Soft sets and soft groups, Information Science, 177 (2007), 2726
2735.
- C. L. Chang: Fuzzy topological spaces, Journal of Mathematical Analysis and Applications,
24(1)(1968), 182190.
- B. Chen: Soft semi-open sets and related properties in soft topological spaces, Applied
Mathematics Information Sciences, 7(1)(2013), 287294.
- B. Chen: Soft local properties of soft semi-open sets, Discrete Dynamics in Nature and
Society, Vol. 2013, Article ID 298032, 6 pages.
- 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.
- F. Feng, Y. M. Li: Soft subsets and soft product operations, Information Sciences,
232(2013), 4457.
- 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.
- 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.
- 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.
- 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.
- F. Feng, X. Y. Liu: Soft rough sets with applications to demand analysis, Int. Workshop
Intell. Syst. Appl. (ISA 2009), (2009), pp. 14.
- C. Gundaz, S. Bayramov: Some results on fuzzy soft topological spaces, Mathematical
Problems in Engineering, (2013), Article ID 935308, 10 Pages.
- 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).
- 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).
- S. Hussain, B. Ahmad : Some properties of soft topological spaces, Computers and Mathe-
matics with Applications, 62(11) (2011) 40584067.
- S. Hussain, B. Ahmad : Soft separation axioms in soft topological spaces, Hacettepe Journal
of Mathematics and Statistics, 44(3) (2015), 559568.
- S. Hussain: A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1)
(2015), 611.
- S. Hussain: On some soft functions, Mathematical Science Letters, 4(1) (2015), 5561.
- S. Hussain: Properties of soft semi-open and soft semi-closed sets, Pensee Journal,
76(2)(2014), 133143.
- S. Hussain: On some generalized structures in fuzzy soft topological spaces, Information
Science Letters, 4(3)(2015), 107115.
- S. Hussain: On some generalized soft mappings, Hacettepe Journal of Mathematics and
Statistics, 45(3)(2016), 743754.
- S. Hussain: On weak and strong forms of fuzzy soft open sets, Fuzzy Information and
Engineering, (8)(2016), 451463.
- 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.
- S. Karatas, B. Kilic, M. Tellioglu: On fuzzy soft connected topological spaces, Journal of
Linear and Topological Algebra, 4(3)(2015), 229240.
- A. Z. Khameneh, A. Kilicman and A. R. Salleh: Fuzzy soft boundary, Annals of Fuzzy
Mathematics and Informatics, 8(5)(2014), 687703.
- Y. K. Kim, W. K. Min: Full soft sets and full soft decision systems, J. Intell. Fuzzy Syst.,
26(2014), 925933.
- 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.
- 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.
- P. K. Maji, R. Biswas, A. R. Roy: Soft set theory, Computers and Mathematics with
Applications, 45(4-5) (2003), 555562.
- P. K. Maji, R. Biswas, A. R. Roy: Fuzzy Soft sets, J. Fuzzy Maths., 9(3) (2001), 589602.
- J. Mahanta, P. K. Das: Results on fuzzy soft topological spaces, Arxiv: 1203.0634v1
[math.GM] 3 Mar. 2012.
- D. Molodtsov: Soft set theory rst results, Computers and Mathematics with Applications,
37(4-5) (1999), 1931.
- D. Molodtsov, V. Y. Leonov, D. V. Kovkov: Soft sets technique and its application,
Nechetkie Sistemy i Myagkie Vychisleniya, 9(1)(2006), 2839.
- M. Mushrif, S. Sengupta, A. K. Ray: Texture classication using a novel soft set theory
based classication algorithm, Springer Berlin, Heidelberg , 254264(2006).
- G. J. Nazaro: Fuzzy topological polysystems, Journal of Mathematical Analysis and Ap-
plications, 41(1973),734742.
- 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.
- A. R. Roy, P. K. Maji: A fuzzy soft set theoretic approach to decision making problems, J.
Comput. Appl. Math., 203(2007), 412418.
- M. Shabir, M. Naz: On soft topological spaces, Computers and Mathematics with Applica-
tions, 61(7)(2011), 17861799.
- B. Tanay and M. B. Kandemir: Topological structure of fuzzy soft sets, Computers and
Mathematics with Applications, 61(10)(2011), 29522957.
- B. P. Varol and H. Aygun: Fuzzy soft topology, Hacettepe Journal of Mathematics and
Statistics, 41(3)(2012), 407419.
- Z. Xiao, K. Gong, S. Xia, Y. Zou: Exclusive disjunctive soft sets, Comput. Math. Appl.,
59(2009), 21282137.
- Z. Xiao, K. Gong, Y. Zou: A combined forecasting approach based on fuzzy soft sets. J.
Comput. Appl. Math., 228(2009), 326333.
- 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.
- L. A. Zadeh: Fuzzy sets, Information and Control, 8(1996),338353.
- Y. Zou, Z. Xiao: Data analysis approaches of soft sets under incomplete information Knowl-
edge Based Syst., 21(2008), 941945.
On properties of fuzzy soft locally connected spaces
Year 2018,
Volume: 47 Issue: 3, 589 - 599, 01.06.2018
Sabir Hussain
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.
References
- B. Ahmad, A. Kharal: Mappings on fuzzy soft classes, Advances in Fuzzy Systems, (2009),
Article ID 407890, 6 Pages.
- B. Ahmad, S. Hussain: On some structures of soft topology, Mathematical Sciences, 6(64)
(2012), 7 Pages.
- H. Aktas, N. Cagman: Soft sets and soft groups, Information Science, 177 (2007), 2726
2735.
- C. L. Chang: Fuzzy topological spaces, Journal of Mathematical Analysis and Applications,
24(1)(1968), 182190.
- B. Chen: Soft semi-open sets and related properties in soft topological spaces, Applied
Mathematics Information Sciences, 7(1)(2013), 287294.
- B. Chen: Soft local properties of soft semi-open sets, Discrete Dynamics in Nature and
Society, Vol. 2013, Article ID 298032, 6 pages.
- 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.
- F. Feng, Y. M. Li: Soft subsets and soft product operations, Information Sciences,
232(2013), 4457.
- 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.
- 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.
- 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.
- 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.
- F. Feng, X. Y. Liu: Soft rough sets with applications to demand analysis, Int. Workshop
Intell. Syst. Appl. (ISA 2009), (2009), pp. 14.
- C. Gundaz, S. Bayramov: Some results on fuzzy soft topological spaces, Mathematical
Problems in Engineering, (2013), Article ID 935308, 10 Pages.
- 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).
- 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).
- S. Hussain, B. Ahmad : Some properties of soft topological spaces, Computers and Mathe-
matics with Applications, 62(11) (2011) 40584067.
- S. Hussain, B. Ahmad : Soft separation axioms in soft topological spaces, Hacettepe Journal
of Mathematics and Statistics, 44(3) (2015), 559568.
- S. Hussain: A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1)
(2015), 611.
- S. Hussain: On some soft functions, Mathematical Science Letters, 4(1) (2015), 5561.
- S. Hussain: Properties of soft semi-open and soft semi-closed sets, Pensee Journal,
76(2)(2014), 133143.
- S. Hussain: On some generalized structures in fuzzy soft topological spaces, Information
Science Letters, 4(3)(2015), 107115.
- S. Hussain: On some generalized soft mappings, Hacettepe Journal of Mathematics and
Statistics, 45(3)(2016), 743754.
- S. Hussain: On weak and strong forms of fuzzy soft open sets, Fuzzy Information and
Engineering, (8)(2016), 451463.
- 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.
- S. Karatas, B. Kilic, M. Tellioglu: On fuzzy soft connected topological spaces, Journal of
Linear and Topological Algebra, 4(3)(2015), 229240.
- A. Z. Khameneh, A. Kilicman and A. R. Salleh: Fuzzy soft boundary, Annals of Fuzzy
Mathematics and Informatics, 8(5)(2014), 687703.
- Y. K. Kim, W. K. Min: Full soft sets and full soft decision systems, J. Intell. Fuzzy Syst.,
26(2014), 925933.
- 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.
- 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.
- P. K. Maji, R. Biswas, A. R. Roy: Soft set theory, Computers and Mathematics with
Applications, 45(4-5) (2003), 555562.
- P. K. Maji, R. Biswas, A. R. Roy: Fuzzy Soft sets, J. Fuzzy Maths., 9(3) (2001), 589602.
- J. Mahanta, P. K. Das: Results on fuzzy soft topological spaces, Arxiv: 1203.0634v1
[math.GM] 3 Mar. 2012.
- D. Molodtsov: Soft set theory rst results, Computers and Mathematics with Applications,
37(4-5) (1999), 1931.
- D. Molodtsov, V. Y. Leonov, D. V. Kovkov: Soft sets technique and its application,
Nechetkie Sistemy i Myagkie Vychisleniya, 9(1)(2006), 2839.
- M. Mushrif, S. Sengupta, A. K. Ray: Texture classication using a novel soft set theory
based classication algorithm, Springer Berlin, Heidelberg , 254264(2006).
- G. J. Nazaro: Fuzzy topological polysystems, Journal of Mathematical Analysis and Ap-
plications, 41(1973),734742.
- 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.
- A. R. Roy, P. K. Maji: A fuzzy soft set theoretic approach to decision making problems, J.
Comput. Appl. Math., 203(2007), 412418.
- M. Shabir, M. Naz: On soft topological spaces, Computers and Mathematics with Applica-
tions, 61(7)(2011), 17861799.
- B. Tanay and M. B. Kandemir: Topological structure of fuzzy soft sets, Computers and
Mathematics with Applications, 61(10)(2011), 29522957.
- B. P. Varol and H. Aygun: Fuzzy soft topology, Hacettepe Journal of Mathematics and
Statistics, 41(3)(2012), 407419.
- Z. Xiao, K. Gong, S. Xia, Y. Zou: Exclusive disjunctive soft sets, Comput. Math. Appl.,
59(2009), 21282137.
- Z. Xiao, K. Gong, Y. Zou: A combined forecasting approach based on fuzzy soft sets. J.
Comput. Appl. Math., 228(2009), 326333.
- 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.
- L. A. Zadeh: Fuzzy sets, Information and Control, 8(1996),338353.
- Y. Zou, Z. Xiao: Data analysis approaches of soft sets under incomplete information Knowl-
edge Based Syst., 21(2008), 941945.