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On soft topological spaces. (English) Zbl 1219.54016
Summary: We introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T i -spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T 1 -space is also presented.

MSC:
54A40Fuzzy topology
54D10Lower separation axioms (T 0 T 3 , etc.)
References:
[1]Zadeh, L. A.: Fuzzy sets, Inf. control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2]Atanassov, K.: Intuitionistic fuzzy sets, Fuzzy sets and systems 20, 87-96 (1986) · Zbl 0631.03040 · doi:10.1016/S0165-0114(86)80034-3
[3]Atanassov, K.: Operators over interval valued intuitionistic fuzzy sets, Fuzzy sets and systems 64, 159-174 (1994) · Zbl 0844.04001 · doi:10.1016/0165-0114(94)90331-X
[4]Gorzalzany, M. B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems 21, 1-17 (1987) · Zbl 0635.68103 · doi:10.1016/0165-0114(87)90148-5
[5]Pawlak, Z.: Rough sets, Int. J. Comput. sci. 11, 341-356 (1982)
[6]Molodtsov, D.: Soft set theory first results, Comput. math. Appl. 37, 19-31 (1999) · Zbl 0936.03049 · doi:10.1016/S0898-1221(99)00056-5
[7]Maji, P. K.; Biswas, R.; Roy, R.: An application of soft sets in a decision making problem, Comput. math. Appl. 44, 1077-1083 (2002) · Zbl 1044.90042 · doi:10.1016/S0898-1221(02)00216-X
[8]Maji, P. K.; Biswas, R.; Roy, R.: Soft set theory, Comput. math. Appl. 45, 555-562 (2003)
[9]Chen, D.: The parametrization reduction of soft sets and its applications, Computers and math. With appl. 49, 757-763 (2005)
[10]D. Pie, D. Miao, From soft sets to information systems, Granular computing, 2005 IEEE Inter. Conf. 2, 617–621.
[11]Kong, Z.; Gao, L.; Wong, L.; Li, S.: The normal parameter reduction of soft sets and its algorithm, J. comp. Appl. math. 56, 3029-3037 (2008) · Zbl 1165.90699 · doi:10.1016/j.camwa.2008.07.013
[12]Zou, Yan; Xiao, Zhi: Data analysis approaches of soft sets under incomplete information, Knowl.-based syst. 21, 941-945 (2008)
[13]Aktaş, H.; Çağman, N.: Soft sets and soft groups, Inf. sci. 177, 2726-2735 (2007) · Zbl 1119.03050 · doi:10.1016/j.ins.2006.12.008
[14]Jun, Y. B.: Soft BCK/BCI-algebras, Computers and math. With appl. 56, 1408-1413 (2008)
[15]Jun, Y. B.; Park, C. H.: Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. sci. 178, 2466-2475 (2008) · Zbl 1184.06014 · doi:10.1016/j.ins.2008.01.017
[16]Feng, F.; Jun, Y. B.; Zhao, X. Z.: Soft semirings, Computers and math. With appl. 56, 2621-2628 (2008)
[17]Ali, M. I.; Feng, F.; Liu, X. Y.; Min, W. K.; Shabir, M.: On some new operations in soft set theory, Computers and math. With appl. 57, 1547-1553 (2009) · Zbl 1186.03068 · doi:10.1016/j.camwa.2008.11.009
[18]Shabir, M.; Ali, M. Irfan: Soft ideals and generalized fuzzy ideals in semigroups, New math. Nat. comput. 5, 599-615 (2009) · Zbl 1178.20061 · doi:10.1142/S1793005709001544