Topological structure of vague soft sets. (English) Zbl 1470.54006

Wang, Chang; Li, Yaya

Abstr. Appl. Anal. 2014, Article ID 504021, 8 p. (2014).

Summary: We introduce vague soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of vague soft open sets, vague soft closed sets, vague soft interior, vague soft closure, and vague soft boundary are introduced and their basic properties and relations are investigated. Furthermore, with the help of examples they established that some properties of topological spaces and soft topological spaces do not hold in vague soft topological spaces. Vague soft connectedness and vague soft compactness are also studied.

MSC:

54A40

Fuzzy topology

References:

[1]	Zadeh, L. A., Fuzzy sets, Information and Computation, 8, 3, 338-353 (1965) · Zbl 0139.24606
[2]	Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 1, 87-96 (1986) · Zbl 0631.03040 · doi:10.1016/S0165-0114(86)80034-3
[3]	Gau, W. L.; Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23, 2, 610-614 (1993) · Zbl 0782.04008 · doi:10.1109/21.229476
[4]	Atanassov, K. T., Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 2, 159-174 (1994) · Zbl 0844.04001 · doi:10.1016/0165-0114(94)90331-X
[5]	Molodtsov, D., Soft set theory—first results, Computers & Mathematics with Applications, 37, 4-5, 19-31 (1999) · Zbl 0936.03049 · doi:10.1016/S0898-1221(99)00056-5
[6]	Jun, Y. B.; Park, C. H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences, 178, 11, 2466-2475 (2008) · Zbl 1184.06014 · doi:10.1016/j.ins.2008.01.017
[7]	Majumdar, P.; Samanta, S. K., Generalised fuzzy soft sets, Computers & Mathematics with Applications, 59, 4, 1425-1432 (2010) · Zbl 1189.03057 · doi:10.1016/j.camwa.2009.12.006
[8]	Maji, P. K.; Biswas, R.; Roy, A. R., Fuzzy soft sets, Journal of Fuzzy Mathematics, 9, 3, 589-602 (2001) · Zbl 0995.03040
[9]	Xu, W.; Ma, J.; Wang, S.; Hao, G., Vague soft sets and their properties, Computers & Mathematics with Applications, 59, 2, 787-794 (2010) · Zbl 1189.03063 · doi:10.1016/j.camwa.2009.10.015
[10]	Wang, C.; Qu, A., Entropy, similarity measure and distance measure of vague soft sets and their relations, Information Sciences, 244, 92-106 (2013) · Zbl 1355.68262 · doi:10.1016/j.ins.2013.05.013
[11]	Shabir, M.; Naz, M., On soft topological spaces, Computers & Mathematics with Applications, 61, 7, 1786-1799 (2011) · Zbl 1219.54016 · doi:10.1016/j.camwa.2011.02.006
[12]	Hussain, S.; Ahmad, B., Some properties of soft topological spaces, Computers & Mathematics with Applications, 62, 11, 4058-4067 (2011) · Zbl 1236.54007 · doi:10.1016/j.camwa.2011.09.051
[13]	Tanay, B.; Kandemir, M. B., Topological structure of fuzzy soft sets, Computers & Mathematics with Applications, 61, 10, 2952-2957 (2011) · Zbl 1222.54009 · doi:10.1016/j.camwa.2011.03.056
[14]	Chen, S. M., Similarity measures between vague sets and between elements, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, 27, 1, 153-158 (1997) · doi:10.1109/3477.552198
[15]	Hong, D. H.; Choi, C. H., Multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets and Systems, 114, 1, 103-113 (2000) · Zbl 0963.91031 · doi:10.1016/S0165-0114(98)00271-1
[16]	Ye, J., Using an improved measure function of vague sets for multicriteria fuzzy decision-making, Expert Systems with Applications, 37, 6, 4706-4709 (2010) · doi:10.1016/j.eswa.2009.11.084
[17]	Bustince, H.; Burillo, P., Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, 79, 3, 403-405 (1996) · Zbl 0871.04006 · doi:10.1016/0165-0114(95)00154-9
[18]	Gunduz, C.; Bayramov, S., Intuitionistic fuzzy soft modules, Computers & Mathematics with Applications, 62, 6, 2480-2486 (2011) · Zbl 1235.16040 · doi:10.1016/j.camwa.2011.07.036
[19]	Jiang, Y.; Tang, Y.; Chen, Q.; Liu, H.; Tang, J.-C., Interval-valued intuitionistic fuzzy soft sets and their properties, Computers & Mathematics with Applications, 60, 3, 906-918 (2010) · Zbl 1201.03047 · doi:10.1016/j.camwa.2010.05.036
[20]	Jiang, Y.; Tang, Y.; Chen, Q., An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, 35, 2, 824-836 (2011) · Zbl 1205.91052 · doi:10.1016/j.apm.2010.07.038
[21]	Zhang, Z., A rough set approach to intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, 36, 10, 4605-4633 (2012) · Zbl 1252.91043 · doi:10.1016/j.apm.2011.11.071