EXTENSION OF SHI'S QUASI-UNIFORMITY TO THE FUZZY SOFT SETS
Abstract
The purpose of this paper is to introduce Shi’s (quasi-)uniformitystructure in the context of fuzzy soft sets. We define the notion of a fuzzysoft (quasi-)uniformity in the sense of Shi. We give the relations between afuzzy soft (quasi-)uniformity and a fuzzy soft cotopology. Also, we investigatethe relations between fuzzy soft remote neighborhood structures which aregenerated by a given fuzzy soft uniformity structure
Keywords
Fuzzy soft set, fuzzy soft cotopology, remote neighborhood, uniformity
References
- Akta¸s, H., C¸ aˇgman, N., Soft sets and soft groups, Information Sciences 177 (13) (2007), 2726-2735.
- Ayg¨unoˇglu, A., C¸ etkin, V., and Ayg¨un, H., An introduction to fuzzy soft topological spaces, Hacettepe Journal of Mathematics and Statistics, to be published.
- C¸ etkin, V., Ayg¨un, H., Hutton uniformity in the context of fuzzy soft sets, submitted.
- Gierz, G., Hofmann, K., Keimel, K., Lawson, J. D., Mislove, M. W., and Scott, D. S., A compendium of continuous lattices, Springer, Berlin, (1980).
- H¨ohle, U., Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Math. 38 (1982), no.3, 289-323.
- Hutton, B., Uniformities on fuzzy topological spaces, J. Math. Anal. and Appl. 58, (1977), 559-571. [7] Jun, Y. B., Lee, K. J., Park, C. H., Soft set theory applied to ideals in d-algebras, Computers and Mathematics with Applications 57 (3) (2009), 367-378.
- Jun, Y. B., Lee, K. J., Zhan, J., Soft p-ideals of soft BCI-algebras, Computers and Mathe- matics with Applications 58 (10) (2009), 2060-2068.
- Kharal, A., Ahmad, B., Mappings on fuzzy soft classes, Advances in Fuzzy Systems, Volume 2009, Article ID 407890.
- Lowen, R., Fuzzy uniform spaces, J. Math. Anal. Appl. 82 (1981), no.2, 370-385.
- Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001), 589-602.