Fuzzy Soft Ultrafilters and Convergence Properties of Fuzzy Soft Filters

Year 2015, Volume: 4 Issue: 8, 92 - 107, 29.05.2015

Izzettin Demir Oya Bedre Ozbakir Ismet Yildiz

Abstract

In the present paper, we study the notion of a fuzzysoft filter by using fuzzy soft sets. We present the concepts of a

Keywords

Fuzzy soft set, fuzzy soft filter base and a fuzzy soft ultrafilter and obtain theirrelated properties. Also, we show how a fuzzy soft topology isderived from a fuzzy soft filter. Moreover, we investigate convergence of fuzzy soft filters in a fuzzy soft

References

• B. Ahmad, A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems, 2009, Article ID 586507, 6 pages, 2009.
• H. Akta¸s, N. C¸ a˘gman, Soft sets and soft groups, Inform. Sci., 177, 2726-2735, 2007. [3] S. Atmaca, ˙I. Zorlutuna, On fuzzy soft topological spaces, Ann. Fuzzy Math. In- form., 5(2), 377-386, 2013.
• A. Ayg¨uno˘glu, H. Ayg¨un, Introduction to fuzzy soft groups, Comput. Math. Appl., 58, 1279-1286, 2009.
• M. H. Burton, M. Muraleetharan, J. Gutierrez Garcia, Generalised filters I, Fuzzy Sets and Systems, 106, 275-284, 1999.
• H. Cartan, Filtres et ultrafiltres, C.R. Acad. Sci. Paris, 205, 777-779, 1937.
• C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24(1), 182-190, 1968. [8] V. C¸ etkin, H. Ayg¨un, On Convergence of Fuzzy Soft Filters, 3rd International Eurasian Conference on Mathematical Sciences and Applications, Vienna, Austria, August 25-28, 2014.
• C¸ . G¨und¨uz, S. Bayramov, Some results on fuzzy soft topological spaces, Mathemat- ical Problems in Engineering, 2013, Article ID 835308, 10 pages, 2013.
• A. Kharal, B. Ahmad, Mappings on fuzzy soft classes, Advances in Fuzzy Systems, 2009, Article ID 407890, 6 pages, 2009.
• Y. C. Kim, A. Ramadan, M. A. Usama, (L,M)-neighborhood spaces, Kangweon- Kyungki Math. Jour., 15 (2), 121-133, 2007.
• Z. Kong, L.Q. Gao, L.F. Wang, Comment on a fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 223, 540-542, 2009.
• R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56, 621-633, 1976.
• X. Ma, N. Sulaiman, H. Qin, T. Herawan, J.M. Zain,
• A new efficient normal parameter reduction algorithm of soft sets, Comput. Math. Appl., 62, 588-598, 2011.
• J. Mahanta, P. K. Das, Results on fuzzy soft topological spaces, arXiv:1203.0634v1, 2012.
• P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (3), 589-602, 2001.
• P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl., 45, 555- 562, 2003.
• D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37, 19-31, 1999. [19] T. J. Neog, D. K. Sut, G. C. Hazarika, Fuzzy soft topological spaces, Int. J. Latest Trend Math., 2, 54-67, 2012.
• M. A. de Prada Vicente, M. Saralegui Aranguren, Fuzzy filters, J. Math. Anal. Appl., 129, 560-568, 1988.
• A.R. Roy, P.K. Maji, A fuzzy soft set theoretic approach to decision making prob- lems, J. Comput. Appl. Math., 203, 412-418, 2007.
• M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61, 1786- 1799, 2011.
• R. S¸ahin, A. K¨u¸c¨uk, Soft filters and their convergence properties, Ann. Fuzzy Math. Inform., 6(3), 529-543, 2013.
• B. Tanay, M.B. Kandemir, Topological structures of fuzzy soft sets, Comput. Math. Appl., 61, 412-418, 2011.
• B.P. Varol, H. Ayg¨un, Fuzzy soft topology, Hacet. J. Math. Stat., 41(3), 407-419, 2012.
• B.P. Varol, H. Ayg¨un, Neighborhood structures of fuzzy soft topological spaces, J. Intell. Fuzzy Syst., DOI 10.3233/IFS-141177.