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An extension of Lowen's uniformity to the fuzzy soft sets

Year 2018, Volume: 6 Issue: 2, 321 - 331, 15.10.2018

İzzettin Demir , Oya Özbakır

Abstract

In this paper, first we define the notion of a saturated fuzzy soft filter. Based on this, we introduce the notion of a fuzzy soft uniformity as a generalization of uniformity in the sense of Lowen. Also, we show how a fuzzy soft topology is derived from a fuzzy soft uniformity. Then, we give a new kind of fuzzy soft neighborhood system and investigate the relationship with a fuzzy soft uniformity. Finally, we show that a fuzzy soft uniformly continuous mapping  is a fuzzy soft continuous.



Keywords

Fuzzy soft set fuzzy soft topology saturated fuzzy soft filter fuzzy soft uniformity fuzzy soft uniformly continuous mapping

References

  • 1] Ahmad B, Kharal A. On fuzzy soft sets. Adv Fuzzy Syst 2009; Article ID 586507: 6 pages.
  • [2] Artico G, Moresco R. Fuzzy proximities compatible with Lowen uniformities. Fuzzy Sets Syst 1987; 21: 85-98.
  • [3] Ayg¨uno˘glu A, Ayg¨un H. Introduction to fuzzy soft groups. Comput Math Appl 2009; 58: 1279-1286.
  • [4] Bayoumi F. On initial and final fuzzy uniform structures. Fuzzy Sets Syst 2003; 133: 299-319.
  • [5] Bayoumi F. On initial and final fuzzy uniform structures Part II. Fuzzy Sets Syst 2006; 157: 1970-1982.
  • [6] Burton MH. Boundedness in uniform spaces and fuzzy uniform spaces. Fuzzy Sets Syst 1993; 58: 195-207.
  • [7] Burton MH. Completeness in fuzzy uniform spaces. Quaestiones Math 1993; 16: 13-36.
  • [8] Chang CL. Fuzzy topological spaces. J Math Anal Appl 1968; 24(1): 182-190.
  • [9] C¸ etkin V, Ayg¨un H. Uniformity structure in the context of soft set. Ann Fuzzy Math Inform 2013; 6(1): 69-76.
  • [10] C¸ etkin V, Ayg¨un H. Extension of Shi’s quasi-uniformity to the fuzzy soft sets. Math Sci Appl E-Notes, 2013; 1(2): 42-50.
  • [11] C¸ etkin V, Ayg¨un H. On convergence of fuzzy soft filters. 3rd International Eurasian Conference on Mathematical Sciences and Applications; 25-28 August 2014; Vienna, Austria.
  • [12] Demir I˙, O¨ zbakır OB. Some properties of fuzzy soft proximity spaces. Sci World J 2015; Article ID 752634: 10 pages.
  • [13] Demir I˙, O¨ zbakır OB, Yıldız I˙. Fuzzy soft ultrafilters and convergence properties of fuzzy soft filters. J New Results Sci 2015; 8: 92-107.
  • [14] G¨uler AC¸ , Kale G. Regularity and normality on soft ideal topological spaces. Ann Fuzzy Math Inform 2015; 9(3): 373-383.
  • [15] H¨ohle U. Probabilistic uniformization of fuzzy topologies. Fuzzy Sets Syst 1978; 1: 311-332.
  • [16] Hussain S. A note on soft connectedness. J Egypt Math Soc 2015; 23: 6-11.
  • [17] Hutton B. Uniformities on fuzzy topological spaces. J Math Anal Appl 1977; 58: 557-571.
  • [18] Katsaras AK. Linear fuzzy neighborhood spaces. J Fuzzy Sets Syst 1984; 16: 143-154.
  • [19] Kharal A, Ahmad B. Mappings on fuzzy soft classes. Adv Fuzzy Syst 2009; Article ID 407890: 6 pages.
  • [20] Kotze W. Uniform spaces. In: H¨ohle U, Rodabaugh SE, editors. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory; Boston, Dordrecht. London: Kluwer Academic Publishers, 1999, pp. 553-580.
  • [21] Lowen R. Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 1976; 56: 621-633.
  • [22] Lowen R. Fuzzy uniform spaces. J Math Anal Appl 1981; 82: 370-385.
  • [23] Lowen R. Fuzzy neighbourhood spaces. Fuzzy Sets Syst 1982; 7: 165-189.
  • [24] Lowen R, Wuyts P. Completeness, compactness and precompactness in fuzzy uniform spaces: Part 1. J Math Anal Appl 1982; 90(2): 563-581.
  • [25] Lowen R, Wuyts P. Completeness, compactness and precompactness in fuzzy uniform spaces: Part 2. J Math Anal Appl 1983; 92(2): 342-371.
  • [26] Ma X, Sulaiman N, Qin H, Herawan T, Zain JM. A new ecient normal parameter reduction algorithm of soft sets. Comput Math Appl 2011; 62: 588-598.
  • [27] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy Math 2001; 9(3): 589-602.
  • [28] Maji PK, Biswas R, Roy AR. Soft set theory. Comput Math Appl 2003; 45: 555-562.
  • [29] Molodtsov D. Soft set theory-first results. Comput Math Appl 1999; 37: 19-31.
  • [30] Neog TJ, Sut DK, Hazarika GC. Fuzzy soft topological spaces. Int J Latest Trend Math 2012; 2: 54-67.
  • [31] O¨ zbakır OB, Demir I˙. On the soft uniformity and its some properties. J Math Comput Sci 2015; 5: 762-779.
  • [32] Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 2007; 203: 412-418.
  • [33] Shabir M, Naz M. On soft topological spaces. Comput Math Appl 2011; 61: 1786-1799.
  • [34] Shi FG. Pointwise uniformities in fuzzy set theory. Fuzzy Sets Syst 1998; 98: 141-146.
  • [35] Soetens E, Wuyts P. A characterisation of fuzzy uniform spaces by coverings. J Math Anal Appl 1993; 180: 275-302.
  • [36] Tanay B, Kandemir MB. Topological structures of fuzzy soft sets. Comput Math Appl 2011; 61: 412-418.
  • [37] Tukey JW. Convergence and Uniformity in Topology. Ann of Math Stud vol 2, Princeton University Press, 1940.
  • [38] Varol BP, Ayg¨un H. Fuzzy soft topology. Hacet J Math Stat 2012; 41(3): 407-419.
  • [39] Weil A. Sur les Espaces a Structure Uniforme et sur la Topologie Generale. Hermann, Paris, 1937.
  • [40] Yıldırım ED, G¨uler AC¸ , ¨ Ozbakır OB. On softeI-baire spaces. Ann Fuzzy Math Inform 2015; 10(1): 109-121.
  • [41] Zhang D. A comparison of various uniformities in fuzzy topology. Fuzzy Sets Syst 2003; 140: 399-422.

Year 2018, Volume: 6 Issue: 2, 321 - 331, 15.10.2018

İzzettin Demir , Oya Özbakır

Abstract

References

  • 1] Ahmad B, Kharal A. On fuzzy soft sets. Adv Fuzzy Syst 2009; Article ID 586507: 6 pages.
  • [2] Artico G, Moresco R. Fuzzy proximities compatible with Lowen uniformities. Fuzzy Sets Syst 1987; 21: 85-98.
  • [3] Ayg¨uno˘glu A, Ayg¨un H. Introduction to fuzzy soft groups. Comput Math Appl 2009; 58: 1279-1286.
  • [4] Bayoumi F. On initial and final fuzzy uniform structures. Fuzzy Sets Syst 2003; 133: 299-319.
  • [5] Bayoumi F. On initial and final fuzzy uniform structures Part II. Fuzzy Sets Syst 2006; 157: 1970-1982.
  • [6] Burton MH. Boundedness in uniform spaces and fuzzy uniform spaces. Fuzzy Sets Syst 1993; 58: 195-207.
  • [7] Burton MH. Completeness in fuzzy uniform spaces. Quaestiones Math 1993; 16: 13-36.
  • [8] Chang CL. Fuzzy topological spaces. J Math Anal Appl 1968; 24(1): 182-190.
  • [9] C¸ etkin V, Ayg¨un H. Uniformity structure in the context of soft set. Ann Fuzzy Math Inform 2013; 6(1): 69-76.
  • [10] C¸ etkin V, Ayg¨un H. Extension of Shi’s quasi-uniformity to the fuzzy soft sets. Math Sci Appl E-Notes, 2013; 1(2): 42-50.
  • [11] C¸ etkin V, Ayg¨un H. On convergence of fuzzy soft filters. 3rd International Eurasian Conference on Mathematical Sciences and Applications; 25-28 August 2014; Vienna, Austria.
  • [12] Demir I˙, O¨ zbakır OB. Some properties of fuzzy soft proximity spaces. Sci World J 2015; Article ID 752634: 10 pages.
  • [13] Demir I˙, O¨ zbakır OB, Yıldız I˙. Fuzzy soft ultrafilters and convergence properties of fuzzy soft filters. J New Results Sci 2015; 8: 92-107.
  • [14] G¨uler AC¸ , Kale G. Regularity and normality on soft ideal topological spaces. Ann Fuzzy Math Inform 2015; 9(3): 373-383.
  • [15] H¨ohle U. Probabilistic uniformization of fuzzy topologies. Fuzzy Sets Syst 1978; 1: 311-332.
  • [16] Hussain S. A note on soft connectedness. J Egypt Math Soc 2015; 23: 6-11.
  • [17] Hutton B. Uniformities on fuzzy topological spaces. J Math Anal Appl 1977; 58: 557-571.
  • [18] Katsaras AK. Linear fuzzy neighborhood spaces. J Fuzzy Sets Syst 1984; 16: 143-154.
  • [19] Kharal A, Ahmad B. Mappings on fuzzy soft classes. Adv Fuzzy Syst 2009; Article ID 407890: 6 pages.
  • [20] Kotze W. Uniform spaces. In: H¨ohle U, Rodabaugh SE, editors. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory; Boston, Dordrecht. London: Kluwer Academic Publishers, 1999, pp. 553-580.
  • [21] Lowen R. Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 1976; 56: 621-633.
  • [22] Lowen R. Fuzzy uniform spaces. J Math Anal Appl 1981; 82: 370-385.
  • [23] Lowen R. Fuzzy neighbourhood spaces. Fuzzy Sets Syst 1982; 7: 165-189.
  • [24] Lowen R, Wuyts P. Completeness, compactness and precompactness in fuzzy uniform spaces: Part 1. J Math Anal Appl 1982; 90(2): 563-581.
  • [25] Lowen R, Wuyts P. Completeness, compactness and precompactness in fuzzy uniform spaces: Part 2. J Math Anal Appl 1983; 92(2): 342-371.
  • [26] Ma X, Sulaiman N, Qin H, Herawan T, Zain JM. A new ecient normal parameter reduction algorithm of soft sets. Comput Math Appl 2011; 62: 588-598.
  • [27] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy Math 2001; 9(3): 589-602.
  • [28] Maji PK, Biswas R, Roy AR. Soft set theory. Comput Math Appl 2003; 45: 555-562.
  • [29] Molodtsov D. Soft set theory-first results. Comput Math Appl 1999; 37: 19-31.
  • [30] Neog TJ, Sut DK, Hazarika GC. Fuzzy soft topological spaces. Int J Latest Trend Math 2012; 2: 54-67.
  • [31] O¨ zbakır OB, Demir I˙. On the soft uniformity and its some properties. J Math Comput Sci 2015; 5: 762-779.
  • [32] Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 2007; 203: 412-418.
  • [33] Shabir M, Naz M. On soft topological spaces. Comput Math Appl 2011; 61: 1786-1799.
  • [34] Shi FG. Pointwise uniformities in fuzzy set theory. Fuzzy Sets Syst 1998; 98: 141-146.
  • [35] Soetens E, Wuyts P. A characterisation of fuzzy uniform spaces by coverings. J Math Anal Appl 1993; 180: 275-302.
  • [36] Tanay B, Kandemir MB. Topological structures of fuzzy soft sets. Comput Math Appl 2011; 61: 412-418.
  • [37] Tukey JW. Convergence and Uniformity in Topology. Ann of Math Stud vol 2, Princeton University Press, 1940.
  • [38] Varol BP, Ayg¨un H. Fuzzy soft topology. Hacet J Math Stat 2012; 41(3): 407-419.
  • [39] Weil A. Sur les Espaces a Structure Uniforme et sur la Topologie Generale. Hermann, Paris, 1937.
  • [40] Yıldırım ED, G¨uler AC¸ , ¨ Ozbakır OB. On softeI-baire spaces. Ann Fuzzy Math Inform 2015; 10(1): 109-121.
  • [41] Zhang D. A comparison of various uniformities in fuzzy topology. Fuzzy Sets Syst 2003; 140: 399-422.
There are 41 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İzzettin Demir

Oya Özbakır

Publication Date October 15, 2018
Submission Date February 5, 2018
Acceptance Date March 20, 2018
Published in Issue Year 2018 Volume: 6 Issue: 2

Cite

APA Demir, İ., & Özbakır, O. (2018). An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp Journal of Mathematics, 6(2), 321-331.
AMA Demir İ, Özbakır O. An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp J. Math. October 2018;6(2):321-331.
Chicago Demir, İzzettin, and Oya Özbakır. “An Extension of Lowen’s Uniformity to the Fuzzy Soft Sets”. Konuralp Journal of Mathematics 6, no. 2 (October 2018): 321-31.
EndNote Demir İ, Özbakır O (October 1, 2018) An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp Journal of Mathematics 6 2 321–331.
IEEE İ. Demir and O. Özbakır, “An extension of Lowen’s uniformity to the fuzzy soft sets”, Konuralp J. Math., vol. 6, no. 2, pp. 321–331, 2018.
ISNAD Demir, İzzettin - Özbakır, Oya. “An Extension of Lowen’s Uniformity to the Fuzzy Soft Sets”. Konuralp Journal of Mathematics 6/2 (October 2018), 321-331.
JAMA Demir İ, Özbakır O. An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp J. Math. 2018;6:321–331.
MLA Demir, İzzettin and Oya Özbakır. “An Extension of Lowen’s Uniformity to the Fuzzy Soft Sets”. Konuralp Journal of Mathematics, vol. 6, no. 2, 2018, pp. 321-3.
Vancouver Demir İ, Özbakır O. An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp J. Math. 2018;6(2):321-3.
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