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

Yıl 2018, Cilt: 6 Sayı: 2, 321 - 331, 15.10.2018

İzzettin Demir Oya Özbakır

Öz

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.



Anahtar Kelimeler

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

Kaynakça

  • 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.

Yıl 2018, Cilt: 6 Sayı: 2, 321 - 331, 15.10.2018

İzzettin Demir Oya Özbakır

Öz

Kaynakça

  • 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.
Toplam 41 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

İzzettin Demir

Oya Özbakır

Yayımlanma Tarihi 15 Ekim 2018
Gönderilme Tarihi 5 Şubat 2018
Kabul Tarihi 20 Mart 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

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. Ekim 2018;6(2):321-331.
Chicago Demir, İzzettin, ve Oya Özbakır. “An Extension of Lowen’s Uniformity to the Fuzzy Soft Sets”. Konuralp Journal of Mathematics 6, sy. 2 (Ekim 2018): 321-31.
EndNote Demir İ, Özbakır O (01 Ekim 2018) An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp Journal of Mathematics 6 2 321–331.
IEEE İ. Demir ve O. Özbakır, “An extension of Lowen’s uniformity to the fuzzy soft sets”, Konuralp J. Math., c. 6, sy. 2, ss. 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 (Ekim 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 ve Oya Özbakır. “An Extension of Lowen’s Uniformity to the Fuzzy Soft Sets”. Konuralp Journal of Mathematics, c. 6, sy. 2, 2018, ss. 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.
 Kapak Resmi İndir
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