Soft Intervals and Soft Ordered Topology

Soft Intervals and Soft Ordered Topology

In this paper, the concept of soft interval is given and an example for soft Scott topology is illustrated by using the soft intervals. A tabular form for all soft closed intervals is presented. Then soft order topology is introduced and some application of it are expressed. Also we show that, the Soft Scott Topology and Soft Order Topology do not have to be same even on the same soft set

___

  • [1] Aktaş, H.; Çağman, N. Soft Sets and Soft Groups, Inform. Sciences. 2007; 177, 2726-2735.
  • [2] Babitha, K.V.; Sunil, J.J. Soft Set Relations and Functions, Comput. Math. Appl. 2010; 60, 1840-1849.
  • [3] Babitha, K.V.; Sunil, J.J. Transitive Closures and Ordering on Soft Sets, Comput. Math. Appl. 2011; 62, 2235-2239.
  • [4] Borah, M.J.; Neog, T.J.; Sut, D.K. Relations on Fuzzy Soft Sets, J. Math. Comput. Sci. 2012; 2(3), 515-534.
  • [5] Çağman, N.; Cıtak, F.; Enginoğlu, S. Fuzzy parametrized fuzzy soft set theory and its applications, Turk. J. Fuzzy Syst. 2010; 1(1), 21-35.
  • [6] Çağman, N.; Karataş, S.; Enginoglu, S. Soft topology, Comput. Math. Appl. 2011; 62, 351-258.
  • [7] Çağman, N.; Enginoğlu, S. Soft matrix theory and its decision making, Comput. Math. Appl. 2010; 59, 3308- 3314.
  • [8] Gierz, G.; Hofmann, K.H.; Keimel, K.; Lawson, J.D.; Mislove, M.; Scott, D.S. Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications 93.
  • [9] Guan, X.; Li, Y.; Feng, F. A new order relation on fuzzy soft sets and its applications, Soft Compt. 2013; 17, 63-70.
  • [10] Hrbacek, K.; Jech, T. Introduction to Set Theory, Marcel Dekker Inc., 1984.
  • [11] Husain, S.; Ahmad, B. Some properties of Soft Topological Spaces, Comput. Math. Appl. 2012; 62, 4058- 4067.
  • [12] Jun, Y.B.; Park, C.H. Applications of Soft Sets in Ideal Theory of BCK/BCI Algebras, Inform. Sciences, 2008; 178, 2466-2475.
  • [13] Jun, Y.B.; Park, C.H. Applications of Soft Sets in Hilbert Algebras, Iran J. Fuzzy Syst. 2009; 6(2), 75-88.
  • [14] Jun, Y.B.; Kim, H.S.; Neggers, J. Pseudo d-algebras, Inform. Sciences, 2009; 179, 1751-1759.
  • [15] Jun, Y.B.; Lee, K.J.; Khan, A. Soft Ordered Semigroups, Math. Log. Quart. 2010; 56(1), 42-50.
  • [16] Maji, P.K.; Biswas, R.; Roy, A.R., Fuzzy Soft sets, Journal Fuzzy Mathematics, 2001; 3, 589-602.
  • [17] Maji, P.K.; Biswas, R.; Roy, A.R. Soft set theory, Comput. Math. Appl. 2003; 45, 555-562.
  • [18] Min, K.W. A Note on Soft Topological Spaces, Comput. Math. Appl. 2011; 62, 3524-3528.
  • [19] Molodtsov, D. Soft Set Theory-First Results, Comput. Math. Appl. 1999; 37, 19-31.
  • [20] Nazmul, S.K.; Samanta, S.K. Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform., 2013; 6, 1- 15.
  • [21] Onyeozili, I.A.; Gwary, T.M. A study the Fundamentals of Soft Set Theory, International of Sciences and Technology Research, 2014; 3(4) 132-143.
  • [22] Park, J.H.; Kim, O.H.; Kwun, Y.C. Some properties of equivalence soft set relations, Comput. Math. Appl. 2012; 63, 1079-1088.
  • [23] Roy, S.; Samanta, T.K. An Introduction of a Soft Topological Spaces Proceeding of UGC sponsored National seminar on Recent trends in Fuzzy set theory, Rough set theory and Soft set theory at Uluberia College on 23rd and 24th September, 2011 ISBN 978-81-922305-5- 9, 9-12, 2011.
  • [24] Sayed, A.F. Continuity of partially ordered soft sets via soft Scott topology and soft sobrification, Bulletin of Mathematical Sciences and Applications, 2014; 3(3), 98- 113.
  • [25] Seselja, B.; Tepavcecic A., A note on a natural equivalence relation on fuzzy power set, Fuzzy Sets and Systems, 2004; 148, 201-210.
  • [26] Sut, D.K. An Application of Fuzzy Soft Relation in Decision Making Problems, International Journal of Mathematics Trends and Technology 2012; 3(2).
  • [27] Shabir, M.; Naz, M. On Soft Topological Spaces, Comput. Math. Appl. 2011; 61, 1786-1799.
  • [28] Tanay, B.; Yaylalı, G. New structures On Partially Ordered Soft Sets and Soft Scott Topology, Ann. Fuzzy Math. Inform., 2014; 7, 89-97.
  • [29] Varol, B.P.; Aygün, H. On soft Hausdorff spaces, Ann. Fuzzy Math. Inform., 2013; 5, 15-24.
  • [30] Yang, H.; Guo, Z. Kernels and Closures of Soft Set Relations, and Soft Set Relation Mappings, Comput. Math. Appl. 2011; 61, 651-662.
  • [31] Zhang, X. On Interval Soft Sets with Applications, International Journal of Computational Intelligence Systems, 2014; 7(1), 186-196.
  • [32] Zorlutuna, İ.; Akdağ, M.; Min, W.K.; Atmaca, S. Remarks on Soft Topological Spaces, Ann. Fuzzy Math. Inform., 2012; 3, 171-185.
Celal Bayar Üniversitesi Fen Bilimleri Dergisi-Cover
  • ISSN: 1305-130X
  • Başlangıç: 2005
  • Yayıncı: Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü
Sayıdaki Diğer Makaleler

B3LYP ve HF Temel Setleri Kullanılarak Bazı 3-Alkil-4-(2-asetoksi-3-metoksibenzilidenamino)-4,5-dihidro-1H-1,2,4-triazol-5-on Bileşiklerinin Deneysel ve Teorik Özelliklerinin İncelenmesi / The Investigation of Experimental and Theoretical Properties of Some 3-Alkyl-4-(2-acetoxy-3-methoxybenzylidenam

Haydar Yüksek, Gül Kotan, Hilal Medetalibeyoğlu, Abdurrahman Gürbüz, Muzaffer Alkan

A numerical approach with residual error estimation for solution of high-order linear differential-difference equations by using Gegenbauer polynomials

Mehmet SEZER, Tuğçe MOLLAOĞLU

Yasemin TAŞYURDU, Zülküf DİLMEN

On the Concept of Limit Inferior and Limit Superior

M Seyyit SEYYİDOĞLU, N Özkan TAN

Preparation of Cerium Oxide Nanoparticles: An Efficient Catalyst to the Synthesis of Dimeric Disulphide Schiff Bases

Sezen SİVRİKAYA, Sefa DURMUS, Aslihan DALMAZ, Mesut OZDİNCER

Sülfonamit İçeren Maleamik Asit Türevi ile 2-Aminopiridinin Proton Transfer Tuzu ve Co(II) ve Cu(II) Komplekslerinin Sentezi, Karakterizasyonu ve Karbonik Anhidraz İzoenzimleri Üzerindeki İnhibisyon Özelliklerinin İncelenmesi

Cengiz YENİKAYA, Halil İLKİMEN, Gözde İMDAT, Metin BÜLBÜL

Serum Alkalen Fosfataz ve Asit Fosfataz Enzimlerinin Aktivileri Üzerine Lizinoprilin In-Vitro Etkisi

Yaşar DEMİR, Nazan DEMİR, Safinur Yıldırım ÇELİK

Toz Metalurjik Cu-Ti Malzemelerin Sinterlenmesi ve Karakterizasyonu

Erdem KARAKULAK

Catechol Derivative RAFT Agent for Surface Functionalization of Magnetic Nanoparticles

Serkan DEMİRCİ

Ali ÖZDEMİR