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Tolerance Soft Set Relation on a Soft Set and its Matrix Applications

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper the tolerance soft set relation on a soft set is defined and some examples are given with their matrix representations. Also, pre-class and tolerance class concepts for a given tolerance soft set relation are introduced and some examples related to these definitions are illustrated. Some theoretical results are proved such as every pre-class contained by a tolerance class and intersection of two pre-classes is a pre-class as well. Moreover, a method to find out the tolerance classes and pre-classes by using matrix representation of a tolerance soft set relation is explained with examples.
Wydawca
Rocznik
Strony
107--122
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Department of Mathematics, Muğla Sıtkı Koçman, University Muğla, Turkey
autor
  • Department of Mathematics Muğla Sıtkı Koçman University Muğla, Turkey
autor
  • Department of Mathematics Muğla Sıtkı Koçman University Muğla, Turkey
Bibliografia
  • [1] Molodtsov D. Soft Set Theory-First Result. Computers and Mathematics with Applications, 1999;37(4-5):19–31. doi:10.1016/S0898-1221(99)00056-5.
  • [2] Pei D, Miao D. From soft sets to information systems. In Proceedings of the IEEE International Conference on Granular Computing, 2005;2:617–621. doi:10.1109/GRC.2005.1547365.
  • [3] Maji P, Biswas R, Roy A. Soft set theory. Computers and Mathematics with Applications, 2003;45(4-5):555–562. doi:10.1016/S0898-1221(03)00016-6.
  • [4] Aktaş H, Çağman N. Soft sets and soft groups. Information Sciences, 2007;117(13):2726–2735. doi:10.1016/j.ins.2006.12.008.
  • [5] Kharal A, Ahmad B. Mappings on soft classes. New Mathematics and Natural Computations, 2011;7(3): 471–481. doi:10.1142/S1793005711002025.
  • [6] Babitha KV, Sunil JJ. Soft set relations and functions. Computers and Mathematics with Applications, 2010;60(7):1840–1849. doi:10.1016/j.camwa.2010.07.014.
  • [7] Babitha K, Sunil J. Transitive closures and ordering on soft sets. Computers and Mathematics with Applications, 2011;62(5):2235–2239. doi:10.1016/j.camwa.2011.07.010.
  • [8] Park J, Kim O, Kwun Y. Some properties of equivalence soft set relations. Computers and Mathematics with Applications, 2012;63(6):1079–1088. doi:10.1016/j.camwa.2011.12.013.
  • [9] Maji P, Roy A, Biswas R. An application of soft sets in a decision making problem. Computers and Mathematics with Applications, 2002;44(8-9):1077–1083. doi:10.1016/S0898-1221(02)00216-X.
  • [10] Çağman N, Enginoglu S. Soft matrix theory and its decision making. Computers and Mathematics with Applications, 2010;59(10):3308–3314. doi:10.1016/j.camwa.2010.03.015.
  • [11] Ibrahim A, Dauda M, Singh D. Composition of soft set relations and construction of transitive closure. Mathematical Theory and Modeling, 2012;2(7):1–11.
  • [12] Yüksel S, Dizman T, Yıldızdan G, Sert U. Application of soft sets to diagnose the prostate cancer risk. Journal of Inequalities and Applications, 2013; 229.
  • [13] Shreider Y. Tolerance spaces. Journal of Cybernetics, 1971;1(2):115–122. doi:10.1080/01969727108545841.
  • [14] Zeeman E. The topology of the brain and visual perception in Topology of 3-manifolds. Englewood Cliffs, NJ: Prentice-Hall, 1962.
  • [15] Zeeman E, Buneman O. Tolerance spaces and the brain. Mathematics Institute, University of Warwick, 1970.
  • [16] Bartol W, Miro J, Pioro K, Rossello F. On the coverings by tolerance classes. Information Sciences, 2004;166(1-4):193–211. doi:10.1016/j.ins.2003.12.002.
  • [17] Zelinka B. Tolerance relation on semilattices. Comment. Math. Univ. Carol., 1975;16(2):333–338. URL http://eudml.org/doc/16690,
  • [18] Chakraborty M, Ahsanullah T. Fuzzy topology on fuzzy sets and tolerance topology. Fuzzy Sets and Systems, 1992;45(1):103–108. doi:10.1016/0165-0114(92)90096-M.
  • [19] Ming P, Ming L. Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Applications, 1980;76(2):571–599. doi:10.1016/0022-247X(80)90048-7.
  • [20] Das M, Chakraborty M, Ghoshal T. Fuzzy tolerance relation, fuzzy tolerance space and basis. Fuzzy Sets and Systems, 1998;97(3):361–369. doi:10.1016/S0165-0114(97)00253-4.
  • [21] Yang H, Guo Z. Kernels and closures of soft set relations and soft set relation mappings. Computers and Mathematics with Applications, 2011;61(3):651–662. doi:10.1016/j.camwa.2010.12.011.
  • [22] Grimaldi R. Discrete and Combinatorial Mathematics (an Applied Introduction). Pearson Addison Wesley, United States of America, fifth edition edition, 2004. ISBN-13:978-0201726343, 10:0201726343.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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