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Tytuł artykułu

Precise Sets in Approximation Spaces and Textures

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Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
In this paper, we propose the notion of precise sets in texture spaces. Precise sets are defined by using textural sections and presections under a direlation. We obtain some properties of definability; it is proved that the family of precise sets under reflexive and transitive direlation is an Alexandroff ditopology. It is observed that sections and presections, which are approximation operators in the textural meaning, are Galois connections. Finally, effective results are given for definability by using textural precise sets.
Wydawca
Rocznik
Strony
353--368
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Hacettepe University, Department of Mathematics and Science Education, 06800 Beytepe, Ankara, Turkey
Bibliografia
  • [1] Uğur AA. Textures and dynamic relational systems, Int. J. Mach. Learn. Cyber., 2016. doi: doi.org/10.1007/s13042-016-0616-x.
  • [2] Brown LM, and Diker M. Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems, 1998;98(2):217-224. URL https://doi.org/10.1016/S0165-0114(97)00358-8.
  • [3] Brown LM, and Diker M. Paracompactness and full normality in ditopological texture spaces, Journal of Mathematical Analysis and Applications, 1998;227(1):144-165. URL https://doi.org/10.1006/jmaa.1998.6090.
  • [4] Brown LM, and Ertürk R. Fuzzy Sets as Texture Spaces, I. Representation Theorems, Fuzzy Sets and Systems, 2000;110(2):227-236. URL https://doi.org/10.1016/S0165-0114(98)00157-2.
  • [5] Brown LM, and Ertürk R. Fuzzy sets as texture spaces, II. Subtextures and quotient textures, Fuzzy Sets and Systems, 2000;110(2):237-245. URL https://doi.org/10.1016/S0165-0114(98)00158-4.
  • [6] Brown LM, Ertürk R, and Dost Ş. Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems, 2004;147(2):171-199. URL https://doi.org/10.1016/j.fss.2004.02.009.
  • [7] Brown LM, Ertürk R, and Dost Ş. Ditopological texture spaces and fuzzy topology, II. Topological Considerations, Fuzzy Sets and Systems, 2004;147(2):201-231. URL https://doi.org/10.1016/j.fss.2004.02.010.
  • [8] Diker M. Textural approach to generalized rough sets based on relations, Information Sciences, 2010;180(8):1418-1433. URL https://doi.org/10.1016/j.ins.2009.11.032.
  • [9] Diker M. Textures and Fuzzy rough sets, Fundamenta Informaticae, 2011;108(3-4):305-336. doi:10.3233/FI-2011-425.
  • [10] Diker M. Definability and textures, Int. Journal Approximate Reasoning, 2012;53(4):558-572. URL https://doi.org/10.1016/j.ijar.2011.12.007.
  • [11] Diker M. Altay Uğur, A. Textures and covering based rough sets, Information Sciences, 2012;184(1):44-33. URL https://doi.org/10.1016/j.ins.2011.08.012.
  • [12] Jarvinen, J. Lattice theory for rough sets, In: Peters J.F., Skowron A., Düntsch I., Grzymała-Busse J., Orłowska E., Polkowski L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. 2007, pp. 400-498. doi: https://doi.org/10.1007/978-3-540-71200-8_22.
  • [13] Jarvinen J, and Kortelainen J. A note on definability in rough set theory, Current Issues in Data and Knowledge Engineering, Akademicka Oficyna Wydawnicza EXIT, Warsaw, 2004 pp. 272-277.
  • [14] Pawlak Z. Rough sets, International Journal of Computer and Information Sciences, 1982;11(5):341-356. doi: https://doi.org/10.1007/BF01001956.
  • [15] Qin K, Yang J, Pei Z. Generalized rough sets based on reflexive and transitive relations, Information Sciences 2008;178(21):4138-4141. URL https://doi.org/10.1016/j.ins.2008.07.002.
  • [16] Tiryaki IU. Fuzzy sets over the poset I, Hacettepe J. Math. Stat., 2008;37(2):143-166.
  • [17] Tiryaki IU. Hyperspaces of ditopological texture spaces and hypertextures, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 2018;67(1):293-309.
  • [18] Yao YY. Two views of theory of rough sets in finite universes, Int. Journal Approximate reasoning, 1996;15(4):291-317. URL https://doi.org/10.1016/S0888-613X(96)00071-0.
  • [19] Yao YY. Constructive and algebraic methods of the theory of rough sets, Information Sciences, 1998;109(1-4):21-47. URL https://doi.org/10.1016/S0020-0255(98)00012-7.
  • [20] Yıldız F, and Brown LM. Real dicompact textures, Topology and its Applications, 2009;156(11):1970-1984. URL https://doi.org/10.1016/j.topol.2009.03.021.
  • [21] Yıldız F, and Brown LM. Categories of dicompact bi-T2 texture spaces and a Banach-Stone theorem, Quaestions Mathematicae 2007;30(2):167-192. URL https://doi.org/10.2989/16073600709486192.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f1bbf108-3e81-426f-b647-3e54f339e603
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