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Continuities and separation axioms in interval-valued topological spaces

Kul Hur|G. Senel|S. M. Mostafa|Jeong Gon Lee
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2023.02|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제25권 제1호|pp. 55-89|DOI 10.30948/afmi.2023.25.1.55

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참고문헌

키워드

Interval-valued setInterval-valued topological spaceInterval-valued continuityT$_{0}$ (T$_{1}$T$_{2}$T$_{3}$T$_{4}$)Interval-valued subspace

초록

In this paper, we define an interval-valued continuity and study its several properties. Next, we define separation axioms T$_{0}$, T$_{1}$, T$_{2}$, T$_{3}$, T$_{4}$ of some types in an interval-valued topological space, discuss some relationships among them and give various examples. Finally, we introduce the concept of interval-valued fuzzy subspaces and obtain some of its properties.

Abstract

In this paper, we define an interval-valued continuity and study its several properties. Next, we define separation axioms T$_{0}$, T$_{1}$, T$_{2}$, T$_{3}$, T$_{4}$ of some types in an interval-valued topological space, discuss some relationships among them and give various examples. Finally, we introduce the concept of interval-valued fuzzy subspaces and obtain some of its properties.

참고문헌 (22)

  1. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)
  2. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  3. M. B. Gorzalczany, "A Method of inference in approximate reasoning based on interval-valued fuzzy sets", Fuzzy Sets and Systems, 21, pp.1~17 (1987)
  4. R. Biswas, "Rosenfeld’s fuzzy subgroups with interval-valued membership functions", Fuzzy Sets and Systems, 63, pp.87~90 (1995)
  5. 강희원, "INTERVAL-VALUED FUZZY SUBGROUPS AND RINGS", 호남수학학술지, 32(4), pp.593~617 (2010), 호남수학회
  6. 장수연, "Interval-valued Fuzzy Normal Subgroups", International Journal of Fuzzy Logic and Intelligent systems, 12(3), pp.205~214 (2012), 한국지능시스템학회
  7. T. T. Dutta, "Interval-valued fuzzy prime and semiprime ideals of a hyper semiring", Ann. Fuzzy Math. Inform, 9(2), pp.261~278 (2015)
  8. Y. B. Jun, "Interval-valued fuzzy subalgebras", ideals in BCK-algebras, 2000, pp.3(3), 435~444
  9. X. Ma, "Some kinds of (∈, ∈ ∨q)-interval-valued fuzzy ideals of BCIalogebras", Inform. Sci, 178, pp.3738~3754 (2008)
  10. S. R. Barbhuiya, "(∈, ∈ ∨q)-interval-valued fuzzy prime ideals of BCK-algebras", International Journal of Advances in Mathematics, 2017(5), pp.31~43 (2017)
  11. T. K. Mondal, "Topology of interval-valued fuzzy sets", Indian J. Pure Appl. Math, 30(1), pp.23~38 (1999)
  12. Young Bae Jun, "INTERVAL-VALUED FUZZY SEMIOPEN, PREOPEN AND $\alpha$-OPEN MAPPINGS", 호남수학학술지, 28(2), pp.241~259 (2006), 호남수학회
  13. 민원근, "Interval-Valued Fuzzy Minimal Structures and Interval-Valued Fuzzy Minimal Spaces", International Journal of Fuzzy Logic and Intelligent systems, 8(3), pp.202~206 (2008), 한국지능시스템학회
  14. 최정열, "INTERVAL-VALUED SMOOTH TOPOLOGICAL SPACES", 호남수학학술지, 32(4), pp.711~738 (2010), 호남수학회
  15. Hongmei Ju, "Similarity measures on interval-valued fuzzy sets and application to pattern recognitions", Fuzzy Information and Engineering, Advances in Soft Computing, 40, pp.875~884 (2007)
  16. M. K. Roy, "I-v fuzzy relations and Sanchez’s approach for medical diagnosis", Fuzzy Sets and Systems, 47, pp.35~38 (1992)
  17. Hongmei Ju, "Application of interval-valued fuzzy sets in medical diagnosis", Asian Fuzzy Systems Society International Conference, pp.126~130 (2006)
  18. Y. Yao, "Interval sets and interval set algebras", Proc. 8th IEEE Int. Conf. on Cognitive Intormatics (ICCI’09), pp.307~314 (2009)
  19. 김준희, "Topological structures based on interval-valued sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(3), pp.273~295 (2020), 기초자연과학연구소[DOI]
  20. 정민석, "Interval-valued relations and their application to category theory", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 24(3), pp.281~299 (2022), 기초자연과학연구소[DOI]
  21. Taqdir. Husain, "Topology and Maps" (1977), Plenum Press
  22. J. C. Kelly, "Bitopological spaces", Proc. London Math. Soc, 13, pp.71~89 (1963)

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