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Topological structures via interval-valued soft sets

이정곤|Young Bae Jun|Kul Hur|G. Senel|Fadhil Abbas
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.10|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제22권 제2호|pp. 133-169|DOI 10.30948/afmi.2021.22.2.133

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참고문헌

키워드

Interval-valued soft topological spaceInterval-valued soft setInterval-valued soft pointInterval-valued soft base and subbaseInterval-valued soft subspaceInterval-valued soft neighborhoodInterval-valued soft closure and interior

초록

Our aim of the research is to study two aspects: First, we define new concept (called an {\it interval-valued soft set}) which combines an interval-valued set with a soft set, and discuss with its algebraic structures and give some examples. Second, we investigate basic topological structures based on interval-valued soft set, for example, subspace, base and subbase, neighborhood, closure and interior, and give some examples.

Abstract

Our aim of the research is to study two aspects: First, we define new concept (called an {\it interval-valued soft set}) which combines an interval-valued set with a soft set, and discuss with its algebraic structures and give some examples. Second, we investigate basic topological structures based on interval-valued soft set, for example, subspace, base and subbase, neighborhood, closure and interior, and give some examples.

참고문헌 (44)

  1. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  2. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)
  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. Z. Pawlak, "Rough sets", International Journal of Information and Computer Sciences, 11, pp.341~356 (1982)
  5. K. Atanassov, "Intuitionistic fuzzy sets", VII ITKR’s Session (1983)
  6. K. Atanassov, "Interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31, pp.343~349 (1989)
  7. W. L. Gau, "Vague sets", IEEE Trans. System Man Cybernet, 23(2), pp.610~614 (1993)
  8. D. Molodtsov, "Soft set theory–First results", Comput. Math. Appl, 37(4-5), pp.19~31 (1999)
  9. P. K. Maji, "Soft set theory", Comput. Math. Appl, 45(4-5), pp.555~562 (2003)
  10. M. I. Ali, "On some new operations in soft set theory", Comput. Math. Appl, 57, pp.1547~1553 (2009)
  11. K. V. Babitha, "Soft set relations and functions", Comput. Math. Appl, 60(7), pp.1840~1849 (2010)
  12. Athar Kharal, "Mappings on soft classes", New Math. Nat. Comput, 7(3), pp.471~481 (2011)
  13. H. Akta¸s, "Soft sets and soft groups", Infor. Sci, 1(77), pp.2726~2735 (2007)
  14. F. Feng, "Soft semirings", Fuzzy Sets and Systems : Theory and Applications, 56(10), pp.2621~2628 (2008)
  15. U. Acar, "Soft sets and soft rings", Comput. Math. Appl, 59, pp.3458~3463 (2010)
  16. Q. M. Sun, "Soft sets and soft modules, Proceedings of Rough Sets and Knowledge Technology", Third International Conference, RSKT 2008, pp.403~409 (2008)
  17. Y. B. Jun, "Soft BCK", BCI-algebras, 2008, pp.56, 1408~1413
  18. Y. B. Jun, "Applications of soft sets in ideal theory in BCK", BCI-algebras, 2008, pp.178, 2466~2475
  19. Y. B. Jun, "Applications of soft sets in Hilbert algebras", Iranian Journal Fuzzy Systems, 6(2), pp.55~86 (2009)
  20. P. Majumdar, "Similarity measure of soft sets", New Mathematics and Natural Computation, 4(1), pp.1~12 (2008)
  21. N. C¸ a˘gman, "Soft set theory and uni-int decision making", European Journal of Operational Research, 207, pp.848~855 (2010)
  22. N. C¸ a˘gman, "Soft matrix theory and its decision making", Comput. Math. Appl, 59, pp.3308~3314 (2010)
  23. M. Shabir, "On soft topological spaces", Comput. Math. Appl, 61, pp.1786~1799 (2011)
  24. N. C¸ a˘gman, "Soft topology", Comput. Math. Appl, 62, pp.351~358 (2011)
  25. W. K. Min, "A note on soft topological spaces", Comput. Math. Appl, 62, pp.3524~3528 (2011)
  26. S. Hussain, "Some properties of soft topological spaces", Comput. Math. Appl, 62(11), pp.4058~4067 (2011)
  27. I. Zorlutuna, "Remarks on soft topological spaces", Ann. Fuzzy Math. Inform, 3(2), pp.171~185 (2012)
  28. A. Aygunoglu, "Some notes on soft topological spaces", Neural. Comput. Appl, 21(1), pp.113~119 (2012)
  29. Sk. Nazmul, "Neighborhood properties of soft topological spaces", Ann. Fuzzy Math. Inform, 6(1), pp.1~15 (2013)
  30. D. N. Georgiou, "Soft set theory and topology", Applied General topology, 14, pp.93~100 (2013)
  31. D. N. Georgiou, "On soft topological spaces", Appl. Math. Inf. Sci, 7(5), pp.1889~1901 (2013)
  32. P. Debnath, "On separation axioms in soft bitopological spaces", Songklanakarin Journal of Science and Technology, 42(4), pp.830~835 (2020)
  33. Sk. Nazmul, "Soft topological soft groups", Math. Sci, 6 (2012), Springer
  34. Sk. Nazmul, "Group soft topology", The Journal of Fuzzy Mathematics, 22(2), pp.435~450 (2014)
  35. Takanori Hida, "Soft topological group", Ann. Fuzzy Math. Inform, 8(6), pp.1001~1025 (2014)
  36. Mohammad K. Tahat, "Soft topological soft groups and soft rings", Soft Computing, 22(21), pp.7143~7156 (2018)
  37. Mohammad K. Tahat, "Soft topological rings", Journal of King Saud University-Science, 31(4), pp.1127~1136 (2019)
  38. Fawzan Sidky, "Soft Topological Soft Modules", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(3), pp.257~272 (2020), 기초자연과학연구소[DOI]
  39. 김준희, "Topological structures based on interval-valued sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(3), pp.273~295 (2020), 기초자연과학연구소[DOI]
  40. Y. Yao, "Interval sets and interval set algebras", Proc. 8th IEEE Int. Conf. on Cognitive Intormatics (ICCI’09), pp.307~314 (2009)
  41. X. Yang, "Combination of interval-valued fuzzy set and soft set", Computers & Mathematics with Applications, 58(3), pp.521~527 (2009)
  42. Mabruka Ali, "Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure", Mathematics, 8(2), pp.178~ (2020), MDPI AG[DOI]
  43. J. C. Kelly, "Bitopological spaces", Proc. London Math. Soc, 13, pp.71~89 (1963)
  44. J. G. Lee, "Continuities and separation axioms in interval-valued topological spaces", Fuzzy Sets and Systems

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