Interval-valued intuitionistic sets and their application to topology
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In this paper, we introduce the new notion of interval-valued intuitionistic sets providing a tool for approximating undefinable or complex concepts. First, we deal with some of its algebraic structures. Also, we define an interval-valued intuitionistic (vanishing) point and obtain some of its properties. Next, we define an interval-valued intuitionistic topology, base (subbase), neighborhood and interior (closure), respectively and study some of each properties, and give some examples.
Abstract
In this paper, we introduce the new notion of interval-valued intuitionistic sets providing a tool for approximating undefinable or complex concepts. First, we deal with some of its algebraic structures. Also, we define an interval-valued intuitionistic (vanishing) point and obtain some of its properties. Next, we define an interval-valued intuitionistic topology, base (subbase), neighborhood and interior (closure), respectively and study some of each properties, and give some examples.
참고문헌 (19)
- D. Coker, "A note on intuitionistic sets and intuitionistic points", Tr. J. of Mathematics, 20, pp.343~351 (1996)
- K. Atanassov, "Intuitionistic fuzzy sets, VII ITKR’s Session", VII ITKR’s Session (1983)
- E. Coskun, "On neighborhood structures in intuitionistic topological spaces", Math. Balkanica (N. S.), 12(3–4), pp.283~909 (1998)
- D. Coker, "An introduction to intuitionistic topological spaces", BUSEFAL, 81, pp.51~56 (2000)
- Sadik Bayhan, "On separation axioms in intuitionistic topological spaces", IJMMS, 27(10), pp.621~630 (2001)
- Sadik Bayhan, "Pairwise separation axioms in intuitionistic topological spaces", Hacettepe Journal of Mathematics and Statistics, 34(S), pp.101~114 (2005)
- Taha H. Jassim, "Completely normal and weak completely normal in intuitionistic topological spaces", International Journal of Scientific and Engineering Research, 4(10), pp.438~442 (2013)
- S. Selvanayaki, "IGPR-continuity and compactness intuitionistic topological spaces", British Journal of Mathematics and Computer Science, 11(2), pp.1~8 (2015)
- C. Bavithra, "Feeble compactness of intuitionistic fell topological space", Ann. Fuzzy Math. Inform, 11(3), pp.485~494 (2016)
- S. Selvanayaki, "Homeomorphism on intuitionistic topological spaces", Ann. Fuzzy Math. Inform, 11(6), pp.957~966 (2016)
- 김준희, "Intuitionistic topological spaces", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 15(1), pp.29~46 (2018), 기초자연과학연구소[DOI]
- 이석종, "Categorical property of intuitionistic topological spaces", 대한수학회논문집, 24(4), pp.595~603 (2009), 대한수학회
- 김준희, "The category of intuitionistic sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 14(6), pp.549~562 (2017), 기초자연과학연구소[DOI]
- 김준희, "Topological structures based on interval-valued sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(3), pp.273~295 (2020), 기초자연과학연구소[DOI]
- Y. Yao, "Interval sets and interval set algebras", Proc. 8th IEEE Int. Conf. on Cognitive Intormatics (ICCI’09), pp.307~314 (2009)
- L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)
- K. T. Atanassov, "Interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31, pp.343~349 (1989)
- S. K. Samanta, "Topology of interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 119, pp.483~494 (2001)
- J. C. Kelly, "Bitopological spaces", Proc. London Math. Soc, 13, pp.71~89 (1963)
