Topological structures based on interval-valued sets
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In this paper, we define an interval-valued set and an interval-valued (vanishing) point, and study some of their properties. In particular, we get the characterization of inclusions, intersections and unions of interval-valued sets. Also, we deal with some properties of the images and the preimages under a mapping. Moreover, we introduce the concept of interval-valued ideals and some of its properties. Next, we define an interval-valued topology, an interval-valued base [rep. subbase] and an interval-valued neighborhood, and find their various properties. Finally, we define an Interval-valued closure [resp. interior] and obtain some of each properties. Moreover, we show that that there is a unique IVT for interval-valued interior [resp. closure] operators
Abstract
In this paper, we define an interval-valued set and an interval-valued (vanishing) point, and study some of their properties. In particular, we get the characterization of inclusions, intersections and unions of interval-valued sets. Also, we deal with some properties of the images and the preimages under a mapping. Moreover, we introduce the concept of interval-valued ideals and some of its properties. Next, we define an interval-valued topology, an interval-valued base [rep. subbase] and an interval-valued neighborhood, and find their various properties. Finally, we define an Interval-valued closure [resp. interior] and obtain some of each properties. Moreover, we show that that there is a unique IVT for interval-valued interior [resp. closure] operators
참고문헌 (18)
- K. Atanassov, "Intuitionistic fuzzy sets" (1983), Sofia
- C. Bavithra, "Feeble compactness of intuitionistic fell topological space", Ann. Fuzzy Math. Inform, 11(3), pp.485~494 (2016)
- 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)
- D. Coker, "A note on intuitionistic sets and intuitionistic points", Tr. J. of Mathematics, 20, pp.343~351 (1996)
- D. Coker, "An introduction to intuitionistic topological spaces", VUSEFAL, 81, pp.51~56 (2000)
- E. Coskun, "On neighborhood structures in intuitionistic topological spaces", Math. Balkanica (N. S.), 12(3–4), pp.283~909 (1998)
- 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)
- J. C. Kelly, "Bitopological spaces", Proc. London Math. Soc, 13, pp.71~89 (1963)
- 김준희, "The category of intuitionistic sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 14(6), pp.549~562 (2017), 기초자연과학연구소[DOI]
- 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
- T. K. Mondal, "Topology of interval-valued fuzzy sets", Indian J. Pure Appl. Math, 30(1), pp.23~38 (1999)
- S. Selvanayaki, "IGPR-continuity and compactness intuitionistic topological spaces", British Journal of Mathematics and Computer Science, 11(2), pp.1~8 (2015)
- S. Selvanayaki, "Homeomorphism on intuitionistic topological spaces", Ann. Fuzzy Math. Inform, 11(6), pp.957~966 (2016)
- 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, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
- L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)