Cubic crisp sets and their application to topology
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
Cubic crisp sets due to classical sets and cubic sets are an important new set theory keeping in mind the underlying dynamics of cubic sets and crisp sets. However, despite its usage importance, not only for theory but also for application, the usage of combine crisp and cubic sets have been overlooked. This dissertation aims to provide insight into a cubic crisp sets and their applications to topology. Firstly, the new concept cubic crisp set is defined and some of its algebraic structures are obtained. In section 4, a cubic topology is defined. In the remainder of this section, we study some properties of cubic crisp topology, with the eventual aim of describing cubic crisp topology directly using cubic crisp closure (interior). These results that are obtained in this section, therefore describe the very close connection between P-cubic crisp topology, P-cubic crisp countable topology, internal P-cubic crisp topology and external P-cubic crisp topology, we are aiming to classify. Examinations with examples of the cubic crisp topology is stated in Section 5. We then considered cubic crisp neighborhood which takes into account the cubic crisp points that are defined in section 6. Moreover, we lay the foundations for a new study of cubic crisp subspaces in Section 7. Throughout this paper, we wish to build up passion in the systematic study of the cubic crisp sets with respect to defined cubic crisp topologies on it.
Abstract
Cubic crisp sets due to classical sets and cubic sets are an important new set theory keeping in mind the underlying dynamics of cubic sets and crisp sets. However, despite its usage importance, not only for theory but also for application, the usage of combine crisp and cubic sets have been overlooked. This dissertation aims to provide insight into a cubic crisp sets and their applications to topology. Firstly, the new concept cubic crisp set is defined and some of its algebraic structures are obtained. In section 4, a cubic topology is defined. In the remainder of this section, we study some properties of cubic crisp topology, with the eventual aim of describing cubic crisp topology directly using cubic crisp closure (interior). These results that are obtained in this section, therefore describe the very close connection between P-cubic crisp topology, P-cubic crisp countable topology, internal P-cubic crisp topology and external P-cubic crisp topology, we are aiming to classify. Examinations with examples of the cubic crisp topology is stated in Section 5. We then considered cubic crisp neighborhood which takes into account the cubic crisp points that are defined in section 6. Moreover, we lay the foundations for a new study of cubic crisp subspaces in Section 7. Throughout this paper, we wish to build up passion in the systematic study of the cubic crisp sets with respect to defined cubic crisp topologies on it.
참고문헌 (35)
- 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)
- Z. Pawlak, "Rough sets", International Journal of Information and Computer Sciences, 11, pp.341~356 (1982)
- K. Atanassov, "Intuitionistic fuzzy sets", VII ITKR’s Session (1983)
- K. T. Atanassov, "Interval-valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31, pp.343~349 (1989)
- W. L. Gau, "Vague sets", IEEE Trans. Systems Man Cybernet, 23(2), pp.610~614 (1993)
- F. Smarandache, "Neutrosophy, Neutrosophic Probability, and Logic" (1998), American Research Press
- D. Molodtsov, "Soft set theory–First results", Computer Math. Applic, 37, pp.19~31 (1999)
- K. M. Lee, "Bipolar-valued fuzzy sets and their basic operations", Proceedings of the International Conference on Intelligent Technologies, pp.307~312 (2000)
- V. Torra, "Hesitant fuzzy sets", Int. J. Intell. Syst, 25, pp.529~539 (2010)
- Y. B. Jun, "Cubic sets", IAnn. Fuzzy Math. Inform, 4(1), pp.83~98 (2012)
- 이정곤, "Octahedron sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 19(3), pp.211~238 (2020), 기초자연과학연구소[DOI]
- 김준희, "IVI-octahedron sets and their application to groupoids", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 20(2), pp.157~195 (2020), 기초자연과학연구소[DOI]
- D. Coker, "A note on intuitionistic sets and intuitionistic points", Tr. J. of Mathematics, 20, pp.343~351 (1996)
- A. A. Salama, "Some Intuitionistic Topological Notions of Intuitionistic Region, Possible Application to GIS Topological Rules", International Journal of Enhanced Research in Management and Computer Applications, 3(5), pp.4~9 (2014)
- 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, "Intuitionistic hyperspaces", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 15(3), pp.207~226 (2018), 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)
- Dongsik Jo, "Topological structures via interval-valued neutrosophic crisp sets", Symmetry, 12, pp.2050~ (2020)[DOI]
- H. Wang, "Interval-valued neutrosophic sets and logic: Theory and applications in computing" (2005), Hexis
- 채갑병, "Interval-valued intuitionistic sets and their application to topology", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 21(1), pp.1~28 (2021), 기초자연과학연구소[DOI]
- 김준희, "Intuitionistic neutrosophic crisp sets and their application to topology", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 21(2), pp.125~145 (2021), 기초자연과학연구소[DOI]
- Akhtar Zeb, "Cubic topology", International Journal of Computer Science and Information Security(IJCSIS), 14(8), pp.659~669 (2016)
- J. C. Kelly, "Bitopological spaces", Proc. London Math. Soc, 13, pp.71~89 (1963)