The category of intuitionistic sets
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First, we introduce the concept of an intuitionistic set as the generalzation of an ordinary set and the specialization of an intuitionistic fuzzy set and thus neutrosophic crisp set, and list its some properties. Second, we introduce the category $\bf ISet$ consisting of intuitionistic sets and morphisms between them and study the category $\bf ISet$ in the view-point of topological universe. Finally, we find relationships between two categories $\bf ISet$ and $\bf NCSet$. In particular, we prove that Two categories $\bf {ISet}$ and $\bf {^{*}NCSet_{*}}$ are isomorphism.
Abstract
First, we introduce the concept of an intuitionistic set as the generalzation of an ordinary set and the specialization of an intuitionistic fuzzy set and thus neutrosophic crisp set, and list its some properties. Second, we introduce the category $\bf ISet$ consisting of intuitionistic sets and morphisms between them and study the category $\bf ISet$ in the view-point of topological universe. Finally, we find relationships between two categories $\bf ISet$ and $\bf NCSet$. In particular, we prove that Two categories $\bf {ISet}$ and $\bf {^{*}NCSet_{*}}$ are isomorphism.
참고문헌 (30)
- K. Atanassov, "Intuitionistic fuzzy sets, VII ITKR's Session" (1983), Sofia
- K. Atanassov, "Intuitionistic fuzzy sets", Polish Symp. on Interval and Fuzzy Mathematics, pp.23~26 (1983)
- K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
- K. Atanassov, "Review and new results on intuitionistic fuzzy sets", pp.1~8, Sofia
- K. Atanassov, "Intuitionistic Fuzzy Sets" (1999), Springer
- K. Atanassov, "On Intuitionistic Fuzzy Sets Theory" (1999), Springer
- Sadik Bayhan, "Pairwise separation axioms in intuitionistic topological spaces", Hacettepe Journal of Mathematics and Statistics, 34, pp.101~114 (2005)
- J. C. Carrega, "The category Set(H)and Fzz(H)", Fuzzy sets and systems, 9, pp.327~332 (1983)
- D. Coker, "A note on intuiyionistic 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. J. Dubuc, "Concrete quasitopoi Applications of Sheaves", Lect. Notes in Math, 753, pp.239~254 (1979)
- M. Eytan, "Fuzzy sets : a topological point of view", Fuzzy sets and systems, 5, pp.47~67 (1981)
- J. A. Goguen, "Categories of V-sets", Bull. Amer. Math. Soc, 75, pp.622~624 (1969)
- C. Gunduz, "The universal coefficient theorem in the category of intuitionistic fuzzy modules", Utilitas Mathematica, 81, pp.131~156 (2010)
- H. Herrlich, "Catesian closed topological categories", Math. Coll. Univ. Cape Town, 9, pp.1~16 (1974)
- K. Hur, "A Note on the category Set(H)", Honam Math. J, 10, pp.89~94 (1988)
- 허걸, "Intuitionistic H-Fuzzy Sets", 순수 및 응용수학, 12(1), pp.33~45 (2005), 한국수학교육학회
- K.Hur, "The category of neutrosophic crisp sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 14(1), pp.43~54 (2017), 기초자연과학연구소
- C. Y. Kim, "Algebras in Cartesian closed topological categories", Lecture Note Series, 1 (1985)
- 이석종, "Categorical property of intuitionistic topological spaces", 대한수학회논문집, 24(4), pp.595~603 (2009), 대한수학회
- 임평기, "The Category V Set(H)", International Journal of Fuzzy Logic and Intelligent systems, 10(1), pp.73~81 (2010), 한국지능시스템학회
- L. D. Nel, "Topological universes and smooth Gelfand Naimark duality, mathematical applica-tions of category theory", Contemporary Mathematics, 30, pp.224~276 (1984)
- A. M. Pittes, "Fuzzy sets do not form a topos", Fuzzy sets and Systems, 8, pp.338~358 (1982)
- D. Ponasse, "Some remarks on the category Fuz(H)of M. Eytan", Fuzzy sets and Systems, 9, pp.199~204 (1983)
- D. Ponasse, "Categorical studies of fuzzy sets", Fuzzy sets and Systems, 28, pp.235~244 (1988)
- A. A. Salama, "Neutrosophic Crisp Set Theory" (2015), The Educational Publisher Columbus
- A. A. Salama, "Some Intuitionistic Topological No-tions 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)
- F. Smarandache, "Neutrosophy Neutrisophic Property, Sets, and Logic" (1998), Amer Res Press
- W. Yang, "Category of generalized intuitionistic fuzzy sets", Chinese Quarterly Journal of Mathematics, 20(2), pp.192~199 (2005)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)