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Concept lattice on cubic sets

Xueyou Chen
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.02|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제21권 제1호|pp. 29-37|DOI 10.30948/afmi.2021.21.1.29

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참고문헌

키워드

Concept latticeGalios connectionCubic set

초록

In 2012, Jun et al. introduced the notion of a cubic set, which is a generalization of Zadeh's fuzzy set. In 1999, Ganter and Wille put forward formal concept analysis theory(FCA), formal context, concept lattice are two main notions and tools. In the paper, we define formal context, Galois connection, concept lattice on cubic sets, and generalize formal concept analysis theory on cubic sets structure.

Abstract

In 2012, Jun et al. introduced the notion of a cubic set, which is a generalization of Zadeh's fuzzy set. In 1999, Ganter and Wille put forward formal concept analysis theory(FCA), formal context, concept lattice are two main notions and tools. In the paper, we define formal context, Galois connection, concept lattice on cubic sets, and generalize formal concept analysis theory on cubic sets structure.

참고문헌 (27)

  1. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  2. Y. B. Jun, "Cubic sets", Ann. Fuzzy Math. Inform, 4(1), pp.83~98 (2012)
  3. 강정기, "Mappings of cubic sets", 대한수학회논문집, 31(3), pp.423~431 (2016), 대한수학회
  4. 김준희, "Cubic relations", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 19(1), pp.21~43 (2020), 기초자연과학연구소[DOI]
  5. Y. B. Jun, "Closed cubic ideals and cubic 0-subalgebras in BCK", BCI-algebras, 2009, pp.4(65–68), 3395~3402
  6. Y. B. Jun, "Cubic structures applied to ideals of BCI-algebras", Comput. Math. Appl, 62(9), pp.3334~3342 (2011)
  7. Y. B. Jun, "Cubic subgroups", Ann. Fuzzy Math. Inform, 2(1), pp.9~15 (2011)
  8. 전영배, "Cubic ideals in semigroups", 호남수학학술지, 35(4), pp.607~623 (2013), 호남수학회
  9. M. Akram, "Cubic KU-subalgebras", J. Pure. Appl. Math, 89(5), pp.659~665 (2013)
  10. N. Yaqoob, "On cubic KU-ideals on KU-algebras", ISRN algebra, pp.10~ (2013)
  11. 안선신, "CUBIC SUBALGEBRAS AND FILTERS OF CI-ALGEBRAS", 호남수학학술지, 36(1), pp.43~54 (2014), 호남수학회
  12. Y. B. Jun, "Neutrosophic cubic sets", New Mathematics and Natural Computation, pp.1~15 (2015)
  13. T. Senapati, "Cubic subalgebras and cubic closed ideals of B-algebras", Fuzzy Inf. Eng, 7(2), pp.129~149 (2015)
  14. V. Chinnadurai, "Some characterizations on cubic sets", Int. J. Multidisciplinary Research and Modern Education, II, pp.258~264 (2016)
  15. T. Mahmood, "Multicriteria decision making based on cubic set", J. of New theory, 16, pp.1~9 (2017)
  16. Xue-Ling Ma, "Generalized cubic relations in Hv-LA-semigroups", Journal of Discrete Mathematical Sciences and Cryptography, 21(3), pp.607~630 (2018)
  17. Young Jun, "Cubic Interval-Valued Intuitionistic Fuzzy Sets and Their Application in BCK", BCI-Algebras, 2018, pp.7(1), 7~[DOI]
  18. J. G. Lee, "A study on cubic H-relations in a topological universe view-point", Mathematics, 8 (2020)[DOI]
  19. B. Ganter, "Formal concept analysis" (1999), Springer-Verlag
  20. R. B˘elohl´avek, "Foundations and Principles" (2002), Kluwer
  21. Y. Djouadi, "Interval-valued fuzzy formal concept analysis", Lecture Notes in Artificial Intelligence Vol, 5722, pp.592~601 (2009)
  22. A. Brito, "Fuzzy formal concept analysis Communications", Computer and Information Science, 831, pp.192~205 (2018)
  23. Xueyou Chen, "Formal topology, Chu space and approximable concept", Proc. of CLA 2005 (2005)
  24. Xueyou Chen, "Chu space and approximable concept lattice in fuzzy setting", Proceedings of Fuzz-IEEE 2007, IEEE international conference of fuzzy systems, pp.1~6 (2007)
  25. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)
  26. 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)
  27. 허걸, "Interval-Valued Fuzzy Relations", 한국지능시스템학회 논문지, 19(3), pp.425~431 (2009), 한국지능시스템학회

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