본문 바로가기
KERD
논문KCI 등재

Topological structures in complete co-residuated lattices

3

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet(meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

Abstract

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet(meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

참고문헌 (29)

  1. R. Bělohlávek, "Bělohlávek : Fuzzy Relational Systems" (2002), Kluwer Academic Publishers
  2. P. Chen, "Alexandroffco-topological spaces", Fuzzy Sets and Systems, 161, pp.2505~2514 (2010)
  3. P. Hájek, "Metamathematices of Fuzzy Logic" (1998), Kluwer Academic Publishers
  4. U. Höhle, "Non-classical logic and their applications to fuzzy subsets" (1995), Kluwer Academic Publishers
  5. U. Höhle, "The Handbooks of Fuzzy Sets Series" (1999), Kluwer Academic Publishers
  6. F. Jinming, "I-fuzzy Alexandrov topologies and specialization orders", Fuzzy Sets and Systems, 158, pp.2359~2374 (2007)
  7. Q. Junsheng, "On(⊙, &)-fuzzy rough sets based on residuated and co-residuated lattices", Fuzzy Sets and Systems, 336, pp.54~86 (2018)
  8. Y. C. Kim, "Join-meet preserving maps and Alexandrov fuzzy topologies", Journal of Intelligent and Fuzzy Systems, 28, pp.457~467 (2015)
  9. "Join-meet preserving maps and fuzzy preorders", Journal of Intelligent and Fuzzy Systems, 28, pp.1089~1097 (2015)
  10. "Categories of fuzzy preorders, approximation operators and Alexandrov topologies", Journal of Intelligent and Fuzzy Systems, 31, pp.1787~1793 (2016)
  11. 고정미, "Preserving Maps and Approximation Operators in Complete Co-Residuated Lattices", 한국지능시스템학회 논문지, 30(5), pp.331~340 (2020), 한국지능시스템학회[DOI]
  12. "Fuzzy complete lattices, Alexandrov L-fuzzy topologies and fuzzy rough sets", Journal of Intelligent and Fuzzy Systems, 38, pp.3253~3266 (2020)
  13. H. Lai, "Fuzzy preorder and fuzzy topology", Fuzzy Sets and Systems, 157, pp.1865~1885 (2006)
  14. Z.M. Ma, "Topological and lattice structures of L-fuzzy rough set determined by lower and upper sets", Information Sciences, 218, pp.194~204 (2013)
  15. J.S. Mi, "Generalized fuzzy rough sets determined by a trianglar norm", Information Sciences, 178, pp.3203~3213 (2008)
  16. J.M. Oh, "Distance functions, upper approximation operators and Alexandrov fuzzy topologies", Journal of Intelligent and Fuzzy Systems, 40(6), pp.11927~11939 (2021)
  17. "Fuzzy Galois connections on L-toplogies", Journal of Intelligent and Fuzzy Systems, 40, pp.251~270 (2021)
  18. "Various fuzzy connections and fuzzy concepts in complete co-residuated lattices", International Journal of Approximate Reasoning, 142, pp.451~468 (2022)
  19. Z. Pawlak, "Rough sets", Internat. J. Comput. Inform. Sci, 11, pp.341~356 (1982)
  20. Z. Pawlak, "Rough sets: Theoretical Aspects of Reasoning about Data, System Theory. Knowledge Engineering and Problem Solving" (1991), Kluwer Academic Publishers
  21. A.M. Radzikowska, "A comparative study of fuzy rough sets", Fuzzy Sets and Systems, 126, pp.137~155 (2012)
  22. A.M. Radzikowska, "Characterisation of main classes of fuzzy relations using fuzzy modal operators", Fuzzy Sets and Systems, 152, pp.223~247 (2005)
  23. S.E. Rodabaugh, "The Handbook of Recent Developments in the Mathematics of Fuzzy Sets" (2003), Kluwer Academic Publishers
  24. Y.H. She, "An axiomatic approach of fuzzy rough sets based on residuated lattices", Computers and Mathematics with Applications, 58, pp.189~201 (2009)
  25. S. P. Tiwari, "Fuzzy rough sets, fuzzy preorders and fuzzy topologies", Fuzzy Sets and Systems, 210, pp.63~68 (2013)
  26. E. Turunen, "Mathematics Behind Fuzzy Logic" (1999), A Springer-Verlag Co
  27. M. Ward, "Residuated lattices", Trans. Amer. Math. Soc, 45, pp.335~354 (1939)
  28. W.Z. Wu, "On charterizations of(Φ, T)-fuzzy approximation operators", Fuzzy Sets and Systems, 154, pp.76~102 (2005)
  29. M.C. Zheng, "Coresiduated lattice with applications", Fuzzy systems and Mathematics, 19, pp.1~6 (2005)

관련 논문AI추천

이 간행물의 다른 논문 (9건)