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Rough set theory applied to fuzzy filters in $BE$-algebras

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The notion of a rough fuzzy filter ina $BE$-algebra is introduced and some properties of such a filter are investigated. The relations between the upper (lower) rough filters and the upper (lower) approximations of their homomorphism images are discussed.

Abstract

The notion of a rough fuzzy filter ina $BE$-algebra is introduced and some properties of such a filter are investigated. The relations between the upper (lower) rough filters and the upper (lower) approximations of their homomorphism images are discussed.

참고문헌 (19)

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  2. S. S. Ahn, "On ideals and upper sets in BE-algebras", Sci. Math. Jpn, 68(2), pp.279~285 (2008)
  3. Sun Shin Ahn, "On generalized upper sets in BE-algebras", 대한수학회보, 46(2), pp.281~287 (2009), 대한수학회
  4. R. Biswas, "Rough groups and rough subgroups", Bull. Pol. Ac. Math, 42(3), pp.251~254 (1994)
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  6. "J. Computational Anal. Appl", 2013, 1456~1466
  7. 강승일, "ROUGH FILTERS OF BE-ALGEBRAS", Journal of Applied Mathematics and Informatics, 30(5), pp.1023~1030 (2012), 한국전산응용수학회
  8. H. S. Kim, "On BE-algebras", Sci. Math. Jpn, 66(1), pp.113~116 (2007)
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  10. N. Kuroki, "Structure of rough sets and rough groups", J. Fuzzy Math, 5(1), pp.183~191 (1997)
  11. N. Kuroki, "The lower and upper approximations in a fuzzy group", Infrom. Sci, 90(1-4), pp.203~220 (1996)
  12. C. R. Lim, "Rough ideals in BCK", BCI-algebras, 2003, pp.51(1), 59~67
  13. B. J. Meng, "On filters in BE-algebras", Sci. Math. Jpn, 71(2), pp.201~207 (2010)
  14. J. N. Mordeson, "Rough set theory applied to (fuzzy) ideals theory", Fuzzy Sets and Sys-tems, 121(2), pp.315~324 (2001)
  15. Z. Pawlak, "Rough sets", Internat. J. Comput. Inform. Sci, 11(5), pp.341~356 (1982)
  16. Z. Pawlak, "Rough sets and fuzzy sets", Fuzzy Sets and Systems, 17(1), pp.99~102 (1985)
  17. Q. M. Xiao, "Rough prime ideals and rough fuzzy prime ideals in semi-groups", Inform. Sci, 176(6), pp.725~733 (2006)
  18. J. Zhan, "The Uncertainties of Ideal Theory on Hemirings" (2015), Science Press
  19. J. Zhan, "A new rough set theory: rough soft hemirings", J. Intell. Fuzzy Systems, 28(4), pp.1687~1697 (2015)

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