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Roughness of filters in lattice implication algebras

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
As a generalization of filters in lattice implication algebras, the notion of rough filters in lattice implication algebras is introduced, and some of their properties are considered.
Rocznik
Strony
341--352
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
autor
  • Department of Applied Mathematics, Southwest Jiaotong University, Chungdu, Sichuan 610031, China
Bibliografia
  • [1] R. Biswas and S. Nanda, Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math. 42 (1994), 251-254.
  • [2] L. Bolc and P. Borowik, Many-Valued Logic, Springer, Berlin, 1994.
  • [3] W. A. Dudek, Y. B. Jun and H. S. Kim, Rough set theory applied to BCI-algebras, Quasigroups Related Systems 9 (2002), 45-54.
  • [4] J. A. Goguen, The logic of inexact concepts, Synthese 19 (1969), 325-373.
  • [5] Y. B. Jun, Implicative filters of lattice implication algebras, Bull. Korean Math. Soc. 34 (1997), 193-198.
  • [6] -, Fantastic filters of lattice implication algebras, Int. J. Math. Math. Sci. 24 (2000), 277-281.
  • [7] -, On n-fold implicative filters of lattice implication algebras, ibid. 26 (2001), 695-699.
  • [8] -, Roughness of ideals in BCK-algebras, Sci. Math. Jpn. 57 (2003), 165-169.
  • [9] Y. B. Jun, Y. Xu and K. Y. Qin, Positive implicative and associative filters of lattice implication algebras, Bull. Korean Math. Soc. 35 (1998), 53-61.
  • [10] S. Y. Kim, E. H. Roh and Y. B. Jun, On ultra filters of lattice implication algebras, Sci. Math. 2 (1999), 201-204.
  • [11] N. Kuroki, Rough ideals in semigroups, Inform. Sci. 100 (1997), 139-163.
  • [12] N. Kuroki and J. N. Mordeson, Structure of rough sets and rough groups, J. Fuzzy Math. 5 (1997), 183-191.
  • [13] C. R. Lim and H. S. Kim, Rough ideals in BCK=BCI-algebras, Bull. Polish Acad. Sci. Math. 51 (2003), 59-67.
  • [14] J. Liu and Y. Xu, On certain filters in lattice implication algebras, Chinese Quart. J. Math. 11 (1996), 106-111.
  • [15] -, Filters and structure of lattice implication algebras, Chinese Sci. Bull. 42 (1997), 1517-1520.
  • [16] V. Novak, First order fuzzy logic, Studia Logica 46 (1982), 87-109.
  • [17] J. Pavelka, On fuzzy logic I; II; III, Z. Math. Logik Grundlag. Math. 25 (1979), 45-52, 119-134, 447-464.
  • [18] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci. 11 (1982), 341-356.
  • [19] -, Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, 1991.
  • [20] F. Wang, Modeling analysis and synthesis of linguistic dynamic systems: a computational theory, in: Proc. IEEE Internat. Workshop on Architecture for Semiotic Modeling and Situation Control in Large Complex Systems, Monterery, CA, 27-30 August 1995, 173-178.
  • [21] -, Outline of a computational theory for linguistic dynamic systems: toward computing with words, Int. J. Intell. Control Systems 2 (1998), 211-224.
  • [22] Y. Xu, Homomorphisms in lattice implication algebras, in: Proc. 5th Many-Valued Logical Congress of China, 1992, 206-211.
  • [23] -, Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20-27.
  • [24] Y. Xu and K. Qin, On filters of lattice implication algebras, J. Fuzzy Math. 1 (1993), 251-260.
  • [25] Y. Xu, D. Ruan, K. Qin and J. Liu, Lattice-Valued Logic, Springer, Berlin, 2003.
  • [26] L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.
  • [27] -, The concept of a linguistic variable and its application to approximate reasoning; I; II; III, Inform. Sci. 8 (1975), 199-249, 8 (1975), 301-357, 9 (1975), 43-80.
  • [28] L. A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Systems 4 (1996), 103-111.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0005-0001
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