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Abstrakty
In this paper, we introduce the notion of a rough set in BCK/BCI-algebras. By introducing the notion of a quick ideal in BCK/BCI-algebras, we obtain some relations between quick ideals and upper (Iower) rough quick ideals in B C K/ B C I- algebras.
Słowa kluczowe
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Rocznik
Tom
Strony
59--67
Opis fizyczny
Bibliogr. 17 poz., tab.
Twórcy
autor
- Department of Mathematics, Hanyang University, Seoul 133-791, Korea
autor
- Department of Mathematics, Hanyang University, Seoul 133-791, Korea
Bibliografia
- [1] R. Biswas, S. Nanda, Rough groups and rough subgroups, Bull. Pol. Ac. Math., 42 (1994) 251-254.
- [2] Z. Bonikowaski, Algebraic structures of rough sets, in: Rough sets, fuzzy sets and knowledge discovery, ed.: W. P. Ziarko, Springer-Verlag, Berlin (1995) 242-247.
- [3] J. M. Font, A. J. Rodrígez, A. Torrens, Wajsberg algebras, Stochastica, 8 (1984) 5-31.
- [4] K. Iséki, S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon., 23 (1978) 1-26.
- [5] T. B. Iwiński, Algebraic approach to rough sets, Bull. Pol. Ac. Math., 35 (1987) 673-683.
- [6] N. Kuroki, Fuzzy congruences and fuzzy normal subgroups, Inform. Sci., 60 (1992) 247-259.
- [7] N. Kuroki, Rough ideals in semigroups, Inform. Sci., 100 (1995) 139-163.
- [8] N. Kuroki, J. N. Mordeson, Structure of rough sets and rough groups, J. Fuzzy Math., 5 (1997) 183-191.
- [9] N. Kuroki, P. P. Wang, The lower and upper approximations in a fuzzy group, Inform. Sci., 90 (1996) 203-220.
- [10] J. Meng, Implicative commutative semigroups are equivalent to a class of BCK-algebras, Semigroup Forum, 50 (1995) 89-96.
- [11] J. Meng, Y. B. Jun, BCK-algebras, Kyung Moon Sa, Seoul 1994.
- [12] J. N. Mordeson, Rough set theory applied to (fuzzy) ideal theory, Fuzzy Sets and Systems, 121 (2001) 315-324.
- [13] D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japon., 31 (1986) 889-894.
- [14] Z. Pawlak, Rough sets, Int. J. Inform. Comp. Sci., 11 (1982) 341-356.
- [15] Z. Pawlak, Rough sets and fuzzy sets, Fuzzy Sets and Systems, 17 (1985) 99-102.
- [16] Z. Pawlak, Rough sets-theoretical aspects of reasoning about data, Kluwer Academic, Norwell, MA (1991) 341-356.
- [17] J. Pomykała, J. A. Pomykała, The stone algebra of rough sets, Bull. Pol. Ac. Math., 36 (1988) 495-508.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0001-0047