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Języki publikacji
Abstrakty
In this paper we consider the problem whether for a map φ : A(B) →B there is a relation R on A(B) such that properties of a map φ* : B → B are reflected to R. This is a converse problem that J.Järvinen proved in [5]. We give an affirmative answer to the problem. Moreover we give equational bases which characterize properties of the map &phi:. This means that the classes of some types of algebras form varieties. Hence, there are full correspondence between properties of relations and varieties of modal algebras.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
41--48
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- School of Information Environment, Tokyo Denki University, Inzai, 270-1382, Japan, kondo@sie.dendai.ac.jp
Bibliografia
- [1] S. Burris and H.P. Sankappanavar, A course in universal algebra, (1981) Springer.
- [2] R. Goldblatt, Logics of time and computation (2nd. edition), CSLI Lecture Notes No.7 (1992)
- [3] T.B. Iwinski, Algebraic approach to rough sets, Bull. Pol. Ac. Math., vol.35 (1987), 673-683.
- [4] J. Järvinen, Knowledge representation and rough sets, TUCS Dissertations 14 (Turku Center for Computer Science, Turku, Finland), (1999).
- [5] J. Järvinen, On the structure of rough approximations, Fundamenta Informaticae vol.53 (2002), 135-153.
- [6] J. Järvinen, M. Kondo and J. Kortelainen Modal-like operators in Boolean lattices, Galois connections and fixed points, Fundamenta Informaticae vol.76 (2007), 129-146.
- [7] M. Kondo, On the structure of generalized rough sets, Information Sciences vol.176 (2006), 589-600
- [8] Z. Pawlak, Rough sets, Int. J.Inform. Comp.Sci., vol.11 (1982), 341-356.
- [9] E. Turunen, BL-algebras of basic fuzzy logic, Mathware and Soft Computing, vol.6 (1999), 49-61.
- [10] Y.Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences vol.111 (1998), 239-259.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0005-0058