The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey
نویسندگان
چکیده
منابع مشابه
Some lattices of closure systems on a finite set
In this paper we study two lattices of significant particular closure systems on a finite set, namely the union stable closure systems and the convex geometries. Using the notion of (admissible) quasi-closed set and of (deletable) closed set we determine the covering relation ≺ of these lattices and the changes induced, for instance, on the irreducible elements when one goes from C to C ′ where...
متن کاملFrom torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
متن کاملFuzzy Closure Systems and Fuzzy Closure Operators
We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F (S) and F (C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.
متن کاملn-closure systems and n-closure operators
It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...
متن کاملOn implicational bases of closure systems with unique critical sets
We show that every optimum basis of a finite closure system, in D. Maier’s sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size of the binary part are also established. We introduce the K-basis of a general closure system, which is a refinement of the canonical basis of V. Duquenne and J.L. Guigues, and d...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2003
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00209-3