PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  closure operator
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote Digital Jordan Curves and Surfaces with Respect to a Closure Operator
Šlapal Josef
Fundamenta Informaticae
|
2021
|
Vol. 179, nr 1
59--74
EN
In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.
2
Content available remote Topological Structure of Relation-based Generalized Rough Sets
Zhang Y.-L., Li J., Li C.
Fundamenta Informaticae
|
2016
|
Vol. 147, nr 4
477--491
EN
Rough set theory is an important tool to deal with vagueness and granularity in information systems. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough set approximations is based on equivalence relations and has been extended to relation-based generalized rough set approximations. In this paper, properties of relation-based generalized rough set approximations are examined, and topological properties of relation-based generalized rough set approximations presents. Necessary and sufficient conditions for the relation-based generalized upper (lower) approximation operators to be topological closure (interior) operators are proposed.
3
Content available remote Crisp and Fuzzy Topological Interior and Closure Operators with Inclusion Degree : Theory and Applications
Fashandi H., Peters J.F.
Fundamenta Informaticae
|
2013
|
Vol. 122, nr 3
207--225
EN
This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a means of dealing with imperfections and small errors, especially in cases such as digital images where boundaries of subsets of an image are not crisp. The properties of the new operators are presented. Applications of the proposed operators are given in terms of rough sets and mathematical morphology.
4
Content available remote Concept Lattices of Subcontexts of a Context
Wang X., Zhang W.
Fundamenta Informaticae
|
2009
|
Vol. 90, nr 1-2
157-169
EN
As an effective tool for data analysis and knowledge processing, the theory of concept lattices has been studied extensively and applied to various fields. In order to discover useful knowledge, one often ignores some attributes according to a particular purpose and merely considers the subcontexts of a rather complex context. In this paper, we make a deep investigation on the theory of concept lattices of subcontexts. An approach to construct the concept lattice of a context is first presented by means of the concept lattices of its subcontexts. Then the concept lattices induced by all subcontexts of the context are considered as a set, and an order relation is introduced into the set. It is proved that the set together with the order relation is a complete lattice. Finally, the top element and the bottom element of the complete lattice are also obtained.
5
Content available remote Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points
Järvinen J., Kondo M., Kortelainen J.
Fundamenta Informaticae
|
2007
|
Vol. 76, nr 1-2
129-145
EN
In this work, four modal-like operators on Boolean lattices are introduced and their theory is presented from lattice-theoretical, topological and algebraic point of view. It is also shown how rough set approximation operators, modal operators in temporal logic, and linguistic modifiers determined by L-sets can be interpreted as modal-like operators.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.