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1
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Fuzzy ideals of ordered semigroups with fuzzy orderings

100%
Huang X., Li Q.
Open Mathematics
|
2016
|
tom 14
|
nr 1
841-856
EN
The purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.
2
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A result forO2-convergence to be topological in posets

100%
Li Q., Zou Z.
Open Mathematics
|
2016
|
tom 14
|
nr 1
237-246
EN
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
3
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The characterizations of upper approximation operators based on special coverings

100%
Wang P., Li Q.
Open Mathematics
|
2017
|
tom 15
|
nr 1
193-202
EN
In this paper, we discuss the approximation operators [...] apr¯NS ${\overline {apr} _{NS}}$ and [...] apr¯S ${\overline {apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.
4
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When doL-fuzzy ideals of a ring generate a distributive lattice?

81%
Gao N., Li Q., Li Z.
Open Mathematics
|
2016
|
tom 14
|
nr 1
531-542
EN
The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended ideals of an L-fuzzy ideal, L-fuzzy extended ideals relative to an L-fuzzy subset, L-fuzzy stable ideals relative to an L-fuzzy subset and their connections are studied in this paper.
5
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The fuzzy metric space based on fuzzy measure

81%
Xie J., Li Q., Chen S., Huang H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
603-612
EN
In this paper, we study the relation between a fuzzy measure and a fuzzy metric which is induced by the fuzzy measure. We also discuss some basic properties of the constructed fuzzy metric space. In particular, we show that the nonatom of fuzzy measure space can be characterized in the constructed fuzzy metric space.
6
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A new view of relationship between atomic posets and complete (algebraic) lattices

81%
Yu B., Li Q., Wu H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
238-251
EN
In the context of the atomic poset, we propose several new methods of constructing the complete lattice and the algebraic lattice, and the mutual decision of relationship between atomic posets and complete lattices (algebraic lattices) is studied.
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