scholarly journals A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies

2019 ◽  
Vol 17 (1) ◽  
pp. 913-928 ◽  
Author(s):  
Lan Wang ◽  
Xiu-Yun Wu ◽  
Zhen-Yu Xiu
Keyword(s):  
Distributive Lattice ◽  
Closure System ◽  
Convex Structure ◽  
Implication Operator ◽  
Closure Systems ◽  
Completely Distributive ◽  
Logical Aspect ◽  
Completely Distributive Lattice

Abstract In this paper, by means of the implication operator → on a completely distributive lattice M, we define the approximate degrees of M-fuzzifying convex structures, M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an M-fuzzifying convex structure, an M-fuzzifying closure system and an M-fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of M-fuzzifying convex structures as well as its relations with M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies by inequalities.

scholarly journals Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiongwei Zhang ◽  
Ibtesam Alshammari ◽  
A. Ghareeb
Keyword(s):  
Distributive Lattice ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Implication Operator ◽  
Completely Distributive ◽  
Countable Compactness ◽  
Definition Of ◽  
Fuzzy Topological Spaces ◽  
Completely Distributive Lattice ◽  
Special Case

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

Metrizability Conditions for Completely Distributive Lattices

1983 ◽  
Vol 26 (4) ◽  
pp. 446-453
Author(s):  
G. Gierz ◽  
J. D. Lawson ◽  
A. R. Stralka
Keyword(s):  
Distributive Lattice ◽  
Essential Extension ◽  
Distributive Lattices ◽  
Interval Topology ◽  
Completely Distributive ◽  
Countable Chain ◽  
Completely Distributive Lattice

AbstractA lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.

scholarly journals Essential completions of distributive lattices

1985 ◽  
Vol 32 (3) ◽  
pp. 361-374 ◽  
Author(s):  
Gerhard Gierz ◽  
Albert R. Stralka
Keyword(s):  
Distributive Lattice ◽  
Salient Feature ◽  
Distributive Lattices ◽  
Compact Topological Space ◽  
Completely Distributive ◽  
Completion Process ◽  
The One ◽  
One Point Compactification ◽  
Essential Completion ◽  
Completely Distributive Lattice

The salient feature of the essential completion process is that for most common distributive lattices it will yield a completely distributive lattice. In this note it is shown that for those distributive lattices which have at least one completely distributive essential extension the essential completion is minimal among the completions by infinitely distributive lattices. Thus in its setting the essential completion of a distributive lattice behaves in much the some way as the one-point compactification of locally compact topological space does in its setting.

Fuzzy generalized convex spaces

2020 ◽  
Vol 39 (3) ◽  
pp. 3907-3919
Author(s):  
Xiu-Yun Wu
Keyword(s):  
Distributive Lattice ◽  
Convex Space ◽  
Completely Distributive ◽  
Generalized Convex Space ◽  
Completely Distributive Lattice ◽  
Convex Spaces

On completely distributive lattice, the notion of fuzzy generalized convex space is introduced. It can be characterized by many means including fuzzy generalized hull space, fuzzy generalized restricted hull space, fuzzy generalized convexly enclosed relation space and fuzzy generalized derived hull space.

Sign in / Sign up

Export Citation Format

Share Document