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.

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 A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

scholarly journals A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Athar Kharal
Keyword(s):  
Open Problem ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Classical Form ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Spaces

Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.

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 Fuzzy Inverse Compactness

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Halis Aygün ◽  
A. Arzu Bural ◽  
S. R. T. Kudri
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Countable Compactness ◽  
Fuzzy Topological Spaces

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

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.

scholarly journals Weakly induced modifications ofI-fuzzy topologies

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Yueli Yue ◽  
Jinming Fang
Keyword(s):  
Full Subcategory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Fuzzy Topological Spaces

The aim of this paper is to study weakly inducedI-fuzzy topological spaces and weakly induced modifications ofI-fuzzy topologies. We give two kinds of weakly inducedI-fuzzy topologies for eachI-fuzzy topology and prove thatI-WIFTOP is a reflective and coreflective full subcategory ofI-FTOP. We also discuss some relationships between several categories.

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