On the determination of fuzzy topological spaces and fuzzy neighbourhood spaces by their level-topologies

Wuyts, P.

doi:10.1016/0165-0114(84)90051-4

Cited by 59 publications

(12 citation statements)

References 5 publications

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“…Remark 2.2. By the discussion in [11], we easily know the converse of Theorem 2.1 is not always correct, since the case of fuzzy topology is not always correct. In the following we will supply a new method to generate I (L)-topological vector spaces by their level L-topologies.…”

Section: Resultsmentioning

confidence: 93%

“…Chen and Li discussed some topological properties of this kind of space in [1] and [6], respectively. Specially, Wang ge-ping [10] obtained a necessary and su cient condition for a chain of L-topological structures on a set X such that there exists an (not unique, in general) I (L)-topological structure of which the level structures are exactly the given chain of L-topological structures, and he gave a simpliÿed proof of main theorem in [11] by using this condition. On the other hand, we introduced the concept of induced I (L)-topological vector spaces and studied some of their properties in [3].…”

Section: Introductionmentioning

confidence: 99%

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I(L)-topological vector spaces and its level topological spaces

Yan

Fang

2005

Fuzzy Sets and Systems

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Section: Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

I(L)-topological vector spaces and its level topological spaces

Yan

Fang

2005

Fuzzy Sets and Systems

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“…(1) Let L = 0 1 ; the topological constructs Top c L have appeared in the literature under different names: the construct FNS of fuzzy neighborhood spaces in Lowen [22,31]; the construct of probabilistic topological spaces in Brock and Kent [3]; the construct of fuzzifying topological spaces in [33,39].…”

Section: The Relationship Between L-fts and Other Constructs In Fuzzymentioning

confidence: 99%

Some Categorical Aspects of Fuzzy Topology

Liu

Zhang

Luo

2000

Journal of Mathematical Analysis and Applications

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Research in recent years has revealed that the construct of fuzzy topological spaces behaves quite differently from that of topological spaces with respect to certain categorical properties. In this paper we discuss some of these aspects. Since the topological construct L-FTS contains nontrivial both initially and finally closed full subconstructs, and each such construct gives rise to a natural autonomous theory of fuzzy topology, it can be said to some extent that fuzzy topology should consist of a system of closely related topology theories, including the classical topology theory as a special case, with each applying to one such subconstruct. Therefore in the first part of this paper the theory of sobriety is established for each finally and initially closed full subconstruct of L-FTS to illustrate this idea. The second topic of this paper is the relationship between the construct of stratified L-fuzzy topological spaces and several other familiar constructs in fuzzy topology, for example, the constructs ofSostak fuzzy topological spaces and L-fuzzifying topological spaces. © 2000 Academic PressKey Words: fuzzy topology; sobriety; frame; topological construct; co-tower extension; total fuzzy topology. PRELIMINARIESAfter a development period of more than 30 years, fuzzy topology has become rather diverse in its topics as well as its methods. The recent book [17] is a comprehensive treatment of the general topology and lattice theoretic aspects of fuzzy topology. In this paper we deal with some categorical properties of the construct of fuzzy topological spaces.

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“…It has been proved that these level decompositions are actually L-topologies on X and the given L-fuzzy topological space can be characterized by them [9,12]. Later in [8], the authors have shed more light on this topic by establishing the lattice structure of these L-topologies.…”

Section: Introductionmentioning

confidence: 99%

On the Level Decompositions by the Range of an L-fuzzy Topological Space

Varghese¹,

Mathew²

2011

Fuzzy Information and Engineering

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This paper is on the level decompositions corresponding to the elements in the range of an L-fuzzy topology on a given set and an investigation into the lattice structure of the same. In general, this lattice is not complete and distributive. However, certain necessary and sufficient conditions for it to be modular, distributive, complete and complemented are derived. Atoms and dual atoms of it along with the conditions for their existence are obtained. Certain related properties of it are also discussed here.

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On the determination of fuzzy topological spaces and fuzzy neighbourhood spaces by their level-topologies

Cited by 59 publications

References 5 publications

I(L)-topological vector spaces and its level topological spaces

I(L)-topological vector spaces and its level topological spaces

Some Categorical Aspects of Fuzzy Topology

On the Level Decompositions by the Range of an L-fuzzy Topological Space

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