On fuzzy function spaces.
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This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets using the connection to the exponential law and gives several examples of such structures.Abstract:
In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such structures. As a special case, we study a notion of fuzzy compact open topology.read more
Citations
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A category of l-fuzzy convergence spaces
TL;DR: In this article, a cartesian closed category of stratified L-topological spaces with non-idempotent stratified fuzzy interior operator is defined and a first characterization of fuzzy convergences stem from stratified l-topologies is established.
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Relationships between L-ordered convergence structures and strong L-topologies
TL;DR: By making use of the intrinsic fuzzy inclusion orders on the fuzzy power set, the relationships between L-ordered convergence spaces and strong L-topological spaces are researched, where L is a commutative unital quantale.
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Stratified L-ordered convergence structures
TL;DR: A new kind of lattice-valued convergence structures on a universal set, called stratified L-ordered convergence structures, are presented by modifying the axiom for stratification L-generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set.
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Pointwise convergence, continuous convergence and even continuity in FNS
TL;DR: The notions of pointwise convergence, continuous convergence and even continuity are discussed and shown to be described entirely using ordinary filters for fuzzy convergence spaces using prefilters.
On fuzzy topological groups and fuzzy continuous functions
TL;DR: In this paper, the set of all fuzzy continuous functions fromafuzzytopological space Y into a fuzzytopologicalspace Z is defined, and fuzzy topological group is defined on the (fuzzy) functionspace FC(Y;Z).
References
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Journal ArticleDOI
Fuzzy topological spaces and fuzzy compactness
TL;DR: It will be shown in a following publication that contrary to the results obtained up to now, the Tychonoff-product theorem is safeguarded with fuzzy compactness.
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A new fuzzy compactness defined by fuzzy nets
TL;DR: In this paper a new fuzzy compactness defined by fuzzy nets, called N-compactness, is given and the notion of R-neighborhood is introduced instead of Qneighbourhood to establish the Moore-Smith convergence theory, for it is perhaps more convennient to use.
Journal ArticleDOI
The categorical topology approach to fuzzy topology and fuzzy convergence
E. Lowen,Robert Lowen,P. Wuyts +2 more
TL;DR: In this paper, the authors have studied fuzzy topology from the point of view of categorical topology and constructed a topological quasitopos based on the theory of convergence in FTS.
Journal ArticleDOI
Characterization of convergence in fuzzy topological spaces
TL;DR: In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X) is calculated from the fuzzy closure and convergence is derived from a fuzzyTopology.