8,753 research outputs found
A Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them
A new class of functions called strongly lower semi-continuous (SLSC) functions is defined and its properties are studied. It is shown that the arbitrary supremum and finite infimum of SLSC functions are again SLSC. Using these functions, an induced fuzzy topological space, called s-induced fuzzy topological space on a topological space (X, T), is introduced. Moreover, some incorrect results on fuzzy topological spaces obtained previously by some authors are identified and modified accordingly. Examples of the newly defined induced space are given and their various properties are investigated. Interrelationships between a fuzzy topological space (X, F) and the s-induced fuzzy topological space generated by the crisp members of F are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied
Maximal element theorems in product FC-spaces and generalized games
AbstractLet I be a finite or infinite index set, X be a topological space and (Yi,{φNi})i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let Ai:X→2Yi be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature
On topological structures of fuzzy parametrized soft sets
In this paper, we introduce the topological structure of fuzzy parametrized
soft sets and fuzzy parametrized soft mappings. We define the notion of
quasi-coincidence for fuzzy parametrized soft sets and investigated basic
properties of it. We study the closure, interior, base, continuity and
compactness and properties of these concepts in fuzzy parametrized soft
topological space
On the Intuitionistic fuzzy topological (metric and normed) spaces
In this paper, we define precompact set in intuitionistic fuzzy metric spaces
and prove that any subset of an intuitionistic fuzzy metric space is compact if
and only if it is precompact and complete. Also we define topologically
complete intuitionistic fuzzy metrizable spaces and prove that any set in a complete intuitionistic fuzzy metric spaces is a topologically
complete intuitionistic fuzzy metrizable space and vice versa. Finally, we
define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear
operators and so we prove that every finite dimensional intuitionistic fuzzy
normed space is complete.Comment: 16 page
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