Abstract
Topology has enormous applications on fuzzy set. An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article. In this research, first we have classified the fuzzy sets and topological spaces, and then we have made relation between elements of them. For expediency, with mathematical view few basic definitions about crisp set and fuzzy set have been recalled. Then we have discussed about topological spaces. Finally, in the last section, the fuzzy topological spaces which is our main object we have developed the relation between fuzzy sets and topological spaces. Moreover, this article has been concluded with the examination of some of its properties and certain relationships among the closure of these spaces.
Highlights
In the area of set theory, fuzzy mathematics differs from conventional mathematics
An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article
Let ( X, F ) be a fuzzy topological space and P is a sub family of F, P is called a base of F if and only if every member of F can be represent as supremum of member of P
Summary
In the area of set theory, fuzzy mathematics differs from conventional mathematics. Cheng-Ming [7] discussed about the product-induced spaces, which is a special fuzzy topological spaces He showed that each topological fuzzy space is isomorphic topologically by a definite space of topology and introduced the basic idea of double points and set up a type of fuzzy points neighborhood formation for example the Q-neighborhood, which is very significant conception in topological fuzzy set. He discussed the dilemma of metrization in fuzzy on topological fuzzy spaces in addition to obtain a metrization hypothesis in fuzzy. We have showed some related theorem of these topics
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