Properties of Fuzzy Length on Fuzzy Set

Abstract

The definition of fuzzy length space on fuzzy set in this research was introduced after the studies and discussion of many properties of this space were proved, and then an example to illustrate this notion was given. Also the definition of fuzzy convergence, fuzzy bounded fuzzy set, and fuzzy dense fuzzy set space was introduced, and then the definition of fuzzy continuous operator was introduced.

Fuzzy Open Mapping and Fuzzy Closed Graph Theorems in Fuzzy Length Space

“…In 2016, Kider and Mousa [12] introduced the definition of fuzzy length space on a fuzzy set and studied many properties of this space. Furthermore, several concepts like fuzzy convergence sequence, fuzzy bounded set, fuzzy dense set, and fuzzy continuous operator are given.…”

“…The essential aim of this paper is to introduce the definition of fuzzy open linear operators and fuzzy closed linear operators to proved main theorems such as fuzzy Baire's theorem, fuzzy open mapping theorem, and fuzzy closed graph theorem in the fuzzy length space given in [12].…”

Fuzzy bicompletable quasi-fuzzy distance space

“…Theorem 2.31: [14] Let (̃, ̃, * ) be a fuzzy distance space on the fuzzy set ̃ if {( , )} is a sequence of fuzzy points in à that is fuzzy converges to  à then {( , )} is fuzzy Cauchy. Proposition 2.32: [14] Suppose that (X,d) is a metric space and let…”

“…Definition 2.33: [14] The mapping h: ̃ →̃ is said to be fuzzy continuous at ̃, if whenever 0 < < 1, we can find 0 < < 1, with ̃̃( h( ),h( )) > (1-) whenever ̃ and ̃Ã ( , ) > (1-). When f is fuzzy continuous at every fuzzy point of ̃, then it is called to be fuzzy continuous on ̃.…”