Open AccessCharacterized Fuzzy R2.5 and Characterized Fuzzy T3.5 Spaces
Author(s) -
A. S. Abd-Allah
Publication year - 2017
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v13i1.5684
Subject(s) - mathematics , fuzzy subalgebra , fuzzy classification , fuzzy number , defuzzification , fuzzy logic , fuzzy mathematics , fuzzy set operations , discrete mathematics , fuzzy measure theory , type 2 fuzzy sets and systems , membership function , fuzzy set , algebra over a field , pure mathematics , artificial intelligence , computer science
This paper, deals with, introduce and study the notions of haracterized fuzzy R2.5 spaces and of characterized fuzzy T3.5 spaces by using the notion of fuzzy function family presented in [21] and the notion of φ1,2ψ1,2-fuzzy continuous mappings presented in [5] as a generalization of all the weaker and stronger forms of the fuzzy completely regular spaces introduced in [11,24,26,29]. We denote by characterized fuzzy T3.5 space or characterized fuzzy Tychonoff space to the characterized fuzzy space which is characterized fuzzy T1 and characterized fuzzy R2.5 space in this sense. The relations between the characterized fuzzy T3.5 spaces, the characterized fuzzy T4 spaces and the characterized fuzzy T3 spaces are introduced. When the given fuzzy topological space is normal, then the related characterized fuzzy space is finer than the associated characterized fuzzy proximity space which is presented in [1]. Moreover, the associated characterized fuzzy proximity spaces and the characterized fuzzy T4 spaces are identical with help of the complementarilysymmetric fuzzy topogenous structure, that is, identified with the fuzzy proximity δ. More generally, the fuzzy function family of all φ1,2ψ1,2-fuzzy continuous mappings are applied to show that the characterized fuzzy R2.5 spaces and the associated characterized fuzzy proximity spaces are identical.