Fuzzy $$\varphi $$ -pseudometrics and Fuzzy $$\varphi $$ -pseudometric Spaces

6533b85dfe1ef96bd12be61d

RESEARCH PRODUCT

Fuzzy $$\varphi $$ -pseudometrics and Fuzzy $$\varphi $$ -pseudometric Spaces

subject

Combinatorics Baire category theorem Pseudometric space Function (mathematics)Space (mathematics)Fuzzy logic Axiom Cauchy sequence Mathematics

description

By replacing the axiom $m(x,x,t) = 1$ for all $x\in X, t>0$ in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom $m(x,x,t) = \varphi (t)$ for all $x\in X, t>0$ where $\varphi : {\mathbb R}^+ \rightarrow (0,1]$ is a non-decreasing function, we come to the concept of a fuzzy $\varphi $-pseudometric space. Basic properties of fuzzy $\varphi $-pseudometric spaces and their mappings are studied. We show also an application of fuzzy $\varphi $-pseudometrics in the words combinatorics.

year	journal	country	edition	language
2017-08-31

https://doi.org/10.1007/978-3-319-66827-7_30

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