A construction of a fuzzy topology from a strong fuzzy metric
| Autor: | Svetlana Grecova, Ingrida Uljane, Alexander P. Sostak |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Lowen $\omega$-functor
Fuzzy set fuzzy topology 02 engineering and technology Fuzzy subalgebra lcsh:Analysis Network topology 01 natural sciences Fuzzy logic Combinatorics 0202 electrical engineering electronic engineering information engineering Fuzzifying topology 0101 mathematics Topology (chemistry) Mathematics Discrete mathematics Fuzzy topology lcsh:Mathematics 010102 general mathematics fuzzifying topology lower semicontinuous functions lcsh:QA299.6-433 Fuzzy metric Fuzzy pseudo metric lcsh:QA1-939 Lower semicontinuous functions Fuzzy mathematics Metric (mathematics) fuzzy metric 020201 artificial intelligence & image processing Geometry and Topology |
| Zdroj: | Applied General Topology, Vol 17, Iss 2, Pp 105-116 (2016) RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| ISSN: | 1989-4147 1576-9402 |
| Popis: | After the inception of the concept of a fuzzy metric by I. Kramosil and J. Michalek, and especially after its revision by A. George and G. Veeramani, the attention of many researches was attracted to the topology induced by a fuzzy metric. In most of the works devoted to this subject the resulting topology is an ordinary, that is a crisp one. Recently some researchers showed interest in the fuzzy-type topologies induced by fuzzy metrics. In particular, in the paper (J.J. Mi\~{n}ana, A. \v{S}ostak, {\it Fuzzifying topology induced by a strong fuzzy metric}, Fuzzy Sets and Systems, 6938 DOI information: 10.1016/j.fss.2015.11.005.) a fuzzifying topology ${\mathcal T}:2^X \to [0,1]$ induced by a fuzzy metric $m: X\times X \times [0,\infty)$ was constructed. In this paper we extend this construction to get the fuzzy topology ${\mathcal T}: [0,1]^X \to [0,1]$ and study some properties of this fuzzy topology.54A |
| Databáze: | OpenAIRE |
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