6533b851fe1ef96bd12a8e3d
RESEARCH PRODUCT
A construction of a fuzzy topology from a strong fuzzy metric
Svetlana GrecovaIngrida UljaneAlexander P. Sostaksubject
Lowen $\omega$-functorFuzzy setfuzzy topology02 engineering and technologyFuzzy subalgebralcsh:AnalysisNetwork topology01 natural sciencesFuzzy logicCombinatorics0202 electrical engineering electronic engineering information engineeringFuzzifying topology0101 mathematicsTopology (chemistry)Lowen $\omega$-functor.MathematicsDiscrete mathematicsFuzzy topologylcsh:Mathematics010102 general mathematicsfuzzifying topologylower semicontinuous functionslcsh:QA299.6-433Fuzzy metricFuzzy pseudo metriclcsh:QA1-939Fuzzy topologyLower semicontinuous functionsFuzzy mathematicsMetric (mathematics)fuzzy metric020201 artificial intelligence & image processingGeometry and Topologydescription
<p>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</p>
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-10-03 | Applied General Topology |