0000000000587382

AUTHOR

Alexander ŠOstak

showing 4 related works from this author

Gradation of Fuzzy Preconcept Lattices

2021

Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.

Theoretical computer scienceLogicComputer scienceMathematics::General Mathematicsfuzzy context; fuzzy preconcept; fuzzy preconcept lattice; fuzzy concept; fuzzy concept lattice; graded fuzzy preconcept lattice0206 medical engineeringfuzzy preconceptContext (language use)02 engineering and technologyFuzzy logic0202 electrical engineering electronic engineering information engineeringFuzzy conceptMathematical Physicsfuzzy preconcept latticeAlgebra and Number TheorySeries (mathematics)lcsh:Mathematicsfuzzy contextfuzzy conceptfuzzy concept latticelcsh:QA1-939graded fuzzy preconcept latticeComputer Science::Programming Languages020201 artificial intelligence & image processingGradationGeometry and Topology020602 bioinformaticsAnalysisAxioms; Volume 10; Issue 1; Pages: 41
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Pointwise k-Pseudo Metric Space

2021

In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map d:J(LX)×J(LX)⟶[0,∞) satisfying some conditions. What is more, it is proved that the category of pointwise k-pseudo metric spaces is isomorphic to the category of symmetric pointwise k-remote neighborhood ball spaces. Besides, some L-topological structures induced by a pointwise k-quasi-pseudo metric are obtained, including an L-quasi neighborhood system, an L-topology, an L-closure operator, an L-interior operator, and a pointwise quasi-uniformity.

PointwisePure mathematicsGeneral Mathematicspointwise <i>k</i>-(quasi) pseudo metricComputer Science::Digital Libraries<i>L</i>-quasi neighborhood systemMetric spaceOperator (computer programming)Metric (mathematics)Computer Science (miscellaneous)QA1-939<i>L</i>-topologyBall (mathematics)pointwise <i>k</i>-remote neighborhood ball systempointwise <i>k</i>-(quasi) pseudo metric; pointwise <i>k</i>-remote neighborhood ball system; <i>L</i>-quasi neighborhood system; <i>L</i>-topologyEngineering (miscellaneous)MathematicsMathematicsMathematics
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George-Veeramani Fuzzy Metrics Revised

2018

In this note, we present an alternative approach to the concept of a fuzzy metric, calling it a revised fuzzy metric. In contrast to the traditional approach to the theory of fuzzy metric spaces which is based on the use of a t-norm, we proceed from a t-conorm in the definition of a revised fuzzy metric. Here, we restrict our study to the case of fuzzy metrics as they are defined by George-Veeramani, however, similar revision can be done also for some other approaches to the concept of a fuzzy metric.

0209 industrial biotechnologyLogicComputer scienceMathematics::General Mathematicst-norm02 engineering and technologyFuzzy logic<i>t</i>-norm020901 industrial engineering & automationGEORGE (programming language)0202 electrical engineering electronic engineering information engineeringt-conormMathematical PhysicsAlgebra and Number Theorybusiness.industrylcsh:MathematicsContrast (statistics)T-normlcsh:QA1-939Fuzzy metric spaceComputingMethodologies_PATTERNRECOGNITIONrestrictMetric (mathematics)<i>t</i>-conormfuzzy metric020201 artificial intelligence & image processingGeometry and TopologyArtificial intelligenceComputingMethodologies_GENERALbusinessAnalysisAxioms
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On t-Conorm Based Fuzzy (Pseudo)metrics

2020

We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fu…

Theoretical computer scienceLogicComputer scienceMathematics::General MathematicsCB-fuzzy (pseudo)metric02 engineering and technology01 natural sciencesFuzzy logic0202 electrical engineering electronic engineering information engineeringCB-fuzzy (pseudo)metric; archimedian t-(co)norms; hamacher t-(co)norm; modular; modular metric; intuinionistic fuzzy metricsmodular0101 mathematicsMathematical PhysicsAlgebra and Number Theoryintuinionistic fuzzy metricslcsh:Mathematicslcsh:QA1-939010101 applied mathematicsNorm (mathematics)hamacher t-(co)normmodular metric020201 artificial intelligence & image processingGeometry and TopologyComputingMethodologies_GENERALarchimedian t-(co)normsAnalysisAxioms
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