Search results for "T-norm"

showing 10 items of 30 documents

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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Weakly algebraizable logics

2000

AbstractIn the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

AlgebraPhilosophyClass (set theory)HierarchyLogicLeibniz operatorMonotonic functionT-norm fuzzy logicsMathematicsJournal of Symbolic Logic
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Fixed points in weak non-Archimedean fuzzy metric spaces

2011

Mihet [Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy $\psi$-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.

Common fixed points Weak non-Archimedean fuzzy metric spaces Fuzzy contractive mappingsDiscrete mathematicsFuzzy classificationMathematics::General MathematicsLogicInjective metric spaceT-normFuzzy subalgebraIntrinsic metricConvex metric spaceComputingMethodologies_PATTERNRECOGNITIONSettore MAT/05 - Analisi MatematicaArtificial IntelligenceFuzzy set operationsFuzzy numberComputingMethodologies_GENERALMathematicsFuzzy Sets and Systems
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From fuzzy metric spaces to modular metric spaces: a fixed point approach

2017

We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.

Discrete mathematics021103 operations researchAlgebra and Number TheoryInjective metric space0211 other engineering and technologiesT-norm02 engineering and technologyEquivalence of metrics01 natural sciencesIntrinsic metricConvex metric space010101 applied mathematicsMetric spaceFixed point fuzzy metric space modular metric spaceSettore MAT/05 - Analisi MatematicaMetric (mathematics)Metric mapSettore MAT/03 - Geometria0101 mathematicsAnalysisMathematicsThe Journal of Nonlinear Sciences and Applications
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Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dyn…

2013

In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.

Discrete mathematicsAlgebra and Number TheoryWeakly compatible mappingApplied MathematicsFixed-point theoremNon-Archimedean Menger PM-spaceT-normt-normFixed pointType (model theory)Fixed pointCommon property (E.A)Dynamic programmingComputational MathematicsMenger's theoremSettore MAT/05 - Analisi MatematicaCommon propertyPairwise comparisonGeometry and TopologyProperty (E.A)AnalysisMathematics
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A note on best approximation in 0-complete partial metric spaces

2014

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Discrete mathematicsArticle SubjectApplied MathematicsInjective metric spacelcsh:MathematicsT-normlcsh:QA1-939Intrinsic metricConvex metric spaceUniform continuityMetric spaceFréchet spaceSettore MAT/05 - Analisi Matematica0-completeness best proximity point fixed point partial metric spaceMetric (mathematics)AnalysisMathematics
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On a pair of fuzzy $\varphi$-contractive mappings

2010

We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.

Discrete mathematicsInjective metric spaceFuzzy mappingT-normFuzzy subalgebraFixed pointCommon fixed pointComputer Science ApplicationsConvex metric spaceIntrinsic metricHausdorff distanceContractive type mappingSettore MAT/05 - Analisi MatematicaModeling and SimulationFuzzy numberCoincidence pointMathematics
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Quantum Finite Automata and Logics

2006

The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.

Discrete mathematicsLindström quantifierNested wordAbstract family of languagesComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Computer Science::Computational ComplexityComputer Science::Digital LibrariesAlgebraTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESMonoidal t-norm logicComputer Science::Programming LanguagesQuantum finite automataEquivalence (formal languages)T-norm fuzzy logicsComputer Science::Formal Languages and Automata TheoryAND gateMathematics
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Multi-valued $$F$$ F -contractions in 0-complete partial metric spaces with application to Volterra type integral equation

2013

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces.

Discrete mathematicsPure mathematicsAlgebra and Number Theory0-completenepartial metric spacesApplied MathematicsInjective metric spaceclosed multi-valued mappingT-normEquivalence of metricsIntrinsic metricConvex metric spaceComputational MathematicsUniform continuityMetric spacefixed pointSettore MAT/05 - Analisi MatematicaFréchet spaceGeometry and TopologyF-contractionAnalysisMathematicsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms

1983

All known connectives 'and'/'or' for fuzzy sets or some classes can be introduced as t-norms/t-conorms, where Ling's representation theorem is used as a basic tool, and which is illustrated by various known and new examples (Section 2). Given a strict negation function and one connective, the other can be constructed, so that the corresponding De Morgan law is valid. In case of given Archimedean connectives, there can be constructed negation functions (Section 3). Given a non-strict Archimedean connective, a negation function and the other connective can be constructed, so that in addition to the De Morgan laws, the excluded middle law and the law of non-contradiction are valid, i.e. the ne…

Discrete mathematicsPure mathematicsRepresentation theoremLogicLaw of excluded middleFuzzy setT-normType (model theory)De Morgan's lawssymbols.namesakeNegationArtificial IntelligencesymbolsComplement (set theory)MathematicsFuzzy Sets and Systems
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