Search results for "Binary operation"

showing 6 items of 6 documents

On a multiplication and a theory of integration for belief and plausibility functions

1987

Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…

Discrete mathematicsPure mathematicsFuzzy measure theoryApplied MathematicsLebesgue integrationMeasure (mathematics)symbols.namesakeChoquet integralSet functionBinary operationsymbolsLocally compact spaceAnalysisMathematicsProbability measureJournal of Mathematical Analysis and Applications
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On Conditioning Operators

1999

The construction of conditional events (so-called measure-free conditioning) has a long history and is one of the fundamental problems in non-deterministic system theory (cf. [6]). In particular, the iteration of measure-free conditioning is still an open problem. The present paper tries to make a contribution to this question. In particular, we give an axiomatic introduction of conditioning operators which act as binary operations on the universe of events. The corresponding axiom system of this type of operators focus special attention on the intuitive understanding that the event ‘α given β’ is somewhere in “between” ‘α and β’ and ‘β implies α’. A detailed motivation of these axioms can …

Algebrasymbols.namesakeComputer scienceBinary operationOpen problemBoolean algebra (structure)Event (relativity)symbolsPropositionType (model theory)AxiomFocus (linguistics)
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Lattices of Jordan algebras

2010

AbstractCommutative Jordan algebras play a central part in orthogonal models. The generations of these algebras is studied and applied in deriving lattices of such algebras. These lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation.

Kronecker productNumerical AnalysisPure mathematicsProjectorsAlgebra and Number TheoryJordan algebraNon-associative algebraBinary operationsLatticeAlgebrasymbols.namesakeBinary operationCommutative Jordan algebraLattice (order)Kronecker matrix productsymbolsDiscrete Mathematics and CombinatoricsGeometry and TopologyNest algebraCommutative algebraCommutative propertyMathematicsLinear Algebra and its Applications
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Facial geometry and speech analysis for depression detection.

2017

Depression is one of the most prevalent mental disorders, burdening many people world-wide. A system with the potential of serving as a decision support system is proposed, based on novel features extracted from facial expression geometry and speech, by interpreting non-verbal manifestations of depression. The proposed system has been tested both in gender independent and gender based modes, and with different fusion methods. The algorithms were evaluated for several combinations of parameters and classification schemes, on the dataset provided by the Audio/Visual Emotion Challenge of 2013 and 2014. The proposed framework achieved a precision of 94.8% for detecting persons achieving high sc…

Decision support systemFacial expressionDepressive DisorderDepressionSpeech recognition05 social sciencesNearest neighbourClassification scheme02 engineering and technologyFacial geometryBinary operationFace0502 economics and business0202 electrical engineering electronic engineering information engineeringDecision fusionHumansSpeech020201 artificial intelligence & image processingPsychologyClassifier (UML)050203 business & managementAlgorithmsAnnual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
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Hyperidentities of some generalizations of lattices

1998

In the paper we present bases and hyperbases of hyperidentities of some generalizations of the variety L of all lattices and the variety D of distributive lattices. We describe the form of hyperidentities of some varieties with two binary operations.

CombinatoricsPure mathematicsAlgebra and Number TheoryDistributive propertyBinary operationHigh Energy Physics::LatticeLattice (order)Distributive latticeMathematicsAlgebra Universalis
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Lambda substitution algebras

1993

In the paper an algebraic metatheory of type-free λ-calculus is developed. Our version is based on lambda substitution algebras (λSAs), which are just SAs introduced by Feldman (for algebraizing equational logic) enriched with a countable family of unary operations of λ-abstraction and a binary operation of application. Two representation theorems, syntactical and semantic, are proved, what directly provides completeness theorems.

AlgebraDiscrete mathematicsUnary operationBinary operationComputer Science::Logic in Computer ScienceCompleteness (logic)Substitution (algebra)Countable setGödel's completeness theoremEquational logicAlgebraic logicMathematics
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