6533b85ffe1ef96bd12c1a83
RESEARCH PRODUCT
Extremal problems of approximation theory in fuzzy context
Svetlana AsmussAlexander P. Sostaksubject
Discrete mathematicsLogicFuzzy setMathematical analysisApproximation algorithmEssential supremum and essential infimumFuzzy logicInfimum and supremumComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceApproximation errorFuzzy numberLinear approximationMathematicsdescription
Abstract The problem of approximation of a fuzzy subset of a normed space is considered. We study the error of approximation, which in this case is characterized by an L -fuzzy number. In order to do this we define the supremum of an L -fuzzy set of real numbers as well as the supremum and the infimum of a crisp set of L -fuzzy numbers. The introduced concepts allow us to investigate the best approximation and the optimal linear approximation. In particular, we consider approximation of a fuzzy subset in the space L p m of differentiable functions in the L q -metric. We prove the fuzzy counterparts of duality theorems, which in crisp case allows effectively to solve extremal problems of the classical approximation theory.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-07-01 | Fuzzy Sets and Systems |