6533b7defe1ef96bd1276661

RESEARCH PRODUCT

On central algorithms of approximation under fuzzy information

Alexander P. SostakSvetlana Asmuss

subject

Mathematical optimizationFuzzy classificationArtificial IntelligenceLogicApproximation errorFuzzy setFuzzy set operationsFuzzy numberApproximation algorithmRound-off errorAlgorithmFuzzy logicMathematics

description

We consider the problem of approximation of an operator by information described by n real characteristics in the case when this information is fuzzy. We develop the well-known idea of an optimal error method of approximation for this case. It is a method whose error is the infimum of the errors of all methods for a given problem characterized by fuzzy numbers in this case. We generalize the concept of central algorithms, which are always optimal error algorithms and in the crisp case are useful both in practice and in theory. In order to do this we define the centre of an L-fuzzy subset of a normed space. The introduced concepts allow us to describe optimal methods of approximation for linear problems using balanced fuzzy information.

yearjournalcountryeditionlanguage
2005-10-01Fuzzy Sets and Systems
https://doi.org/10.1016/j.fss.2005.05.018