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Definition of general aggregation operators through similarity relations
Various extensions of the original max and min aggregation operators in fuzzy set theory are successfully used in practical applications, but lack a clear conceptual model supporting them. Giving these operators a meaningful and simple interpretation is the topic of this paper. Aggregation operators are seen as different methods to measure distances to the essential reference points of the feature space, called Ideals. It has been proved that every general aggregation operator can be associated with a corresponding metric, in which the result of its application is the distance to the Ideal. Some widely used operators correspond to familiar l - p norms, and new operators can be defined by specifying different metrics. Heterogeneous combinations of ANDs and ORs are treated in such a way that the distributivity and De Morgan's laws hold. Applications to fuzzy constraint satisfaction problem and fuzzy control are discussed and interpreted geometrically. Classical operators are particular cases of the proposed semantic model, and several other examples are given.
History
Journal
Fuzzy sets and systemsVolume
114Issue
3Pagination
437 - 453Publisher
Elsevier Science BVLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0165-0114Language
engPublication classification
C1.1 Refereed article in a scholarly journalCopyright notice
2000, Elsevier Science B.V.Usage metrics
Keywords
fuzzy setsoperatorsrelationsmulticriteria analysisdefuzzificationScience & TechnologyTechnologyPhysical SciencesComputer Science, Theory & MethodsMathematics, AppliedStatistics & ProbabilityComputer ScienceMathematicsFUZZY-LOGICMEMBERSHIPCONTROLLERDESIGNMODELArtificial Intelligence and Image Processing
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