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Such systems are used for representing and \nprocessing vague linguistic If-Then-rules, and they have been increasingly applied \nin the field of control engineering, pattern recognition and expert systems. The \nmethodology of rule interpolation is required for deducing plausible conclusions \nfrom sparse (incomplete) rule bases. For this purpose the well-known fuzzy \ninference mechanisms have to be extended or replaced by more general ones. The \nmethods proposed so far in the literature for rule interpolation are mainly \nconceived for the application to fuzzy control and miss certain logical \ncharacteristics of an inference. First, a set of axioms is proposed in this paper. With \nthis, a definition is given for the notion of interpolation, extrapolation, linear \ninterpolation and linear extrapolation of fuzzy rules. The axioms include all the \nconditions that have been of interest in the previous attempts and others which \neither have logical characteristics or try to capture the linearity of the interpolation. \nA new method for linear interpolation and extrapolation of compact fuzzy \nquantities of the real line is suggested and analyzed in the spirit of the given \ndefinition. The method is extended to non-linear interpolation and extrapolation \nas well.", "digital" : null, "printed" : null, "sourceYear" : 2010, "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : true, "conferencePublication" : false, "nationalOrigin" : true, "missingAuthor" : false, "oaType" : "NONE", "oaCheckDate" : "2024-02-21", "oaFree" : false, "citationCount" : 65, "citationCountUnpublished" : 0, "citationCountWoOther" : 58, "independentCitCountWoOther" : 56, "nationalOriginCitationCount" : 20, "foreignEditionCitationCount" : 46, "doiCitationCount" : 45, "wosCitationCount" : 32, "scopusCitationCount" : 43, "wosScopusCitationCount" : 45, "wosScopusCitationCountWoOther" : 45, "wosScopusIndependentCitationCount" : 45, "wosScopusIndependentCitationCountWoOther" : 45, "independentCitationCount" : 63, "selfCitationCount" : 2, "unhandledCitationCount" : 0, "citingPubCount" : 65, "independentCitingPubCount" : 63, "citingPubCountWoOther" : 58, 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