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On the use of fuzzy rule interpolation techniques for monotonic multi-input fuzzy rule base models
Constructing a monotonicity relating function is important, as many engineering problems revolve around a monotonicity relationship between input(s) and output(s). In this paper, we investigate the use of fuzzy rule interpolation techniques for monotonicity relating fuzzy inference system (FIS). A mathematical derivation on the conditions of an FIS to be monotone is provided. From the derivation, two conditions are necessary. The derivation suggests that the mapped consequence fuzzy set of an FIS to be of a monotonicity order. We further evaluate the use of fuzzy rule interpolation techniques in predicting a consequent associated with an observation according to the monotonicity order. There are several findings in this article. We point out the importance of an ordering criterion in rule selection for a multi-input FIS before the interpolation process; and hence, the practice of choosing the nearest rules may not be true in this case. To fulfill the monotonicity order, we argue with an example that conventional fuzzy rule interpolation techniques that predict each consequence separately is not suitable in this case. We further suggest another class of interpolation techniques that predicts the consequence of a set of observations simultaneously, instead of separately. This can be accomplished with the use of a search algorithm, such as the brute force, genetic algorithm or etc.
History
Event
International Conference on Fuzzy Systems (2009 : Jeju Island, Korea)Pagination
1736 - 1740Publisher
IEEELocation
Jeju Island, KoreaPlace of publication
Piscataway, N. J.Start date
2009-08-20End date
2009-08-24ISSN
1098-7584ISBN-13
9781424435968ISBN-10
142443596XLanguage
engPublication classification
E1.1 Full written paper - refereedTitle of proceedings
FUZZ-IEEE 2009 : Proceedings of the IEEE International Conference on Fuzzy SystemsUsage metrics
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No categories selectedKeywords
brute forceengineering problemsfuzzy inference systemsfuzzy rule base modelsfuzzy rule interpolationinterpolation processinterpolation techniquesmathematical derivationmonotonicitymultiinputordering criteriarule selectionsearch algorithmsScience & TechnologyTechnologyPhysical SciencesComputer Science, Artificial IntelligenceComputer Science, Theory & MethodsMathematics, AppliedComputer ScienceMathematics
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