Fuzzy partitions: A way to integrate expert knowledge into distance calculations

Authors:
Serge Guillaume;Brigitte Charnomordic;Patrice Loisel
Affiliations:
Irstea, UMR ITAP, 361 rue J.F. Breton - BP 5095, F-34196 Montpellier, France;INRA-SupAgro, UMR 729 MISTEA, F-34060 Montpellier, France;INRA-SupAgro, UMR 729 MISTEA, F-34060 Montpellier, France
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

This work proposes a new pseudo-metric based on fuzzy partitions (FPs). This pseudo-metric allows for the introduction of expert knowledge into distance computations performed on numerical data and can be used in various types of statistical clustering or other applications. The knowledge is formalized by a FP, in which each fuzzy set represents a linguistic concept. The pseudo-metric is designed to respect the FP semantics. The univariate case is first studied, and the pseudo-metric behavior is discussed using synthetic experiments. Then, a multivariate version is proposed as a Minkowski-like combination of univariate distances or semi-distances. The value of the proposal is illustrated with two real-world case studies in the fields of Biology and Precision Agriculture.