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Fuzzy partitions: a way to integrate expert knowledge into distance calculations. (English) Zbl 1321.62072
Summary: 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.

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H86 Multivariate analysis and fuzziness
Full Text: DOI
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