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Semi-valuation et métrique associée. (Semi-valuation and associated metric). (French) Zbl 0571.06007

We start by defining semi-valuations and some related concepts such as intervaluation and H-independence which have several applications in practice. We can, by choosing adequate cases of semi-valuations identify intervaluations either by interclass inertia or by information between subsystems. As for H-independence we can identify it by set independence or vector independence or stochastic independence... We thoroughly study a particular case of semi-valuation: conditional semi-valuation. We demonstrate that it has the metric properties of an upper valuation.

MSC:

06A12 Semilattices
06A06 Partial orders, general
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H25 Factor analysis and principal components; correspondence analysis
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