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Structure of possibilistic information metrics and distances: properties. (English) Zbl 0703.94002
Summary: Systematic analysis of identities and inequalities satisfied by possibilistic information distances is conducted. The analysis is based on their representations as discrete sums and on certain inequalities for rearrangements of sequences. These identities and inequalities express several properties that are usually deemed characteristic of information distances and measures. In the companion paper those properties are used to obtain several axiomatic characterizations of possibility distances.
The basic distance is \(g(p,q)\) defined for the distributions \(p=(p_ 1,\dots,p_ n)\) and \(q=(q_ 1,\dots,q_ n)\) such that \(p_ i\leq q_ i\), \(i=1,\dots,n\). They serve to define a metric \(G(p,q)=g(p,p\vee q)+g(q,p\vee q)\) and a distance \(H(p,q)=g(p\wedge q,p)+g(p\wedge q,q)\). All these distances are, in turn based on the \(U\)-uncertainty information function.

94A17 Measures of information, entropy
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI
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