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Fuzzy inferences and conditional possibility distributions. (English) Zbl 0633.68100
Let \(X_ i\) \((i=1,2)\) be two variables taking values in finite universes of discourse \(U_ i\) and associated with possibility distributions \(f_ i: U_ i\to [0,1]\). After an observation of \(X_ 1\), we can deduce a characterization of \(X_ 2\) by means of an inference process. We define \(q(x_ 2| x_ 1)\) for \(x_ i\in U_ i\) as some fuzzy implication and we introduce the possibility distribution \(\bar p(x_ 1,x_ 2)=f_ 1(x_ 1)\sqcap q(x_ 2| x_ 1)\), for a t-norm \(\sqcap\). We exhibit some reasons to say that \(q(\cdot | \cdot)\) and \(f(\cdot,\cdot)\) may be respectively regarded as a conditional and a joint possibility distribution, corresponding to marginal properties with regard to the use of a t-conorm \(\sqcup\). A property of non-interactivity of the variables, with respect to \(\sqcap\), is bound with the definition of \(q(\cdot | \cdot)\) and \(p(\cdot,\cdot)\). In this way, we suggest justifications of the choice of particular implications in inference processes.

68T99 Artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI
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