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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.

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