Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
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We discuss some relationships between the fuzzy subset concepts of possibility, truth and certainty. We show, for A and B fuzzy subsets of X, that the possibility of A given B is related to the truth of A given B through a Sugeno-like integral. Furthermore, we show that if B is a normal fuzzy subset than Poss[A |B] is always at least as large as the certainty [A | B]. On the other hand if the maximum membership in B is less than 0.5 the certainty is always as least as large as the possibility.