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In this paper, we propose a statistics model to better understand the probabilistic interpretation for fuzzy sets. The model shows the relationship between the two kinds of statistics: the set-valued statistics for fuzzy sets and the conventional probability statistics for membership functions. Our model overcomes the shortcomings in previous approaches. The results of this paper provide a theoretical interpretation to Zadeh's insight that possibility relates to soft constraints restricting the values of language variables.
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Liang et al. (1996) studied this question.
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