What does a probabilistic interpretation of fuzzy sets mean? |
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Authors: | Ping Liang Fengming Song |
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Affiliation: | Coll. of Eng., California Univ., Riverside, CA ; |
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Abstract: | 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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