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What does a probabilistic interpretation of fuzzy sets mean?

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2 Author(s)
Ping Liang ; Coll. of Eng., California Univ., Riverside, CA, USA ; Fengming Song

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

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:4 ,  Issue: 2 )