Rule acquisition and adjustment based on set-valued mapping
Information Sciences—Informatics and Computer Science: An International Journal
The structure analysis of fuzzy sets
International Journal of Approximate Reasoning
A probabilistic fuzzy approach to modeling nonlinear systems
Neurocomputing
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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