Title :
What does a probabilistic interpretation of fuzzy sets mean?
Author :
Liang, Ping ; Song, Fengming
Author_Institution :
Coll. of Eng., California Univ., Riverside, CA, USA
fDate :
5/1/1996 12:00:00 AM
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
Keywords :
fuzzy set theory; possibility theory; probability; statistical analysis; fuzzy sets; language variable restrictions; membership functions; possibility; probabilistic interpretation; set-valued statistics; soft constraints; statistics model; Constraint theory; Fuzzy sets; H infinity control; Histograms; Humans; Natural languages; Probability; Statistical distributions; Statistics;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
