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Probabilities from fuzzy observations
Yager R. (ed) Information Sciences32 (1):1-31,1984.Type:Article
Date Reviewed: Mar 1 1985

The author extends the notion of obtaining probabilities from observations of a random experiment to incorporate fuzzy subset theory. A probability measure PF(E) is derived for fuzzy event E being equal to :9I where n = a fuzzy subset measuring the degree to which Bi representing outcomes of a random variable V, and :9I = a fuzzy subset measuring the degree to which Bi is contained in E.

This is shown to be a true generalization of traditional (non-fuzzy) probability measures. This includes showing f(x) = 1 for x = the set of all values for V, :9I When E is crisp (non-fuzzy), then the traditional probability measure occurs.

The author uses a definition of specificity to measure the amount of information in the observations. The measure is the integral over the variable :G a of the inverse of the cardinality of the :G a -level set (the crisp set of values whose membership function equals or exceeds :G a). The informativeness of a fuzzy set is the log of the product of this specificity measure times the cardinality of the set. Moreover, conditional probabilities are defined and discussed in this context, as are means. As the author points out, this could be the beginning of a theory of fuzzy statistics.

Reviewer:  Donald H. Kraft Review #: CR108647
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Probability And Statistics (G.3 )
 
 
Statistical Computing (G.3 ... )
 
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