The Merging of Fuzzy and Crisp Information

by Colin B. Brown, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Washington, Seattle, Wash.; also, Erskine Fellow, Univ. of Canterbury, Christ Church, New Zealand,


Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 1, Pg. 123-133


Document Type: Journal Paper

Abstract:

Crisp information is defined as countable data for which moments are available. These moments are then used as constraints on the information entropy to obtain an unbiased probability distribution. In opposition to this objective viewpoint, subjective information in the form of verbal statements are also available. A quantitative statement of these is obtained by fuzzy support measures. This statement has two parts which refer to the gravity of information and its effect on the objective probability. These two parts are then analyzed by fuzzy set theory and established by a fuzzy conditional relation as a modification of the probability. The modification is obtained by a merging process which allows the subjective support for the objective probability to be detected.

Subject Headings: Probability | Fuzzy sets | Entropy methods | Probability distribution

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