Title :
Measuring fuzzy uncertainty
Author :
Pal, Nikhil R. ; Bezdek, James C.
Author_Institution :
Machine Intelligence Unit, Indian Stat. Inst., Calcutta, India
fDate :
5/1/1994 12:00:00 AM
Abstract :
First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Some relationships between several existing and the new measures are established, and some new properties are derived. The relative merits and drawbacks of different measures for applications are discussed. A weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced. Finally, we comment on the construction of measures that may assess all of the uncertainties associated with a physical system
Keywords :
fuzzy set theory; additive classes; discrete fuzzy sets; fuzziness measures; fuzzy uncertainty measures; multiplicative class; nonnegative monotone increasing concave functions; weighted fuzzy entropy; Additives; Digital images; Entropy; Face detection; Fuzzy sets; Fuzzy systems; Image analysis; Machine vision; Measurement uncertainty; Probability distribution;
Journal_Title :
Fuzzy Systems, IEEE Transactions on