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Uncertainty measures for interval type-2 fuzzy sets. (English) Zbl 1141.28010
Based on the representation theorem for interval type-2 fuzzy sets, 4 types of new uncertainty measures are introduced and discussed, namely cardinality, fuzziness, variance and skewness. Note that the first uncertainty measures for this type of fuzzy sets, namely the centroid, was introduced already in [N. N. Karnik and J. M. Mendel, Inf. Sci. 132, No. 1–4, 195–220 (2001; 0982.03030)]. The authors give formulae for computing the introduced uncertainty measures, discuss their properties and include several illustrative examples.
MSC:
28E10Fuzzy measure theory
94D05Fuzzy sets and logic in connection with communication