In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull. As a consequence of this result, we prove that the centroid defuzzification of a general type-2 fuzzy set can be reduced to the easier-to-compute case when for each x, the corresponding fuzzy degree of membership is convex.
CITATION STYLE
Kreinovich, V., & Sriboonchitta, S. (2017). For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10061 LNAI, pp. 211–218). Springer Verlag. https://doi.org/10.1007/978-3-319-62434-1_17
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