Publication Date
9-2016
Abstract
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.
Comments
Technical Report: UTEP-CS-16-65
Published in Proceedings of the 15th Mexican International Conference on Artificial Intelligence MICAI'2016, Cancun, Mexico, October 25-29, 2016, Springer Lecture Notes in Artificial Intelligence.