For multi-interval-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull: A theorem

• Main Authors: Vladik Kreinovich, Songsak Sriboonchitta
• Format: Book Series
• Published: 2018
• Subjects: Mathematics; Agricultural and Biological Sciences
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85028459632&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/46738
• Institution: Chiang Mai University

© Springer International Publishing AG 2017. 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.