Paper Info
Title
For Multi-interval-valued Fuzzy Sets, Centroid Defuzzification Is Equivalent to Defuzzifying Its Interval Hull: A Theorem.
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.
Year
DOI
Venue
2016
10.1007/978-3-319-62434-1_17
ADVANCES IN COMPUTATIONAL INTELLIGENCE, MICAI 2016, PT I
Field
DocType
Volume
Discrete mathematics,Certainty,Pattern recognition,Defuzzification,Algebra,Fuzzy logic,Fuzzy set,Artificial intelligence,Hull,Mathematics,Centroid
Conference
10061
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Vladik Kreinovich11091281.07
Songsak Sriboonchitta211045.41