In this paper, we introduce the centroid and generalized centroid of a type-2 fuzzy set (both of which are essential for implementing a type-2 fuzzy logic system), and explain how to compute them. For practical use, we show how to compute the centroid of interval and Gaussian type-2 fuz...
,zn))=x0j-μ(y0)j2σj-2. and, where Y is the set of all class labels and Cy={i:zi=(xi,y)}, (6.2)βj=∑i=1nx0j-μ(y0)j2σj-2=σj-2∑y∈Y∣Cy∣-1σ(y)j2. The negation of this β-NCM forms a natural ranking function for feature filtering since it measures the ...
An interval type‐2 fuzzy set (IT2FS)contains the infinite number of embedded membership functions (MFs) defined as type‐1 fuzzy sets. The center of gravity (COG) of an IT2FS is obtained by integrating the centroids of all these MFs. However, obtaining the COG of an IT2FS in a ...
Computing the centroid of an interval type-2 fuzzy set (IT2 FS) is an important type-reduction method. The aim of this paper is to develop a new method to calculate the centroid of an IT2 FS when the problems of centroid computation of an IT2 FS are continuous. For the continuous ...
Melgarejo, M., "A fast recursive method to compute the generalized centroid of an interval type-2 fuzzy set," Proc. North Amer. Fuzzy Inf. Process. Soc., San Diego, CA, pp. 190-194, June 2007.Melgarejo, M. A Fast Recursive Method to Compute the Generalized Centroid of an Interval ...
Cai, "Advantages of the enhanced opposite direction searching algorithm for computing the centroid of an interval type-2 fuzzy set," Asian J. Control, Vol. 14, No. 5, pp. 1422-1430 (2012).Hu, H.;Wang, Y.; Cai, Y.: Advantages of Enhanced Opposite Direction Searching Algorithms for ...
Wu, "Properties of the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule," 2005, pp. 341-346.J.M. Mendel and H.W. Wu, Properties of the centroid of an interval type-II fuzzy set, including the centroid of a fuzzy granule, The 2005 IEEE ...
The centroid of a triangular type-2 fuzzy set can be considered as a subsequent analytical extension of the \\\{KM\\\} type-reduction procedure dedicated to interval type-2 sets. The centroid of a Gaussian type-2 fuzzy set is recursively expressed by an independent procedure.JanuszT....
They partition the objects into groups, or clusters, so that objects within a cluster are “similar” to one another and “dissimilar” to objects in other clusters. Similarity is commonly defined in terms of how “close” the objects are in space, based on a distance function. The “...
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