Construction of Strong-Uniform Fuzzy Partitions of Arbitrary Dimensions

Abstract

Strong-uniform fuzzy partition is necessary for the accuracy of fuzzy partition-based histograms. Most previous research focused on constructing one-dimensional strong-uniform fuzzy partitions. While to the best of our knowledge, few have been reported for high-dimensional cases. In order to fill this theoretical vacancy, this paper proves the existence of high-dimensional strong-uniform fuzzy partitions via proposing an analytic formula to construct strong-uniform fuzzy partitions of arbitrary dimensions.