Construction of Strong-Uniform Fuzzy Partitions of Arbitrary Dimensions

TL;DR

This paper introduces a method to construct strong-uniform fuzzy partitions in high-dimensional spaces, addressing a gap in existing research which mainly focused on one-dimensional cases, thereby enhancing the accuracy of fuzzy partition-based histograms.

Contribution

It provides the first proof of the existence of high-dimensional strong-uniform fuzzy partitions and proposes an analytic formula for their construction.

Findings

Proves the existence of high-dimensional strong-uniform fuzzy partitions.

Develops an analytic formula for constructing these partitions.

Addresses a theoretical gap in fuzzy partition research.

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.