Improving approximation properties of fuzzy transform through non-uniform partitions

Abstract

Function reconstruction is one of the valuable properties of the Fuzzy Transform and its inverse. The quality of reconstruction depends on how dense the fuzzy partition of the function domain is. However, the partition should be denser where the function exhibits faster variations, while the partition can be less dense where the function is moving slowly. In this paper, we investigate the possibility of having non-uniform fuzzy partitions, in order to better accommodate a different behavior of function across its domain.