New representations of the generalized uniform fuzzy partitions: Generalized normal case

In this research, new representations of basic functions are proposed based on the new types of fuzzy partition and a subnormal generating function. The generalized uniform fuzzy partitions in subnormal case, i.e. in case a generating function K is not normal (generalized normal case), and simpler form of fuzzy transform (FzT) components based on these new representations of the generalized uniform fuzzy partitions are indicated. The main properties of a new uniform fuzzy partition are suggested. New theorems and lemmas are proved.

Keywords:

Fuzzy partition , Fuzzy transform , Basic function , The membership functions , Generating Function , Ruspini condition