Iterative mean aggregation

We propose an iterative definition of mean aggregation, based on fuzzy bases for n-dimensional positive real vectors. We introduce four fuzzy similarity measures, which are called left similarity, right similarity, relative similarity, and geometrical similarity measures. We define a mean aggregation function of fuzzy bases based on left similarity measure, and then define the Iterative Mean Aggregation (IMA) of fuzzy bases based on the mean aggregation function. We prove some of the properties of IMA and fuzzy similarity measures theoretically, and finally we give some applications and experimental results in agreement with our theoretical results