Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances

In this paper, we extend the concept of the perturbation of fuzzy sets based on normalized Minkowski distances and present some new conclusions on perturbation raised by various operations of fuzzy sets. These operations are induced by triangular norms and conorms. Furthermore, we discuss the perturbation of fuzzy reasoning.

► Perturbation problem is an important research topic in fuzzy reasoning.
► We propose new measures of perturbation of fuzzy sets by a class of distances.
► We present new conclusions on perturbation raised by operations of fuzzy sets.
► We discuss the perturbation of fuzzy reasoning for some fuzzy implications.