An approach to measure the robustness of fuzzy reasoning

Fuzzy reasoning is intensively used in intelligent systems including fuzzy control, classification, expert systems, and networks to name a few dominant categories of such architectures. As being a fundamental construct permeating so many diverse areas, fuzzy reasoning was studied with respect to its fundamental properties such as robustness. The notion of robustness or sensitivity becomes of paramount importance by leading to a more comprehensive understanding of the way in which reasoning processes are developed. In this study, we introduce and study properties of some measures of robustness (or sensitivity) of fuzzy connectives and implication operators and discuss their relationships with perturbation properties of fuzzy sets. The results produced here are compared and contrasted with the previous findings available in the literature.