Similarity-based Reasoning from the Perspective of Extensionality

Abstract

Similarity-based reasoning systems consider the notion of similarity as crucial for their motivation and the whole design. However, similarity can be seen not only as a general notion but also as a particular family of binary fuzzy relations modeling a fuzzy equality. Moreover, these relations are tightly connected to another crucial notion -to the extensionality of fuzzy sets. This contribution focuses on this natural bridge and studies similarity-based reasoning fuzzy inference systems from the point of view of extensionality. Robustness of these systems is the first property that is considered in the newly setup framework. However, the potential impact and topics of interest are much wider.