Similarity-based reasoning, SimilarityExtensionality, Extensional fuzzy numbers, Approximate reasoning

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 set-up framework. However, the potential impact and topics of interest are much wider.