Transforming Family Resemblance Concepts into Fuzzy Sets

This article aims to clarify fundamental aspects of the process of assigning fuzzy scores to conditions based on family resemblance (FR) structures by considering prototype and set theories. Prototype theory and set theory consider FR structures from two different angles. Specifically, set theory links the conceptualization of FR to the idea of sufficient and INUS (Insufficient but Necessary part of a condition, which is itself Unnecessary but Sufficient for the result) sets. In contrast, concept membership in prototype theory is strictly linked to the notion of similarity (or resemblance) in relation to the prototype, which is the anchor of the ideational content of the concept. After an introductive section where I elucidate set-theoretic and prototypical aspects of concept formation, I individuate the axiomatic properties that identify the principles of transforming FR structures into fuzzy sets. Finally, I propose an algorithm based on the power mean that is able to operationalize FR structures considering both set-theoretic and prototype theory perspectives.