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.

本文旨在通过考虑原型和设置理论来阐明基于家庭相似性（FR）结构为条件分配模糊得分的过程的基本方面。原型理论和集合论从两个不同角度考虑了FR结构。具体而言，集合论将FR的概念化与充足和INUS（条件的不足但必要的部分，本身本身不是必需的，但对于结果而言足够的）的概念联系起来。相反，原型理论中的概念成员关系严格地与原型相关的相似性（或相似性）概念联系在一起，而相似性是概念概念内容的基础。在介绍性部分之后，我阐述了概念形成的集合理论和原型方面，我将确定将FR结构转换为模糊集的原理的公理属性进行个性化处理。最后，我提出了一种基于幂均值的算法，该算法能够同时考虑集合论和原型论的观点，从而使框架结构可操作。