Fuzzy Logic and Zadeh Algebra

• 作者: Paavo Kukkurainen
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: AFS FUZZY LOGIC System Zadeh ALGEBRA Simple Concepts MEMBERSHIP FUNCTIONS
• 年，卷（期）: 2017,（7）
• 页码范围: 353-365
• 页数: 13页
• 分类号: O1

摘要

In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.