TITLE:
Fuzzy Logic and Zadeh Algebra
AUTHORS:
Paavo Kukkurainen
KEYWORDS:
AFS Fuzzy Logic System, Zadeh Algebra, Simple Concepts, Membership Functions
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.7,
July
7,
2017
ABSTRACT: 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.