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Fuzzy Logic and Zadeh Algebra
School of Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland
- 1 School of Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland
Advances in Pure Mathematics·Volume 07 (2017)·Pages 353–365·Published 6 July 2017·DOI10.4236/apm.2017.77022
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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 R m 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.
KeywordsAFS Fuzzy Logic SystemZadeh AlgebraSimple ConceptsMembership Functions
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