Fuzzy Logic and Zadeh Algebra
Kukkurainen, Paavo (2017)
Post-print / final draft
2017
Scientific Research
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2017122156010
https://urn.fi/URN:NBN:fi-fe2017122156010
Tiivistelmä
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 in-
terpreted 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 in-
troduction where the binary relation Rm of a simple concept m is
de ned more general in De nition 2.10. Then every chain of member-
ship functions form a Zadeh algebra. It demands a lot of preliminaries
before we obtain this desired result.
Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple
concepts we construct fuzzy logic concepts. Simple concepts can be in-
terpreted 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 in-
troduction where the binary relation Rm of a simple concept m is
de ned more general in De nition 2.10. Then every chain of member-
ship functions form a Zadeh algebra. It demands a lot of preliminaries
before we obtain this desired result.
Lähdeviite
Kukkurainen, P., (2017). Fuzzy Logic and Zadeh Algebra. Advances in Puhe Mathematics, Vol 7, Issue 7. p. 350-365. DOI: 10.4236/apm.2017.77022.
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