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.
Highlights
Starting with simple concepts such as “young people” or “tall people” it is possible to form AFS logic system ((EM, ∨, ∧,′)
In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra
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
Summary
Starting with simple concepts such as “young people” or “tall people” it is possible to form AFS logic system ((EM , ∨, ∧,′). For any ζ ∈ EM , let μζ : X → [0,1] be a membership function of the concept ζ. { } assume that all the elements μζ in the set μζ | ζ ∈ EM satisfy the three conditions, Definition 2.17. Let. be a set of membership functions of the concept ζ of the AFS fuzzy logic ( ) system ( EM , ∨, ∧,′). According to Proposition 3.4 a chain μζ ζ∈EM corresponding to the chain ( )ζ ζ∈EM satisfies the seven Zadeh algebra axioms and forms some Zadeh algebra, Proposition 3.5. In the conclusion it is illustrated the research motivation and contribution of this paper
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