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Term Functions and Fundamental Relation of Fuzzy Hyperalgebras

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Reza Ameri at University of Tehran
Reza Ameri
T Nozari
T Nozari
T Nozari
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Abstract

We introduce and study term functions over fuzzy hyperalgebras. We start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra. We present the form of generated subfuzzy hyperalgebra of a given fuzzy hyperalgebra as a generalization of universal algebras and multialgebras. Finally, we characterize the form of the fundamental relation of a fuzzy hyperalgebra.
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... They introduced the fuzzy polynomial function (term function) over the algebra of all nonzero fuzzy subsets of a fuzzy hyperalgebra. This was an important tool to construct the fundamental relation as a main concept on fuzzy hyperalgebra where the factor fuzzy hyperalgebra was considered as a universal algebra [8]. In another study, Ameri et al. explored fuzzy soft hyperalgebras as the generalization of soft hyperalgebras and soft algebras [9]. ...
... Remark 2.7. [8] LetS be a fuzzy hyperalgebra and ζ be an equivalence relation on S. The quotient set S/ζ can be regarded as a hyperalgebra with the following hyperoperations for all k ∈ {1, ..., n i }, and i ∈ I : ...
... , χ c n ) (y) > 0 for some n ∈ N, p ∈ P n A (F * (A)), c 1 , . . . , c n ∈ A (see [8]). ...
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