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Keywords:
extensions; algebraic completely distributive lattices; fuzzy connectives
extensions; algebraic completely distributive lattices; fuzzy connectives
Summary:
The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications and also make a study on the behaviors of $R$-implication and reciprocal implication. Finally, we construct two classes of infinitely $\bigvee$-distributive uninorms and infinitely $\bigwedge$-distributive uninorms.
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