Geodesic
Extensions of fuzzy connectives on ACDL
Kybernetika, Tome 55 (2019) no. 3, pp. 472-494 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2019-3-0472
Classification : 03B52, 03E72, 06D10
Keywords: extensions; algebraic completely distributive lattices; fuzzy connectives 
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     author = {Liu, Hui and Zhao, Bin},
     title = {Extensions of fuzzy connectives on {ACDL}},
     journal = {Kybernetika},
     pages = {472--494},
     year = {2019},
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     zbl = {07144949},
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Liu, Hui; Zhao, Bin. Extensions of fuzzy connectives on ACDL. Kybernetika, Tome 55 (2019) no. 3, pp. 472-494. doi: 10.14736/kyb-2019-3-0472

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