Geodesic
Left and right semi-uninorms on a complete lattice
Kybernetika, Tome 49 (2013) no. 6, pp. 948-961 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.
Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.
Classification : 03B52, 03E72, 06B23
Keywords: fuzzy connective; uninorm; left (right) semi-uninorm; upper (lower) approximation 
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     author = {Su, Yong and Wang, Zhudeng and Tang, Keming},
     title = {Left and right semi-uninorms on a complete lattice},
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Su, Yong; Wang, Zhudeng; Tang, Keming. Left and right semi-uninorms on a complete lattice. Kybernetika, Tome 49 (2013) no. 6, pp. 948-961. http://geodesic.mathdoc.fr/item/KYB_2013_49_6_a7/