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Left and right semi-uninorms on a complete lattice. (English) Zbl 1286.03098
Summary: 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.

MSC:
03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
06B23 Complete lattices, completions
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