Kybernetika 49 no. 6, 948-961, 2013

Left and right semi-uninorms on a complete lattice

Yong Su, Zhudeng Wang and Keming Tang

Abstract:

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.

Keywords:

uninorm, fuzzy connective, left (right) semi-uninorm, upper (lower) approximation

Classification:

03B52, 03E72

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