Kybernetika 54 no. 3, 427-442, 2018

On a special class of left-continuous uninorms

Gang LiDOI: 10.14736/kyb-2018-3-0427


This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region $A(e)$ and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions $I: [0,1]^{2}\rightarrow[0,1]$ for which a uninorm $U$ of this special class exists in such a way that $I$ is the residual implications derived from $U$.


uninorm, ordinal sum, internal operator, residual implication, triangular subnorm


06F05, 03E72, 03B52


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