On a special class of left-continuous uninorms

Li, Gang

Kybernetika, Tome 54 (2018) no. 3, pp. 427-442

Abstract (VO)

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 $U$.

Détail

DOI : 10.14736/kyb-2018-3-0427

Classification : 03B52, 03E72, 06F05
Keywords: uninorm; internal operator; ordinal sum; residual implication; triangular subnorm

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