Characterizing Functions of n-Uninorms With Continuous Underlying Functions

The characterizing set-valued functions were introduced for uninorms with continuous underlying functions and these set-valued functions were useful for the complete characterization of such uninorms. In this article, we study the characterizing functions of n-uninorms with continuous underlying t-norms and t-conorms. We will show that an n-uninorm with continuous underlying functions possesses n characterizing set-valued functions, where the graphs of these characterizing set-valued functions cover the set of all points of discontinuity of the respective n-uninorm. Moreover, for i = 1, . . . , n, the ith characterizing set-valued function divides the unit square into the two sets, where below the graph of the ith characterizing set-valued function, the n-uninorm attains values smaller than the local neutral element e(i) and above the graph of the ith characterizing set-valued function, the n-uninorm attains values greater than the local neutral element e(i).

Automated summary

This article studies the characterizing functions of n-uninorms with continuous underlying t-norms and t-conorms. These functions can divide the points of discontinuity of n-uninorms and have specific properties.