Averaging operators on the unit interval
Mai Gehrke, Carol L. Walker, Elbert A. Walker · International Journal of Intelligent Systems · 1999
In working with negations and t-norms, it is not uncommon to call upon the arithmetic of the real numbers even though that is not part of the structure of the unit interval as a bounded lattice. To develop a self-contained system, we incorporate an averaging operator, which provides a (continuous) scaling of the unit interval that is not available from the lattice structure. The interest here is in the relations among averaging operators and t-norms, t-conorms, negations, and their generators. ©1999 John Wiley & Sons, Inc.