On modularity property for uninorms with continuous underlying functions

In literature, for the four common classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions.We discuss this modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain.

Keywords:

aggregation functions , uninorms , Modularity , Functional equations