On pseudo-homogeneous triangular norms, triangular conorms and proper uninorms

In this paper, quasi-homogeneous t-norms are generalized and then pseudo-homogeneous t-norms are introduced and characterized. It is shown that only some particular strict t-norms and the minimum t-norm TMTM are pseudo-homogeneous. The concepts of pseudo-homogeneous t-conorms and proper uninorms are given as well. Different from t-norms, only the maximum t-conorm SMSM is pseudo-homogeneous and any proper uninorm is not pseudo-homogeneous.