Mathematically, relations M1 and M2 are logical opposites, as are consensus relations M∗ 1 and M∗ 2 (Bezdek et al., 1978). It is interesting to discuss the cardinality of these various preference and consensus relations. In this case, the cardinality of a relation is the number of possible combinations of that matrix type. It is obvious that there is only one possible matrix for M1. The cardinality of all the preference or consensus relations discussed here is given in Equation (9.15), where the symbol ||denotes cardinality of the