Equivalence Classes of Proximity Relations with Full Consistency

摘要

This paper studies the equivalence classes of a scalar domain obtained from either the max-min composition of a proximity relation or the weighted combination of multiple proximity relations. Previous work shows that the weighted combination of fully consistent proximity relations is still consistent with each of the proximity relations prior to the combination. In this paper, we prove that, for proximity relations on domain D with fully consistent constrain, the card(D)-1 times max-min composition on either the weighted combination or each of the original proximity relations can obtain the same equivalence classes.