Interestingness measures for fixed consequent rules

Many different rule interestingness measures have been proposed in the literature; we show that, under two assumptions, at least twelve of these measures are proportional to Confidence. We consider rules with a fixed consequent, generated from a fixed data set. From these assumptions, we prove that Satisfaction, Ohsaki's Conviction, Added Value, Brin's Interest/Lift/Strength, Brin's Conviction, Certainty Factor/Loevinger, Mutual Information, Interestingness, Sebag-Schonauer, Ganascia Index, Odd Multiplier, and Example/counter-example Rate are all monotonic with respect to Confidence. Hence, for ordering sets of partial classification rules with a fixed consequent, the Confidence measure is equivalent to any of the twelve other measures.