On the Dual-Monotonicity of Threshold Functions

A necessary condition for a threshold function in terms of comparability was first reported by Paull and McCluskey [4] who have established a chain of conditions later called 1-monotonicity, 2-monotonicity, and k-monotonicity, in general. Each of these conditions entails its predecessors, and is stricter than them; the union of this denumerable set of conditions is called complete monotonicity by Winder. Winder [5] has given an extensive treatment of these ideas and has offered an efficient procedure for the design of threshold devices.