A nonsimple conjoint measurement model

Abstract

The nonsimple conjoint measurement model examined in this paper maps each (a1, a2, a3) in A1 x A2 x A3 into [omega]1(a1)[phi]2(a2) + [omega]2(a1)[phi]3(a3), where each of [omega]1, [omega]2, [phi]2, and [phi]3 is a real-valued function, so as to preserve a binary relation >= on A1 x A2 x A3 by [greater, double equals] in the numerical system.The principle structure of the present model is similar to the structure of the simple models. But in the nonsimple model, we define two different identity elements of A1 for its different multiplicative effects on the other two components A2 and A3, whereas in the simple model, one identity element for each component is defined.