A nonsimple conjoint measurement model

The nonsimple conjoint measurement model examined in this paper maps each (a₁, a₂, a₃) in A₁ × A₂ × A₃ into ω₁(a₁)φ₂(a₂) + ω₂(a₁)φ₃(a₃), where each of ω₁, ω₂, φ₂, and φ₃ is a real-valued function, so as to preserve a binary relation ≥ on A₁ × A₂ × A₃ by ≧ 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.