Two New Preference Structures

Abstract

In this chapter we define partial interval order and partial semiorder structures. In order to ensure terminology coherence we require the following properties: (i) partial structures must coincide with corresponding total structures when R = o; (ii) partial structures must coincide with a quasi order (partial preorder) structure when property I c I is satisfied and with a partial order structure when I = {(a,a), ∀ a ∈ A}, (iii) partial structures must be compatible with a numerical representation.