Relational measures and integration in preference modeling

Based on a set of criteria and a measuring lattice, we introduce relational measures as generalizations of fuzzy measures. The latter have recently made their way from the interval [0,1]⊆R to the ordinal or even to the qualitative level. We proceed further and introduce relational measures and relational integration. First ideas of this kind, but for the real-valued linear orderings stem from Choquet (1950s) and Sugeno (1970s). We generalize to not necessarily linear orders and handle it algebraically and in a point-free manner. We thus open this area of research for treatment with theorem provers which would be extremely difficult for the classical presentation of Choquet and Sugeno integrals. Our specification of the relational integral is operational. It can immediately be translated into the programming language of RelView and, hence, the tool can be used for solving practical problems.