Ordinal Preference Models Based on S-Integrals and Their Verification

Abstract

This paper discusses the ordinal preference models based on S-integrals. In parallel with the cardinal preference models based on Choquet integrals, there are various S-integrals: S-integral, SS-integral, CPTS-integral and BCS-integral.

First, we verify the ordinal models. To this aim, two psychological experiments have been conducted, where all the preferences of subjects could be modeled by S-, SS-, CPTS- and BCS-integrals. A counter example to BCSintegral models is also shown.

Next, we consider Savage’s Omelet problem in multi-criteria decision making. There are many admissible preference orders of acts depending on the consequents of acts. We find that there exist some preferences which cannot be modeled even by the BCS-integral.

Finally, to breakthrough the difficulty of BCS-integral models, we propose hierarchical preference models by which we can model the above counter examples.