A Fuzzily Partitioned Interval Function Model for Ordinal Regression

Abstract

In this paper, we propose a fuzzily partitioned interval function model for ordinal regression as an extension of the interval UTA method. UTA method is known as a decision-aiding tool in multiple criteria decision problems. In UTA method, an additive utility function compatible to given preference information is identified under the assumption of the additive independence. However, this assumption is rather strong as is known in multiattribute utility theory. In this paper, we propose an interval utility model identified under a weaker assumption. We assume that the utility function is expressed by a fuzzy reasoning model with additive interval utility functions, a generalized additive utility function model. We show that the proposed model can be identified by solving a linear programming problem under given preference information and that preference evaluation can be done easily by using the identified model. We examine the performance of the proposed model by numerical experiments assuming that the decision maker has a utility function under the assumption of utility independence.