Agent preference relations: strict, indifferent and incomparable

ABSTRACT

In traditional preference modeling approaches, agents can express preferences among a pair of alternatives in three distinct ways: either an agent has a strict preference of one alternative compared to the other, or is indifferent between both alternatives, or considers the two alternatives as incomparable. These three preference relations are disjunct, and take the crisp binary values of 0 and 1 only. We propose in this paper a fuzzy preference model to relax these dichotomous conditions: an agent can have at the same time a degree of preference, indifference and incomparability among any pair of alternatives, taking values in the interval [0,1]. This increased preference modeling flexibility allows for a far more detailed analysis of the agents' (partial) preference orderings, which can now be analyzed at different degrees of precision. We illustrate how this analysis can be performed on the preference relations of an individual agent, as well as in the case of two interacting agents. While incomparabilities are inherent to our preference model, it may be useful to resolve these incomparabilities to transform the partial orderings into linear orders. We therefore also present a model of reasoning for the resolution of such incomparabilities by an agent who forms beliefs over the expected orderings.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.11 Distributed Artificial Intelligence
            Subjects: Multiagent systems

General Terms:
Algorithms, Design, Measurement, Theory

Keywords:
(Fuzzy) multi criteria decision making, incomparability, multi-agent systems