Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions

Abstract

This paper develops a comprehensive framework for bipolar preference modeling using possibility theory to capture both positive and negative dimensions of decision-making. It distinguishes between positive preferences—which reflect desired, satisfactory outcomes—and negative preferences—which identify and exclude unacceptable options. Negative preferences are modeled within a possibilistic logic framework to assess the tolerability of solutions, while positive preferences employ guaranteed possibility to quantify desirability.

The study formally defines the syntactic representation of these preferences and establishes criteria for their coherence, ensuring that a solution cannot simultaneously be deemed desirable and unacceptable. Additionally, the paper addresses the challenge of merging preferences from multiple agents by introducing operators that fuse both negative and positive preference sets, and it outlines a mechanism for restoring consistency when conflicts arise.

Finally, it explores various strategies for selecting optimal solutions based on feasibility, exclusion of negative preferences, and maximization of positive satisfaction, offering conjunctive, disjunctive, and cardinality-based approaches. This integrated methodology not only deepens the theoretical understanding of bipolar preference structures in artificial intelligence but also enhances practical decision-making processes by providing a structured and robust approach to handling conflicting preference information.