A lattice-theoretic model of three-way conflict analysis

Abstract

Pawlak conflict analysis uses a three-valued situation table for representing the ratings of a set of agents on a set of issues. This paper examines a lattice-theoretic basis of three-way conflict analysis. Qualitatively, we adopt a triangle, namely, an MS.F-bilattice, to characterize the structures of agents ratings, which gives an intuitive and effective tool for ordering a single agent and a pair of agents. We consider a strength ordering and a rating ordering to construct MS.F-bilattices. By applying the principles of three-way decision as thinking in threes, we trisect, according to the rating ordering, the nine pairs of ratings into three regions: potential opposition (PO), potential conflict (PC), and potential support (PS) regions. For each region, according to the strength ordering, we construct the weak, medium, and strong three subregions. Quantitatively, we introduce opposition-alliance and support-alliance measures based on the rating ordering for one issue to trisect these pairs of ratings into PO, PC, and PS regions. We study opposition strength, conflict strength, and support strength measures based on strength ordering for one issue to trisect each of the three regions into three subregions. Finally, we extend the five types of measures for a set of issues. The lattice-theoretic model of three-way conflict analysis clarifies the semantics of pairs of ratings by two agents and gives a different perspective on trisection methods in conflict analysis. To demonstrate the value of the proposed methods, we analyze a case study of the development planning of the Gansu Province of China.