Three-way conflict analysis based on incomplete situation tables: A tentative study

Abstract

The existing three-way conflict analysis models focus on complete situation tables and rarely involve incomplete situation tables. In this paper, we give a preliminary approach to three-way conflict analysis models based on incomplete situation tables. Firstly, we construct three-way conflict analysis models based on an incomplete three-valued situation table (ITVST). We use two different methods to establish the models. One is to establish straightly the model based on the original ITVST. The other is to convert the ITVST into a complete three-valued situation table (TVST) by supplementing the missing values with the maximum probability value method, which is called a complete TVST induced by the maximum probability value method. Then we construct the three-way conflict analysis model based on the induced complete TVST. Secondly, to deal with more uncertainty and complexity in the actual decision-making process, we generalize an ITVST to an incomplete many-valued situation table (IMVST) and establish the corresponding three-way conflict analysis models. Finally, we further extend an IMVST to an incomplete interval-valued situation table (IIVST) and construct three-way conflict analysis models based on an IIVST. We use examples to demonstrate the process of constructing conflict, neutrality, and alliance relations of agents on incomplete situation tables. Some algorithms and basic properties are also addressed.