Trisection-fusion and fusion-trisection methods of three-way conflict analysis with Pythagorean fuzzy information

Abstract

A basic task of Pawlak conflict analysis is to cluster agents based on their attitudes towards various issues. When ratings of agents are imprecise and uncertain, for example, as represented by a Pythagorean fuzzy situation table, single-measure based methods fall short in ensuring the accuracy of agent clusters. Multi-measure based conflict analysis methods are more effective for generating higher-quality agent clusters. The objective of this paper is to propose two new multi-measure based methods under uncertainty represented by Pythagorean fuzzy sets. We introduce three distinct conflict measures regarding an issue by leveraging the maximum positive and negative agents. The first measure is based on support degrees, the second measure incorporates opposition degrees, and the third measure considers both support and opposition degrees. These measures trisect a set of agents into three disjoint coalitions concerning an individual issue. For multiple issues, we propose two models by combing the two fundamental tasks, namely, trisection and fusion. A trisection-fusion model amalgamates a family of trisections generated from multiple issues based on conflict measures regarding single issues. Matrix representations of trisections are provided, and trisection fusions are transformed into a series of matrix operations. A fusion-trisection model trisects the set of agents according to fused conflict measures on multiple issues. To demonstrate the value of the two models, we apply them in assisting decision-makers in Hunan Province, China, to adjust development plans. The experimental results show that multi-measure based models offer decision-makers more comprehensive guidance.