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Three-way Conflict Analysis: Alliance, Conflict, and Neutrality Reducts of Three-valued Situation Tables

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Abstract

In a three-valued situation table, there are different levels of importance for different issues with respect to the alliance, conflict, and neutrality relations, and it is necessary to distinguish all issues as reducible and irreducible elements to filter out the key issues for solving conflicts. However, we have not observed studies of issue reduction for three-valued situation tables in three-way conflict analysis. In this paper, first, we give the matrix representations of alliance, conflict, and neutrality relations and reveal the relationship between two agents in the framework of a matrix. Then, we propose the concepts of alliance, conflict, and neutrality reducts of three-valued situation tables and define reducible and irreducible elements with respect to the alliance, conflict, and neutrality relations. Additionally, we design sequential forward and backward heuristic algorithms for constructing the alliance, conflict, and neutrality reducts. Finally, we give discernibility matrices for computing the sets of all alliance, conflict, and neutrality reducts, and we employ several examples to illustrate how to construct all alliance, conflict, and neutrality reducts. We provide an application of issue reduction to help the government of Gansu Province make a development plan for next year.

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Acknowledgements

We would like to thank the anonymous reviewers very much for their professional comments and valuable suggestions. This work was supported in part by the National Natural Science Foundation of China (Nos. 62076040, 61603063), Hunan Provincial Natural Science Foundation of China (Nos. 2020JJ3034, 2020JJ4598), the Scientific Research Fund of Chongqing Key Laboratory of Computational Intelligence (No. 2020FF04), the Scientific Research Fund of Hunan Provincial Education Department (Nos. 18C0220, 19B027), and a Discovery Grant from the NSERC, Canada.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, P.R. China

    Guangming Lang

  2. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, P.R. China

    Guangming Lang

  3. Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, Hunan, 410081, P.R. China

    Guangming Lang

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  1. Guangming Lang
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Correspondence to Guangming Lang.

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Lang, G. Three-way Conflict Analysis: Alliance, Conflict, and Neutrality Reducts of Three-valued Situation Tables. Cogn Comput 14, 2040–2053 (2022). https://doi.org/10.1007/s12559-021-09905-x

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