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Three-way conflict analysis with similarity degree on an issue set

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Abstract

The present paper introduces a new model of three-way conflict analysis with similarity degree on an issue set. Specifically, we introduce an evaluation of similarity degree, from a relative quantitative point of view, to evaluate the attitude similarity between any two agents. Based on similarity degree, we define a trisection of all pairs of agents on an issue set, and propose a three-level conflict model induced by such a trisection. More importantly, we solve the threshold-selection problem for three-level conflict analysis on multiple issues. We prove that the trisection model (resp. the three-level conflict model) defined in this paper is a conservative extension of the corresponding trisection model (resp. three-level conflict model) defined in Yao 2019 on multiple issues. Therefore, the present paper extends and improves the results of Yao 2019 on multiple issues.

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Notes

  1. When \(Y=\{v\}\), the difference degree (resp. similarity degree) of \(u_i\) and \(u_j\) on Y should be technically denoted by \(d_{\{v\}}(u_i,u_j)\) (resp. \(e_{\{v\}}(u_i,u_j)\)). However, we will simply use \(d_{v}(u_i,u_j)\) (resp. \(e_{v}(u_i,u_j)\)), when such expression does not cause ambiguity.

  2. Since \(A^{(\alpha ,\beta )}_Y\) is the result of replacing in \(C^{(\alpha ,\beta )}_Y\) all \(SC^{\alpha }_Y,\) \(WC^{(\alpha ,\beta )}_Y\) and \(NC^{\beta }_Y\) by \(NA^{\alpha }_Y,\) \(WA^{(\alpha ,\beta )}_Y\) and \(SA^{\beta }_Y\), respectively, in this part we only provide the ways of obtaining the final optimal three-level conflict, with the ways of obtaining the final optimal three-level alliance being similar.

  3. Here we informally express the three sets of pairs of agents, the meaning of which should be clear.

  4. As we see, the concept of reference agent, namely Definition 3.33, is defined on any issue set Y, and Y may contain multiple issues. However, in this paper we will only use this concept to induce the trisection of all agents on a single issue. In the future, we will use Definition 3.33 to induce the trisection of all agents on multiple issues.

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Acknowledgements

The authors are particularly grateful to the anonymous reviewers for their valuable comments and helpful suggestions. This work is supported by the Fundamental Research Funds for the Central Universities (No. YJS2215) and the Natural Science Basic Research Program of Shaanxi Province (No. 2023-JC-YB-005).

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Wenyan Xu & Bing Jia

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  1. Wenyan Xu
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Correspondence to Wenyan Xu.

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Xu, W., Jia, B. Three-way conflict analysis with similarity degree on an issue set. Int. J. Mach. Learn. & Cyber. 15, 405–427 (2024). https://doi.org/10.1007/s13042-023-01917-3

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