Trust recommendation mechanism-based consensus model for Pawlak conflict analysis decision making

Abstract

Conflict analysis has become a hot issue in management science. In the context of conflict analysis, there are three attitudes for agents to describe the opinion, including supportive, opposite, and neutral. Then, the conflict situation is discussed and analyzed. In this paper, we propose an extended Pawlak conflict model concerning the trust mechanism to solve the problem of the reaching consensus process. Firstly, the degree of conflict is defined by the weights of agents considering the penalty factors, and an extended Pawlak conflict model is presented. Then, the trust recommendation mechanism is proposed to modify the opinions of agents and reach conflict consensus. Four kinds of feedback mechanism are discussed by using four perspectives: 1) without the penalty factors and no limit to the range of adjustments; 2) without the penalty factors and the attitude of agents vary from pessimistic to neutral; 3) with the penalty factors and no limit to the range of adjustments; 4) with the penalty factors and the attitude of agents vary from pessimistic to neutral. Furthermore, this paper presents a process of reaching consensus based on the trust recommendation mechanism for the conflict analysis problem. Finally, a case study is used to validate the effectiveness and superiority of the proposed method. A comparative analysis is completed for the parameters and the maximum alliances could be obtained with the original Pawlak conflict model.

Introduction

Conflict is widespread in our lives and everyone encounters conflict. It is widely used in our lives and plays a vital role in many situations, including commercial negotiations, government, labor disputes, the dispute of economic interest, etc. Conflict is described as a phenomenon that there are inconsistencies in the issues between agents from various backgrounds. The main problem of the research on conflict analysis is how to model the conflict problem, including how to express the uncertainty of agreement, neutrality, and disagreement among the agents. In the past decades, there have been many mathematical tools for conflict analysis and resolution. Furthermore, plenty of scholars applied conflict analysis to various fields [1], [2], [4], [6], [7], [13], [21], [27], [28], [29], [30], [35], [40], including government or commercial negotiations [7], [29], political and litigation [7], [13], [21], [40], tourism development [1], [2], [4], labor disputes [40], marine space conflict [6], mining operations [30] and water allocation issues [13], [14], [27]. Mudasir [35] studied the impact of conflict on people's emotions. All the existing models and methodologies focus on how to establish a conflict model.

Granule computing is a new perspective to analysis the problem in the modern life and many scholars devoted their efforts to the field [5], [15], [19], [20], [47], [49]. Rough set, as a mathematical tool to describe granule information and uncertainty decision-making problems, is widely used in handling conflict analysis recently. Pawlak [26] proposed a model in conflict analysis by the method of rough set and use $\{-1,0,+1\}$ to describe the attitude of agents. From the perspective of agents, the means of $\{-1,0,+1\}$ are opposite, neutral, and support. Then, Pawlak defined the degree of conflict between the variety of agents and classified the conflict situation as conflict, alliance, and no alliance. There are many scholars studying conflict issues in the decades. Ding [9] explored the conflict problem in the decision-making problem. Oliveira Silva [31] presented a new conflict framework of combining Dempster-Shafer Theory (DST) with a PROMETHEE-based approach. Yao et al. [42] explored the application of three-way decision making in conflict analysis and categorize the conflict problem as strong conflict, weak conflict, and none conflict for a better description of conflict issues. Lang et al. [17] classified the agents as conflict set, neutral set, and alliance set combined with the theory of decision rough set. Then, Lang [18] proposed a new conflict analysis model based on the framework of three-way decision making and defined some new measures of alliance and conflict for three-way conflict analysis [19]. Zhi et al. [48] studies conflict analysis problem under one-vote veto combined with three-way concept lattice. Sun [33] extended the Pawlak analysis model and established a new mathematic model on two universes. Sun [32] presented an improved Pawlak conflict model and utilized the thought of three-way decision making based on probability rough sets under the framework of two universes. However, the existing models focus on the extension of the Pawlak conflict model to describe the conflict situation. Fewer researches take into account the issue of the conflict consensus. In real life, there are various conflict problems and they split into two categories, including irreconcilable conflict and reconcilable conflict. Irreconcilable conflict means agents are unwilling to compromise due to harm to self-interest. Reconcilable conflict means agents could compromise for some controversial problems, such as conflict of interest between land acquisition and demolition and the economics dispute issues. For the reconcilable conflict problems, they need a process where agents are willing to modify their opinions to hold the attitude solving problems called consensus reaching process. For this purpose, this paper explores conflict consensus and the resolution of conflict problems. The resolution of conflicts is based on mutual coordination and mutual compromise between the individuals, and finally, a consensus can be reached. Therefore, we propose a trust recommendation mechanism to reconsider the model of conflict analysis based on the conflict consensus.

In the process of conflict analysis, due to the differences in individual knowledge backgrounds and the interests of the representatives, there are inconsistencies in their own opinions. The reaching conflict consensus process plays a significant role in conflict analysis. For the adjustment of opinions, the feedback mechanism is used to control the consensus process and includes two aspects: 1) identification of inconsistent agents; 2) the interactions of their opinions [10], [11], [12], [22], [43], [44], [45], [46]. In the previous research, consensus mechanisms are mainly used to solve group decision-making problems and few people have applied them to conflict problems to resolve conflict situations. In real life, conflicts need to be solved and conflict resolution needs to reach group consensus. Hence, it is practical to apply consensus mechanisms to conflict analysis respectively. Furthermore, the process of reaching conflict consensus needs the trust relationship of the agents. Recently, many scholars study the influence of trust relationships on decision making. Wu [36] proposed a dual trust propagation and produce adjustment opinion by trusting third partners based on a trust mechanism, connecting relationships that were not fully trusted. A distributed language trust decision space was defined [38] and the definition of a new social network was presented, describing the trust relationship between groups of networks. Nevertheless, fewer researches consider the influence of trust relationships on conflict analysis. Therefore, this paper applies the trust relationship model to the resolution of conflict problems to achieve the consistency of conflict situations.

Conflict analysis plays a significant role in our life. The research for the conflict problem is worthy and meaningful. The previous study of conflict analysis is based on the assumption that a conflict situation is static. The conflict situation is dynamically changing instead of a static state. Therefore, based on the assumption that the conflict situation is dynamic, this paper presents a conflict analysis model combining the trust recommendation mechanism with the group consensus of the conflict situation. Individuals make some concessions appropriately, which is a way to resolve conflict issues. Facing conflict situations, keeping conflict issues alive is not what everyone expects. The results agents hope is that some agents can change their opinions while maintaining a certain level of loss or threshold level and conflict consensus could be reached. Traditional conflict issues have rarely studied how to resolve this problem, and group decision-making provides a direction to solve conflict issues. This paper presents a model of conflict analysis and makes conflict problems reach consistency. The research in this article is based on the following assumptions:

1) In conflict, the number of agents in the conflict system is not less than two;

2) The agents are willing to modify the inconsistent issues in a problem-solving manner.

According to the assumptions, we present a model of the conflict analysis based on conflict consensus. In this model, the conflict degree is redefined by the punishment factors, and the rough set is utilized to describe the conflict problems. Then, the trust recommendation mechanism is proposed aiming at interactions for opinions of agents including four models to adjust the opinions. Based on the proposed model, the algorithm for reaching conflict consensus is presented. Finally, a numerical example is utilized to verify the effectiveness and superiority of the proposed model. This paper has two main contributions. On the one hand, the new conflict model is established and the definitions of conflict degree are given. On the other hand, the trust recommendation mechanism is proposed and the minimum adjustment conflict consensus model (MACCM) is built. And we discuss this model in four cases building three models. This paper gives a new direction to research conflict analysis.

The rest of this paper is structured as follows. Section 2 provides the basic concepts regarding the classical Pawlak conflict analysis model. An extended Pawlak conflict analysis model is presented in Section 3. Subsequently, in Section 4, a numerical example is provided to illustrate the consensus reaching process for conflict analysis and verify the effectiveness and practicability of the proposed method. Finally, concluding remarks are presented in Section 5.