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Top1. Introduction
Conflict is a common phenomenon that is an ever-present part of life. Conflict analysis is used to analyze real-world conflicts that is widely applied in decision-making negotiations and cooperation, issues related to pollution and environmental resources (Delgado & Romero, 2016; He et al., 2020), the hydropolitical and military conflicts (Ali et al.,2018a; Aljefri et al., 2019; Nassereddine et al., 2020), and trade disputes (Walker et al., 2012). Achievements in conflict analysis include both theoretical and application advancements, particularly in diversifying methodologies, such as the combination of rough set theory (Ali et al., 2018b; Lang et al., 2017; Rehman et al., 2020; Sun et al., 2020; Yao, 2019), analytic hierarchy process (AHP) (Ke et al., 2012; Silva et al., 2019), matrix analysis (Wu et al., 2020a; Xu et al., 2010), multi-objective and multi-criteria decision analysis (Fasth et al., 2020; Lee, 2012; Wu et al., 2020b), fuzzy clustering analysis (Munda, 2009), Bayesian belief networks (Giordano et al., 2013), the fuzzy method (Yu et al.,2019a; Wu et al.,2020b), grey system theory (Delgado & Romero, 2016; Han et al., 2013), and Dempster-Shafer Theory (DST) (Silva & Teixeira, 2018; Silva et al., 2019).
Conflict analysis includes four basic elements, namely, the player, a feasible option, a feasible state and preference information of the player. Among these elements, preference information, the drivers of the conflict, which is a stable psychological tendency of a decision-makers (DMs) to a feasible state, has a substantial effect on the evolution of the conflict situation (Hipel et al., 2020). A key problem about preference information in the process of conflict analysis is the preference decision making, that is, the preference ranking of DMs. Numerous studies have increasingly proposed the issues regarding preference information in conflict analysis, which includes preference strength (Yu et al., 2019b; Fasth et al., 2020), hybrid preference (Xu et al., 2013), reciprocal preferences (Wu et al.,2020a), fuzzy preference and uncertain preference (Bashar et al., 2014; Kuang et al., 2013; Li et al., 2004; Li et al., 2014; Yu et al., 2019a; Wu et al., 2020b).
Among the aforementioned studies, Li et al. (2004) suggested a new preference structure to handle the uncertain preference or unknown preference in the comparison of two states, a stability analysis is conducted after obtaining two sets of preference rankings. Lee (2012) established a two-goal game model with multi-objective programming to analyze strategic interaction for conflict analysis. Kuang et al. (2013) applied interval grey numbers to express fuzzy preferences and proposed grey-based solution concepts in a conflict analysis model, which can be used to analyze a conflict with two players having uncertain preferences. Two studies proposed behavioral parameter satisfaction thresholds by using Boolean logic 0-1 interval numbers to depict the players’ fuzzy preferences (Bashar et al., 2012; Bashar et al., 2014). On this basis, Wu et al. (2020b) introduced a preference function represented by interval numbers for both quantitative and qualitative criteria to derive the preference, indifference and incomparability relations of alternatives in conflict analysis. Fasth et al. (2020) presented a cardinal ranking (CAR) method to refine the ordinal ranking regarding the strength of preference between each pair of elements in the ranking. Silva et al. (2019) proposed a methodology integrating Dempster-Shafer Theory (DST) for combining expert knowledge, and analytic hierarchy process (AHP) for ranking the states of a play. Ali et al. (2019) constructs a dynamic conflict model that considers DMs’ evolutional attitude using the option prioritization, which describes how the evolutional attitude of a play ensued change in the overall structure of the conflict.
Following this line of research, we find that all these studies are mainly based on the following assumptions: there is only one decision maker (DM) of each party in a conflict, and differences, such as the DMs’ power and objective weights, are not considered. Preference ranking is consistent with the total order structure; thus, decision makers are precisely aware of their preference. DMs’ preference information are usually derived in conflict analysis based on the reality of the situation (He, 2019). The incommensurability and intransitive of the DMs’ preference decision-making in conflict analysis are neglected. Few studies investigated how decision situations in which the decision making is made by two or more DMs with different preferences of each party and objectives determine the evolution and the equilibrium of a conflict.