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Conflict analysis aims to identify the intrinsic reasons and find a feasible consensus strategy for a conflict situation. Rough set theory was used to study conflict analysis decision-making in the late 90s. The basic way to express the attitudes of every agent are against, favorable and neutral for any issue in the original Pawlak conflict analysis model. The notion of three-way decision (3WD) was initially developed as a means to interpret decision rules induced in probabilistic rough sets. In this paper, we first present the framework of three-way decision (3WD) using probabilistic rough set over two universes. With respect to the probabilistic positive, negative and boundary regions over two universes, we build the rules for making a decision of acceptance, rejection and non-commitment, respectively. So, there is an one-to-one correspondence between the three attitudes of every agent for any issue in a conflict situation and the three decisions in the probabilistic rough set over two universes. Based on this, we present an improved Pawlak conflict analysis model by using the principle of three-way decision based on probabilistic rough set over two universes. We construct the conflict decision-making information system under the framework of two universes. Then we define the favorable issues set and against issues set of any agent between the agent set and the dispute set over conflict decision-making information system, respectively. Furthermore, according to the principle of Bayesian risk decision-making process over two universes, we calculate the threshold value parameters used in the lower and upper approximations of a feasible consensus strategy over conflict decision-making information system. Finally, we present the decision rules and the algorithm of finding a feasible consensus strategy for conflict situation based on three-way decision-making with the probabilistic approximations over two universes. Compared with the original Pawlak conflict analysis model, the proposed model not only provides a new perspective and methodology to handle the conflict analysis problems but also overcomes the limitations of the original model. Lastly, we illustrate the idea and basic principles established in this paper by analyzing a conflict decision-making scenario. [ABSTRACT FROM AUTHOR]

As financial markets grow increasingly complex and dynamic, accurately predicting stock price trends becomes crucial for investors and financial analysts. Effectively identifying and selecting the most predictive attributes has become a challenge in stock trends prediction. To address this problem, this study proposes a new attribute reduction model. A rough set theory model is built by simplifying the prediction process and combining it with the long short-term memory network (LSTM) to enhance the accuracy of stock trends prediction. Firstly, the Ensemble Empirical Mode Decomposition (EEMD) is utilized to decompose the stock price data into a multi-granularity information system. Secondly, due to the numerical characteristics of stock data, a kernel function is applied to construct binary relationships. Thirdly, recognizing the noise inherent in stock data, the double-quantitative rough set theory is utilized to improve fault tolerance during the construction of decision attributes' lower and upper approximations. Moreover, calculate the correlation between conditional and decision attributes, and retain highly correlated conditional attributes for prediction. The kernel multi-granularity double-quantitative rough set based on the EEMD (EEMD-KMGDQRS) model proposed identifies the key factors behind stock data. Finally, the efficacy of the proposed model is validated by selecting 356 stocks from diverse industries in the Shanghai and Shenzhen stock markets as experimental samples. The results show that the proposed model improves the generalization of attribute reduction results through a fault tolerance mechanism by combining kernel function with multi-granularity double-quantitative rough set, thereby enhancing the accuracy of stock trends prediction in subsequent LSTM prediction processes. [ABSTRACT FROM AUTHOR]