In the traditional graph model for conflict resolution (GMCR), decision-makers (DMs) are often assumed to have equal influence and operate independently, using actual or fuzzy numbers to quantify their preferences. However, in some conflicts, a leader with more significant power may emerge to guide the situation. In addition, DMs usually express their preferences linguistically to capture subjective nuances and uncertainties, but their preferences can be incomplete due to limitations in knowledge, time, or uncontrollable variables. To address these issues, our study extends incomplete linguistic preference relations (ILPRs) to conflict resolution within a power asymmetry framework. Initially, we define distinct graph models tailored for the leader and follower. Subsequently, considering DMs’ attitudes toward the risks inherent in ILPRs, we develop four types of logical representations of three incomplete linguistic power asymmetry stability concepts (ILPASCs) for the leader and five for the follower, resulting in 32 stability concepts under power asymmetry. We also propose matrix representations for these stability concepts to aid calculations and explore their interrelationships. Finally, we present an empirical case study on power asymmetry in environmental governance to validate the effectiveness and superiority of our developed method.

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimize the training error of the models on historical training data or alternatively to iteratively minimize the intracluster variance of the clusters obtained via online data partitioning. This recognizes the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimizing the training error may potentially lead to overfitting while minimizing the intracluster variance does not necessarily ensure the optimized prototype-based models to attain improved classification outcomes. To achieve better classification performance while avoiding overfitting for zero-order EISs, this article presents a novel multiobjective optimization approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final nondominated set of the resulting optimized models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimization approach in improving the classification performance of zero-order EISs.

In this article, a new data-driven autonomous fuzzy clustering (AFC) algorithm is proposed for static data clustering. Employing a Gaussian-type membership function, AFC first uses all the data samples as microcluster medoids to assign memberships to each other and obtains the membership matrix. Based on this, AFC chooses these data samples that represent local models of data distribution as cluster medoids for initial partition. It then continues to optimize the cluster medoids iteratively to obtain a locally optimal partition as the algorithm output. Moreover, an online extension is introduced to AFC enabling the algorithm to cluster streaming data chunk-by-chunk in a “one pass” manner. Numerical examples based on a variety of benchmark problems demonstrate the efficacy of the AFC algorithm in both offline and online application scenarios, proving the effectiveness and validity of the proposed concept and general principles.

In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches.