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Multi-view clustering is a widely-used technique that seeks to categorize data obtained from various sources. As a representative method, multi-view fuzzy clustering has attracted growing attention. However, it becomes quite challenging when feature-redundant and incomplete data is presented. Despite the existing studies on dimension reduction and imputation methods, several issues remain unresolved. There is an excessive concern on the imputation, without considering that interpolation methods lead to accuracy degradation. Moreover, most of the methods usually process these two steps separately, resulting in inefficiency. To address these issues, we propose a discriminative embedded incomplete multi-view fuzzy c-means clustering method. We construct the indicator matrix to guide the learning of the common membership function, and design the projection matrix to construct embedding spaces. Subsequently, we develop an iterative optimization algorithm that solves the resultant problem. We demonstrate that the projection matrix can be achieved through the utilization of eigenvalue decomposition. Through extensive experimental studies on various benchmark datasets, the proposed method demonstrates the effectiveness and efficiency compared to the existing state-of-the-art clustering algorithms. [ABSTRACT FROM AUTHOR]

A Temporal Knowledge Graph (TKG) is designed for the effective modelling of the temporal relationships and dynamics of entities, events and concepts. Owing to its temporal attributes, a TKG offers greater benefits for reasoning than a static knowledge graph (KG). However, existing approaches for TKG reasoning do not consider coherent relationships between numerous facts, a term borrowed from specific parlance reflecting the interaction between objectives, such as observation and removal agents. This characteristic suggests that the model can obtain more insights from simultaneous coherent relationships. To address this problem, we develop a label-based process to construct a TKG from temporal event data in these domains. Based on the process, we build a specific TKG called Simulated Agent Interaction Knowledge Graph (SAIKG). In addition, we propose a novel TKG reasoning mechanism, termed the Coherence Mode. It is premised on an event coherence manner, enabling the prediction of unknown facts. Extensive experimental studies on different datasets demonstrate the effectiveness of the Coherence Mode integrated with typical models. [ABSTRACT FROM AUTHOR]

Fuzzy logic operations realized by triangular norms (t-norms and t-conorms) have been intensively studied in their theoretical setting and used in various applications. These operations are inherently numeric constructs yielding numeric results. We pose a question whether two t-norms produce distinct results. The problem is formally expressed as a certain hypothesis testing where a null hypothesis concerns equality of medians of membership grades produced by the two triangular norms. In the sequel, we extend a discussion on composition operations constructed with the aid of both t-norms and t-conorms (s–t and t–s composition operators). A comprehensive suite of experiments deals with a collection of commonly encountered triangular norms including those endowed with some parameters. The null hypothesis is tested with regard to the pairs of triangular norms as well as the same triangular norm but having two values of its parameter. We introduce a concept of granular t-norms (more specifically, t-norms operating on granular arguments) and discuss an idea of granular equivalence of logic operators. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models and the extension of classical fuzzy models have been widely used in many domains. From a holistic perspective, regardless of the design methods and rules adopted in a fuzzy model, the determination of fuzzy sets is a pivotal issue. In the proposed methods, instead of traditional data clustering with no directional tendency, we introduce an optimization algorithm that can adjust the position of the prototypes of zero- and first-order fuzzy models to learn internal structure information from the data in the process of parameter identification. Furthermore, to build a granular fuzzy model, the prototypes are then scaled to more robust intervals by generating information granularity with specific semantics such that they split the whole output space. Particle swarm optimization algorithm is applied to adjust both the locations of the prototypes and the allocation of information granularity to improve the performance of the data-driven models. Experimental studies on synthetic and real-world datasets are provided to demonstrate the effectiveness of these methods. [ABSTRACT FROM AUTHOR]