Diffusion models have emerged as a leading technique for generating images due to their ability to create high-resolution and realistic images. Despite their strong performance, diffusion models still struggle in managing image collections with significant feature differences. They often fail to capture complex features and produce conflicting results. Research has attempted to address this issue by learning different regions of an image through multiple diffusion paths and then combining them. However, this approach leads to inefficient coordination among multiple paths and high computational costs. To tackle these issues, this paper presents a Diffusion Fuzzy System (DFS), a latent-space multi-path diffusion model guided by fuzzy rules. DFS offers several advantages. First, unlike traditional multi-path diffusion methods, DFS uses multiple diffusion paths, each dedicated to learning a specific class of image features. By assigning each path to a different feature type, DFS overcomes the limitations of multi-path models in capturing heterogeneous image features. Second, DFS employs rule-chain-based reasoning to dynamically steer the diffusion process and enable efficient coordination among multiple paths. Finally, DFS introduces a fuzzy membership-based latent-space compression mechanism to reduce the computational costs of multi-path diffusion effectively. We tested our method on three public datasets: LSUN Bedroom, LSUN Church, and MS COCO. The results show that DFS achieves more stable training and faster convergence than existing single-path and multi-path diffusion models. Additionally, DFS surpasses baseline models in both image quality and alignment between text and images, and also shows improved accuracy when comparing generated images to target references.

With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We introduce the Fuzzy Reasoning Chain (FRC) framework, which integrates LLM semantic priors with continuous fuzzy membership degrees, creating an explicit interaction between probability-based reasoning and fuzzy membership reasoning. This transition allows ambiguous inputs to be gradually transformed into clear and interpretable decisions while capturing conflicting or uncertain signals that traditional probability-based methods cannot. We validate FRC on sentiment analysis tasks, where both theoretical analysis and empirical results show that it ensures stable reasoning and facilitates knowledge transfer across different model scales. These findings indicate that FRC provides a general mechanism for managing subtle and ambiguous expressions with improved interpretability and robustness.

The rapid advancement of Large Language Models (LLMs) has significantly enhanced the capabilities of Multi-Agent Systems (MAS) in supporting humans with complex, real-world tasks. However, MAS still face challenges in effective task planning when handling highly complex tasks with uncertainty, often resulting in misleading or incorrect outputs that hinder task execution. To address this, we propose XAgents, a unified multi-agent cooperative framework built on a multipolar task processing graph and IF-THEN rules. XAgents uses the multipolar task processing graph to enable dynamic task planning and handle task uncertainty. During subtask processing, it integrates domain-specific IF-THEN rules to constrain agent behaviors, while global rules enhance inter-agent collaboration. We evaluate the performance of XAgents across three distinct datasets, demonstrating that it consistently surpasses state-of-the-art single-agent and multi-agent approaches in both knowledge-typed and logic-typed question-answering tasks. The codes for XAgents are available at: https://github.com/AGI-FHBC/XAgents.

In the field of artificial intelligence, understanding, distinguishing, expressing, and computing the negation in knowledge is a fundamental issue in knowledge processing and research. In this paper, we examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics etc. Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective: contradictory negation, opposite negation, and intermediary negation. To establish a mathematical foundation that fully reflects the intrinsic connections, properties, and laws of these different forms of negation, we introduce SCOI: sets with contradictory negation, opposite negation and intermediary negation, and LCOI: logic with contradictory negation, opposite negation and intermediary negation, and we proved the main operational properties of SCOI as well as the formal inference relations in LCOI.

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.

Since its inception, Fuzzy Set has been widely used to handle uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs) have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degree. To address this, Interval Type-2 Fuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, which enhanced flexibility in modelling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs and that limits the interpretability and effectiveness of decision models. This study proposes a socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and its application in multicriteria decision-making (MCDM) problems. Our methodology is structured in two phases. The first phase involves an interactive process between the DM and the decision analyst, in which a modified version of Deck-of-Cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgment and that resulted in an IT2FS model that better captures uncertainty in DM's linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining an appropriate mathematical representation of such information, aggregation rules, and an admissible ordering principle. The proposed framework enhances the reliability and effectiveness of fuzzy decision-making not only by accurately representing DM's personalized semantics of linguistic information.

Fine-grained emotion recognition (FER) plays a vital role in various fields, such as disease diagnosis, personalized recommendations, and multimedia mining. However, existing FER methods face three key challenges in real-world applications: (i) they rely on large amounts of continuously annotated data to ensure accuracy since emotions are complex and ambiguous in reality, which is costly and time-consuming; (ii) they cannot capture the temporal heterogeneity caused by changing emotion patterns, because they usually assume that the temporal correlation within sampling periods is the same; (iii) they do not consider the spatial heterogeneity of different FER scenarios, that is, the distribution of emotion information in different data may have bias or interference. To address these challenges, we propose a Spatio-Temporal Fuzzy-oriented Multi-modal Meta-learning framework (ST-F2M). Specifically, ST-F2M first divides the multi-modal videos into multiple views, and each view corresponds to one modality of one emotion. Multiple randomly selected views for the same emotion form a meta-training task. Next, ST-F2M uses an integrated module with spatial and temporal convolutions to encode the data of each task, reflecting the spatial and temporal heterogeneity. Then it adds fuzzy semantic information to each task based on generalized fuzzy rules, which helps handle the complexity and ambiguity of emotions. Finally, ST-F2M learns emotion-related general meta-knowledge through meta-recurrent neural networks to achieve fast and robust fine-grained emotion recognition. Extensive experiments show that ST-F2M outperforms various state-of-the-art methods in terms of accuracy and model efficiency. In addition, we construct ablation studies and further analysis to explore why ST-F2M performs well.

The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data using fuzzy color model. By taking fuzzy approach to color modeling, we could make a soft decision for the vague regions between neighboring colors. The proposed fuzzy color model defined a three dimensional fuzzy color ball and color membership computation method with two inter-color distances. With the fuzzy color model, we developed a new fuzzy clustering algorithm for an efficient partition of color data. Each fuzzy cluster set has a cluster prototype which is represented by fuzzy color centroid.

ABSTRACT: A new cluster validity index is proposed for fuzzy clusters obtained from fuzzy c-means algorithm. The proposed validity index exploits inter-cluster proximity between fuzzy clusters. Inter-cluster proximity is used to measure the degree of overlap between clusters. A low proximity value refers to well-partitioned clusters. The best fuzzy c-partition is obtained by minimizing inter-cluster proximity with respect to c. Well-known data sets are tested to show the effectiveness and reliability of the proposed index.