In this paper, some issues related to high-dimensional discrete fuzzy numbers are studied. Firstly, an enhancement has been made to the previously established theorem concerning the representation of one-dimensional, discrete fuzzy numerical entities, and the definition of high-dimensional discrete fuzzy numbers has been given based on the idea of this improved representation theorem. Then, we proposed a sufficient condition for a fuzzy set of Rn to be an n-dimensional discrete fuzzy number in order to be used conveniently in application, and a special high-dimensional discrete fuzzy number is introduced based on this result. Subsequently, we derive the average computation formula for an n-cell discrete fuzzy number that arises from the combination of trapezoidal-shaped and triangular-shaped fuzzy numbers, and introduce a partial ordering relation within the n-dimensional discrete fuzzy number domain. In the end, we provide a case to clarify how our obtained findings can be harnessed to establish a priority order for objects that are characterized by multi-channel uncertain discrete digital data.
Uncertainty Classification, Optimal Feature Subset Selection, and Sequential problems are some of the critical problems in machine learning. The optimal feature subset in uncertainty classification plays a critical role. The main problem of classification is the handling of ambiguous data. Various classification methods decrease generalization performance if the ambiguity is present in the input features itself. This paper addresses the above problems by designing an Incremental Fuzzy Extreme Learning Machine algorithm (I-FELM) for batch and an Incremental Fuzzy Online Sequential Extreme Learning Machine algorithm (IF-OSFELM) for sequential input. The optimal feature subset is selected by using seven feature subset selection methods - F-Score, Students’ T-test, Kullback-Leibler divergence, Kolmogorov-Smirnov test, Information Gain, Symmetric uncertainty, and Gain Ratio. For fuzzification, the trapezoidal membership function is used. The experimental results are calculated for the proposed algorithms using the clinical data set. In order to check the efficiency of the proposed algorithms, two Precision Agriculture expert systems are developed: 1. IoT-based plant disease classification and 2. ML-based Crop Yield Prediction that helps the remote farmer with expert advice, in which the proposed algorithms are exploited. Statistical approaches are used for validation and hypothetical testing.
Density peaks clustering (DPC) algorithm is a robust density-based clustering method that is extensively used to analyze datasets characterized by irregular structures and noise. However, it still has some issues. On the one hand, the local density of DPC may cause centers in low-density clusters to be easily ignored. On the other hand, the allocation method of DPC often leads to a chain reaction if the samples are assigned incorrectly. To address above issues, a novel density peaks clustering algorithm based on support point and nearest neighbor relationship (DPC-SN) is proposed. First, the local density is redefined to mitigate the impact of density variations between any two clusters. Second, the concept of boundary degree is presented to detect the boundary points. Then, a multi-step assignment method is proposed to assign non-center points by introducing the idea of shared nearest neighbor, which avoids continuous clustering error. Finally, DPC-SN is compared and analyzed with various typical clustering algorithms on synthetic and real datasets. The experimental results verify the effectiveness of the DPC-SN.
Swarm intelligence (SI) algorithms are widely used in feature selection (FS) problems. Yet, they often get trapped in local optima and have limited search capability. To address these issues, this paper proposes a reflective learning-based particle swarm optimization (PSO) algorithm named RPSO for FS problems. The main goal is to develop an efficient FS method by using domain knowledge and historical update information. Initially, a novel hybrid initialization is designed, incorporating the maximal information coefficient (MIC), ReliefF, and random initialization to generate a high-quality initial population. An exploration and exploitation switch strategy accelerates convergence and prevents stagnation. An adaptive movement strategy improves particle updates by considering feature importance, thereby improving adaptability. Finally, a reflective learning strategy utilizes the historical update information of particles to guide particle movement, thereby enhancing algorithmic reliability. Experimental results on 20 benchmark datasets demonstrate that RPSO outperforms the original PSO and other comparison algorithms across key performance metrics, validating the effectiveness of the four designed strategies. Thus, RPSO is a promising SI algorithm for FS problems.
The third generation of neural networks is called Spiking Neural Networks (SNNs) and presents an energy-efficient and physiologically realistic alternative to the traditional Artificial Neural Networks (ANNs). This review discusses the latest advances in SNN models, learning algorithms, and their implementation on neuromorphic hardware. Besides reinforcement learning techniques such as REINFORCE, supervised techniques, such as SpikeProp and unsupervised Spike-Timing-Dependent Plasticity (STDP), are considered in the context of reward-based learning. The performance of the neurological systems technologies, including the IBM TrueNorth, the FPGA-based, and the Intel Loihi, is checked. Despite significant improvement in parallel processing and energy usage in these systems, there are still problems with accuracy of the synapses, training complexity, and scalability. FPGA-based systems are promising in real-time processing, though they have programmability issues that limit their deployment. The article outlines the key limitation of SNN models, namely their inability to handle large datasets and difficult learning tasks. To advance the performance of neuromorphic systems, research is underway on hybrid SNN-ANN models and memristor-based synaptic storage. This review is aimed at proving that SNNs have potential in such areas as computer vision, robotics, and speech recognition, and their role in overcoming the barrier between artificial and biological neural systems.
Sentiment classification on social media data plays a crucial role in applications such as opinion mining, product analysis, and market forecasting. To overcome limitations in semantic understanding, and model robustness, a novel sentiment classification framework is introduced by integrating Human Memory Optimization with a Stacking Ensemble Fusion Voting (HMSEV) mechanism. A hybrid term frequency-inverse document frequency - bidirectional encoder representations from transformers approach effectively captures both statistical and contextual textual features. Additionally, an enhanced feature selection technique, knowledge-based genetic algorithm-relieff and partial reinforcement optimization, adaptively filters semantically rich, class-relevant features. The HMSEV model fuses CNN and BiLSTM outputs and refines them through human memory optimization, inspired by cognitive recall behavior, to strengthen relevant patterns and suppress noise. Ensemble voting stabilizes predictions across five sentiment classes. Implemented in Python and evaluated on the Amazon dataset, the proposed model achieves 98% accuracy, significantly outperforming existing approaches in both precision and generalizability.
In this paper, we introduce two construction approaches for uninorms on a bounded lattice by virtue of uninorms determined on its sublattices. We also demonstrate that the uninorms obtained by our approaches distinguish themselves from the existing ones because the uninorms defined on sublattices stem from combinations of t-norms and t-conorms. Additionally, we describe some examples to illustrate these uninorms.
Stock market prediction refers to forecasting the future price of a company’s shares or other financial instruments traded on an exchange. Accurately predicting these prices offers the potential for significant profits. However, developing a deep learning (DL) model for stock market forecasting is a challenging task. This is primarily due to the inherent volatility and non-linear patterns in market behavior, along with the limitations of historical data, which often fail to capture all the influencing factors. Additionally, the task becomes more complex because external events and investor sentiment can significantly affect market dynamics, further complicating the modeling process. Hence, this research introduces a novel Stock Market Price Prediction (SMP) model that enhances forecasting accuracy through a multi-phase approach comprising preprocessing, feature extraction, feature selection, and prediction stages. Initially, an adaptive Z-score normalization technique is employed for pre-processing the input data, which effectively standardizes the data, mitigating the impact of different data scales and improving the model’s overall performance. Subsequently, a set of technical indicators-based features, including Average True Range (ATR), Rate of Change (RoC), Relative Strength Index (RSI), Average Directional Movement Index (ADM), William’s %R (WILLR), Money Flow Index (MFI), and Triple Exponential Average (TRIX), are extracted from the preprocessed data to capture a comprehensive view of the market’s behavior. Then, the improved wrapper-filter model in the feature selection phase helps address the challenge of high-dimensionality by identifying and retaining only the most relevant features, thus reducing overfitting and enhancing model efficiency. Finally, the prediction phase leverages an ensemble deep learning model composed of an improved Attention-based SqueezeNet (IA-SQN), Deep Convolutional Neural Networks (DCNN), and GhostNet classifiers for producing the final predicted outcomes. The integration of these models allows the method to harness the strengths of each, improving prediction robustness and accuracy. Furthermore, the suggested model is evaluated against the traditional methods. From the analysis, the proposed EC (IA-SQN[Formula: see text]GSNet[Formula: see text]DCNN) attained less Mean Absolute Error (MAE) of 0.466376, and Mean Squared Logarithmic Error (MSLE) of 0.004, which is exceptionally better than the traditional approaches. Therefore, the proposed method not only improves forecasting accuracy but also enhances decision-making and efficiency in trading operations.
We introduce a group-action-based mechanism that converts a crisp subset [Formula: see text] into an induced fuzzy set by measuring, for each [Formula: see text], the proportion of the orbit of [Formula: see text] that intersects [Formula: see text]. This orbit-density membership is constant on orbits, admits sharp min-max bounds under subgroup refinement, provides a symmetry-induced alternative to classical rough membership, and is compatible with equivariant maps under mild bijectivity/measurecompatibility assumptions. To remove finiteness restrictions, we extend the construction to measurable [Formula: see text]-spaces by replacing orbit cardinalities with an orbit probability system [Formula: see text], yielding a measure-based membership [Formula: see text] that preserves the structural invariance principles of the finite setting. We further propose a simple sanity-check and observability protocol: if the chosen observable is already [Formula: see text]-invariant, the induced membership collapses to a crisp decision, whereas non-invariant observables generically produce nontrivial boundary regions. A numerical illustration on a permutation-symmetry model is included to demonstrate how the framework distinguishes invariant versus observable features in an orbit-structured uncertainty model.
In survey sampling, the accurate estimation of the population mean is often compro- mised by two major challenges: uncertainty arising from incomplete, imprecise, or vague data and correlated measurement errors (CMEs) arising from systematic or interde- pendent inaccuracies in recorded values. The traditional estimation methods generally assume precise measurements and independent errors, making them unsuitable under such conditions. This study proposes a strong methodological framework that incorpo- rates methodologies to address both uncertainty and CMEs. By employing a combina- tion of neutrosophic theory with CME, we develop a neutrosophic estimation framework for the population mean estimation in simple random sampling (SRS) that maintain effeciency under uncertainty and CME. The theoretical properties of the proposed esti- mators are analysed and their performance is demonstrated through a simulation study and some real data applications. The findings confirm that jointly addressing uncertainty and CMEs provides more reliable estimates of the population mean, and enhancing the validity of statistical inferences in complex situations.
Classical risk analysis based on probability theory fails to be effective in situations with incomplete information, where either sufficient historical data is lacking or the real prob- ability cannot be distinguished within a set of probabilities [Formula: see text]. These two types of incomplete information can be characterized by uncertainty theory and sub-linear ex- pectation theory, respectively. In this paper, we conduct risk analysis for systems with incomplete information using a novel framework called U-S chance theory, derived from sub-linear expectation theory and uncertainty theory. Within this framework, the cal- culation formulas for upper and lower chance distributions are obtained. Furthermore, we define the risk index and expected loss, and derive their formulas. Finally, the main results on risk index and expected loss are applied to various incomplete information systems, such as series systems, parallel systems, and so on.
The main objective of this article is to propose novel constructions of uninorms on bound- ed lattices by closure operators or (and) interior operators. Firstly, new constructions of uninorms on bounded lattices via three closure operators are presented. Secondly, new constructions of uninorms on bounded lattices via three interior operators are proposed. This work establishes the conditions for a binary operation to be a uninorm on bounded lattices. We compare the generalized structures presented in this paper with the exist- ing ones and provide some examples to highlight the differences. Finally, additional new constructions of uninorms on bounded lattices are proposed based on closure operators and interior operators.
Link prediction has long been regarded as a fundamental problem in networked data analysis and mining, owing to its importance in a wide range of real-world applications, including social network analysis, recommendation systems, and biological network modeling. Over the years, numerous approaches have been proposed to address this problem, ranging from similarity-based heuristics and probabilistic models to dimensionality reduction and deep learning (DL)-based representation learning techniques. These methods aim to capture latent relational patterns among nodes in order to infer missing or potential links. Recently, graph neural networks (GNNs) have emerged as a powerful DL paradigm for graph-structured data representation learning and have demonstrated strong performance in complex link prediction tasks. In particular, multi-view GNN-based approaches have gained increasing attention by integrating different GNN architectures to capture complementary structural perspectives, such as local neighborhood proximity and global graph topology. This strategy enables the learning of richer node embeddings and improves task-driven prediction performance. However, the integration of multiple GNN layers and architectures often introduces feature uncertainty and noise amplification, which can degrade model stability and predictive accuracy. To address these challenges, this paper proposes AFGNN, a novel framework that integrates adaptive neuro-fuzzy inference with multi-view graph neural learning. By leveraging a robust fuzzy neural architecture with an adaptive inference engine, our proposed AFGNN model dynamically regulates the fusion of view-specific embeddings, enhances reasoning capability, and suppresses uncertainty during representation learning. Extensive experiments on benchmark graph datasets demonstrate the effectiveness and superiority of AFGNN compared with state-of-the-art GNN-based link prediction models.
Metric betweenness and fuzzy betweenness relations are revisited and their relationship with indistinguishability operators is established. Proximity relations (fuzzy reflexive and symmetric binary relations) do not generate betweenness and fuzzy betweenness relations in general but what we call pre-betweenness and fuzzy pre-betweenness rela- tions. How to obtain their betweenness closure, i.e., the smallest betweenness or fuzzy betweenness relation containing them, is studied. Operations between ternary and fuzzy ternary relations similar to the sup-[Formula: see text] products of proximity relations are studied and their relationship with the betweenness closures is established.
Fetal Arrhythmia is an abnormality of cardiac function that causes the heartbeat to be slow, fast, or both. This abnormality results in premature atrial or ventricular contractions that demand transplacental medications such as flecainide at high dosages. To detect this syndrome/disease, this article introduces a Cooperative Feature Classification Technique (CFCT) based on Deep Ensemble Learning (DEL). The process begins with nonlinear cardiogram feature extraction, followed by classification of the extracted features using predefined time intervals. Both steps are performed in sequence, with ensemble factor detection occurring between them. The ensemble factor, in this context, refers to a statistical measure that summarizes the consensus output or agreement among multiple models in the ensemble learning process. If the ensemble factor detected in both steps matches, the dysfunction is classified as an abnormality and verified using existing clinical data.If the ensemble factors differ between the feature extraction and classification steps, the classification of extracted features proceeds without interrupting the extraction process. This approach ensures that the nonlinearity of the cardiogram signals is preserved. The entire process is then repeatedly checked for uniqueness or similarity using the second hidden layer of the deep learning paradigm, continuing until a maximum value is reached. This organized sequence enhances classification precision by reducing errors.
In regression modeling, collinearity among input variables, unevenness in the output observations, and outlier points can affect parameter estimation and reduce the optimality of the models. Several approaches exist to address these problems, including penalized and nonparametric models. However, each has its challenges and performs well only for a specific purpose, leaving the other problems unaddressed. In this paper, with a primary focus on fuzzy regression models, we propose a method based on a new linear uniform model that covers the functions of all these methods, such as reducing and controlling collinearity, coping with unevenness in a dataset, and outlier effects, as well as addressing the problems in their structures, such as the lack of closed form, the nonlinearity of the model parameter formula relation, and the single-purpose nature of the obtained models. Furthermore, when the normal distribution is assumed, it performs better than the best method for model fit, i.e., the least-squares method. In this paper, we demonstrate the optimal performance of the proposed method in addressing the aforementioned problems through various numerical and practical examples and compare it with other existing methods.
We here first propose the idea of lambda-statistical convergence and lambda-strong summability of order gamma involving difference operator for uncertain sequences in conjunction with fuzzy numbers and demonstrate an interesting result. We also define aforesaid notion of lambda-statistical convergence by considering some other setting, namely, measure, distribution, mean, almost surely and uniform almost surely, and then discuss the relationship among these newly defined notions. Furthermore, we offer some illustrative examples to clarify the relationships between these different types of statistical convergence.
This paper extends the study of uncertain sequences by defining the limit superior (lim sup) and limit inferior (lim inf) within uncertainty theory. We establish their properties and propose theorems linking these concepts to existing convergence notions of almost surely, uniformly almost surely, in measure, in mean, and in distribution. Examples illustrate the distinctions between these convergence modes, and we discuss implications for the theoretical development of uncertainty theory.
Globally, e-commerce and social media sites are rapidly improving every day. Social media is a dynamic platform where people can share their thoughts and feelings. Sentiment analysis plays a crucial role in understanding public sentiment. The existing method has some drawbacks, including difficulties in emotion detection and a small amount of data used for analysis. However, for cross-domain sentiment analysis using the WEBEmo dataset, the proposed model combines the convolutional neural network (CNN) and recurrent neural network (RNN) methods. This dataset contains both text and emoticon data. In the pre-processing stage, sentences are divided into individual tokens, which are then converted into numerical form using word embedding techniques such as Word2Vec and the GloVe process. Finally, padding is applied to ensure that each input preparation has an identical length. Convolutional layers are added to reduce dimensionality and extract local features from pre-processed data. Finally, the Long Short Term Memory (LSTM) approach is used to capture both long-range dependencies and context information. This hybrid model’s parameters are being tuned to improve sentiment analysis accuracy. The experimental results show that the proposed hybrid CNN-RNN model outperforms state-of-the-art methods on the WEBEmo dataset, with an accuracy of 96.02%. This model also provides numerous performance analyses. In contrast to DANN, this model improves cross-domain flexibility while overcoming the limitations of individual techniques like LSTM, RNN, and CNN. It is well-defined for sentimental analysis tasks that require both local and sequential feature learning.
This article explores the increasing need for home health care services (HHCS) in developed nations due to rising life expectancy and changing family structures. To this end, we introduce a sophisticated two-stage stochastic programming model designed for the HHCS. The main objective is to efficiently assign caregivers to patients and optimize their travel routes, a complex task made more challenging by factors such as the stochastic nature of patient service times and the need for caregivers to have specific skills to respond to diverse patient demands. The proposed model aims to minimize various costs, including those associated with caregivers, travel, service provision, and penalties for untimely arrivals (for early or late arrivals). Simultaneously, it seeks to maximize patient-caregiver preferences to enhance overall satisfaction and quality of care. One notable aspect of the model is its consideration of stochastic service times, providing a more resilient solution to the inherent unpredictability of HHCS. To validate the effectiveness of the proposed approach, the model undergoes rigorous testing using real-world data obtained from an actual HHC center. The experimental results demonstrate the superior cost efficiency of the proposed model compared to traditional deterministic models, showcasing its potential to significantly improve the overall effectiveness of HHCS in terms of resource allocation, service quality, and patient satisfaction.
