Fuzzy Sets and Systems最新文献

With the growing complexity and frequency of cyber threats, there is a pressing need for more effective defense mechanisms. Machine learning offers the potential to analyze vast amounts of data and identify patterns indicative of malicious activity, enabling faster and more accurate threat detection. Ensemble methods, by incorporating diverse models with varying vulnerabilities, can increase resilience against adversarial attacks. This study covers the usage and evaluation of the relevance of an innovative approach of ensemble classification for identifying intrusion threats on a large CICIDS2017 dataset. The approach is based on the distributivity equation that appropriately aggregates the underlying classifiers. It combines various standard supervised classification algorithms, including Multilayer Perceptron Network, k-Nearest Neighbors, and Naive Bayes, to create an ensemble. Experiments were conducted to evaluate the effectiveness of the proposed hybrid ensemble method. The performance of the ensemble approach was compared with individual classifiers using measures such as accuracy, precision, recall, F-score, and area under the ROC curve. Additionally, comparisons were made with widely used state-of-the-art ensemble models, including the soft voting method (Weighted Average Probabilities), Adaptive Boosting (AdaBoost), and Histogram-based Gradient Boosting Classification Tree (HGBC) and with existing methods in the literature using the same dataset, such as Deep Belief Networks (DBN), Deep Feature Learning via Graph (Deep GFL). Based on these experiments, it was found that some ensemble methods, such as AdaBoost and Histogram-based Gradient Classification Tree, do not perform reliably for the specific task of identifying network attacks. This highlights the importance of understanding the context and requirements of the data and problem domain. The results indicate that the proposed hybrid ensemble method outperforms traditional algorithms in terms of classification precision and accuracy, and offers insights for improving the effectiveness of intrusion detection systems.

This paper proposes an integrated robust stabilization and anti-disturbance control scheme for nonlinear systems using a polynomial fuzzy model approach. To estimate unknown disturbances, an equivalent-input-disturbance (EID) estimator is employed. The proposed approach incorporates a novel fuzzy model assisted by EID estimator into the sum-of-squares-based approach, utilizing a polynomial fuzzy model-based observer to estimate the disturbance effect. A suitable fuzzy rule-based control law is developed by utilizing the parallel distributed compensation approach and the output of the EID estimator. To ensure stability, fuzzy membership functions are converted into sum-of-square polynomials using a polynomial curve fitting approach, allowing their exact shape information to be used in the stability condition. The addressed system is transformed into an augmented system by incorporating the system, observer, and filter states, simplifying the analysis. Gain matrices for the controller and observer are obtained using Lyapunov stability theory and sum-of-squares methods to confirm asymptotic stabilization of the fuzzy system. Two numerical examples are presented to demonstrate the effectiveness of the proposed control design method.

This paper proposes a methodology for assessing the subjective policy reflection in national trade policies through the use of Choquet integral. Specifically, we introduce three fuzzy measures that reflect different policies based on the trade items included in data on the annual trade amounts of selected national animal products from 2010 to 2020. The Choquet expected utility serves as a tool for evaluating subjective policy reflection, allowing for the comparison of national economic policies across selected countries. To demonstrate the practical application of the proposed methodology, we provide specific numerical values that represent the evaluation of subjective policy reflection. Furthermore, we present a decision-making strategy that pertains to the allocation of subsidies on imports and exports of trade transaction amounts, assuming that government subsidies are budgeted using the Choquet expected utility. The proposed methodology offers a valuable framework for policymakers and stakeholders, facilitating in-depth analysis and improvement of the effectiveness of national trade policies.

In the existing works, the classical fuzzy relation inequality (FRI) with double-composed operators has been introduced to describe the P2P network system. In this work, considering the successful rate of the line connection within the P2P network system, we establish the so-called tri-composed FRI, with a weighted-max-min composition, for the first time. We study the solutions induced through paths and further construct the complete solution set of the tri-composed FRI using the path-induced solutions. Moreover, the whole solution set could be fully determined by all the path-induced solutions and its unique maximum solution. Furthermore, considering a specific optimal management objective in the P2P network, we further study the min-max optimization problem with the tri-composed FRI constraints. A path-based algorithm is proposed for handling the problem we studied, accompanied by an illustrative example.

We consider the binomial decomposition of ordered weighted averaging (OWA) functions proposed by Calvo and De Baets (1998) in the framework of Choquet integration. Our aim in the paper is to further investigate the equivalence between the two representations of OWA functions involved in the binomial decomposition: the usual canonical representation in terms of the order statistics, and the binomial representation in terms of the binomial OWA functions. We describe and discuss in detail the linear transformations that relate the coefficients of these two equivalent representations: the original expression of the weights in terms of the coefficients of the binomial representation, and its inverse, the expression of those coefficients in terms of the weights. In both cases simple and direct proofs are presented. Moreover, we consider the linear transformations between the two representations in the general linear algebra framework of unconstrained linear combinations of binomial OWA functions. In this perspective we obtain compact matrix expressions for the linear transformations, which also offer new insight on the geometry of the coefficient constraints in the binomial representation of OWA functions.

The generalized extended Bonferroni mean (GEBM) is a powerful tool for modeling the complex process of aggregating information, whether it is homogeneously or heterogeneously connected, within a composite aggregation structure. It maintains several favorable characteristics and effectively captures the diverse and interconnected nature of expert opinions or criteria, which is commonly observed in various decision-making contexts. This research expands upon the existing GEBM framework by applying it to the specific domains of q-rung orthopair fuzzy sets (q-ROFSs) and extended q-rung orthopair fuzzy sets (Eq-ROFSs). Furthermore, it examines the transformation processes among different variants of GEBMs. To facilitate the development of generalized aggregation functions, the de Morgan triplets for q-ROFSs and Eq-ROFSs are established. By introducing an isomorphism, the transformation relationship between the aggregation functions for q-ROFSs and Eq-ROFSs is analyzed. Based on this foundation, the Bonferroni mean de Morgan triplet-based GEBMs for q-ROFSs and Eq-ROFSs are proposed, and the keeping-order relations for these proposed GEBMs are discussed. Finally, several special cases of the GEBMs for q-ROFSs and Eq-ROFSs are obtained, and several relevant theorems are verified.

This paper presents a novel hybrid architecture, denoted as EFNN-Nul0 (evolving neuro-fuzzy system based on null-unineurons), meticulously crafted for stress identification within the realm of pattern classification. The model seamlessly integrates neural networks, fuzzy systems, and n-uninorms to cultivate knowledge within an adaptive, real-time learning context. Neuro-fuzzy rules, encapsulating interdependencies among input features through IF-THEN type relationships, are formulated utilizing null-unineurons derived from n-uninorms. This construction enables the articulation of both AND- and OR-connections, thereby augmenting the interpretability of the generated rules. The evolution of neurons is facilitated by an extended adaptation of the autonomous data partition method (ADPA). To dynamically interpret the evolution of rules, the paper introduces (i) a mechanism that tracks changes in rules over data stream samples, providing insights into the process dynamics as a structural active learning component, and (ii) a concept for incrementally updating feature weights. These weights encapsulate the varying impact levels of features on stress identification, enabling the reduction of rule length by effectively masking out less significant features. The outcomes of the rules are represented by certainty vectors, recursively updated through an indicator-based recursive weighted least squares (I-RWLS) approach. Neuron activation levels play a pivotal role in determining the weights, ensuring stable local learning. The effectiveness of the proposed model is substantiated through a comprehensive comparison with existing hybrid and evolving approaches in the literature, focusing on binary and multi-class pattern classification. Aspects that identify special characteristics of neuro-fuzzy models related to interpretability will also be demonstrated in this work. The results demonstrate the model's superior performance, characterized by consistently higher accuracy trend lines over time. Furthermore, the model's interpretability is underscored by the coherent neuro-fuzzy rules, contributing to its remarkable accuracy (the EFNN-Nul0 achieved approximately 99% accuracy in stress identification), establishing its efficacy in addressing stress identification within classification problems.

By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize the pairs of fuzzy sets that form fuzzy rough sets w.r.t. a t-similarity relation θ on U, for certain t-norms and implicators. If U is finite or the range of θ and of the fuzzy sets is a fixed finite chain, we establish conditions under which fuzzy rough sets form lattices. We show that this is the case for the min t-norm and any S-implicator defined by an involutive negator and the max co-norm.

Fuzzifying the crisp functions is a well-known methodology to study the problems under fuzzy uncertainty. The traditional way for fuzzifying the crisp functions is based on the extension principle. In this paper, by referring to the expression in decomposition theorem, we present a new methodology to fuzzify the crisp functions for non-normal fuzzy sets. The main purpose of this paper is to establish the equivalence between the fuzzy functions obtained from the extension principle and the expression in decomposition theorem under the proposed concept of compatibility. The practical cases regarding the equivalences are also studied in order to be used for the practical problems.

Consider a separable metric space $(X,d)$, and let $\left(K\right(X),\tilde{d})$ denote the space of non-empty compact subsets of X equipped with the Hausdorff metric. This paper aims to introduce and investigate the concepts of two general fractal dimensions and general dimensions within the framework of $\left(K\right(X),\tilde{d})$. In particular, we explore a relationship between the general fractal dimensions of a set Z of a self-similar sequence space and their counterparts in the space of compact subsets $K\left(Z\right)$.