Fuzzy Sets and Systems最新文献

This paper mainly considers the post-inverse matrix of a fuzzy relation matrix in terms of addition-min composition. A necessary and sufficient condition for the consistency of the inverse matrix problem is given by transforming the problem into a series of particular fuzzy relation equations. The uniqueness of the post-inverse is also investigated. Furthermore, it is proved that the search for the minimal solutions of the particular fuzzy relation equations can be converted into solving a linear system. Based on these discussions, an algorithm is constructed for solving a post-inverse of a given fuzzy relation matrix.

In this paper, we investigate several classes of binary operations within the preordered framework. First, we give the definition of quasi-t-subnorm on preordered sets. Subsequently, we research two classes of quasi-t-subnorms by means of Adjunctions and Left Galois Connections respectively. Meanwhile, we introduce new preorders differing from the inclusion order on powersets. Importantly, quasi-t-subnorms can be defined on powersets with preorders. Then we get a class of extensive binary operations via Adjunctions between preordered sets and the preordered sets consisting of powersets, which generalizes the previous results. The relationship between related binary operations is explored at last.

Consider $(Y,\rho )$ as a complete metric space and $S$ as the space of probability Borel measures on Y. Let ${\bar{\dim }}_B^{\Psi ,\Phi }\left(E\right)$ be the general upper box dimension of the set $E\subset Y$. We begin by proving that the general packing dimension of the typical compact set, in the sense of the Baire category, is at least $\inf \left\{{\bar{\dim }}_B^{\Psi ,\Phi }\right(B(x,r)\left)\right|x\in Y,r>0\}$ where $B(x,r)$ is the closed ball in Y with center at x and radii $r>0$. Next, we obtain some estimates of the general upper and lower box dimensions of typical measures in the sense of the Baire category. Finally, we demonstrate that if $S$ is equipped with the weak topology and under some assumptions then the set of measures possessing the general upper and lower correlation dimension zero are residual. Furthermore, the general upper correlation dimension of typical measures (in the sense of the Baire category) is approximated through the general local lower and upper entropy dimensions of Y.

Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we prove that it is possible to define a simplification logic on fuzzy sets in which the membership value structure is not necessarily distributive. For this purpose, we replace the structure of the complete dual Heyting algebra by the so-called weak complete dual Heyting algebra. We demonstrate the soundness and completeness of this simplification logic, and provide a characterisation of the operations defining weak complete dual Heyting algebras.

Three basic issues of granular computing are construction or definition of granules, measures of granules, and computation or reasoning with granules. This paper reviews the main theories of granular computing and introduces the definition of spatial granules. A granule is composed of one or more atomic granules. The rationality of this definition is explained from the four aspects: simplicity, applicability, measurability and visualization. A one-to-one correspondence is established between the granules and the points in the unit hypercube, and the coarsening and refining of the granules are the descending and ascending dimensions of the points, respectively. The weak fuzzy tolerance relation and weak fuzzy equivalence relation are defined so as to study on all fuzzy binary relations. The notion of layer granularity/fineness is introduced and each granule can be easily denoted by two numbers, which can be used to pre-process macro knowledge space and greatly improve the search speed. This paper also discusses the main properties of granules including the necessary and sufficient conditions of coarse-fine relation and the main principles of granular space.

Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-overlap and pseudo-grouping functions, respectively. These functions can be applied in problems where distinct orders of their arguments yield different values, i.e., in non-symmetric contexts. Intending to reduce the complexity of pseudo-overlap and pseudo-grouping functions, we propose new construction methods for these functions from generalized concepts of additive and multiplicative generators. We investigate the isomorphism between these families of functions. Finally, we apply these functions in an illustrative problem using them in a time series prediction combined model using the IOWA operator to evidence that using these generators and functions implies better performance.

The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for instance, the ability to anticipate the computational cost required for generating operators with different properties. This is of paramount importance in image processing and decision making scenarios, where the identification of the most optimal operator is essential. Furthermore, it facilitates the examination of how constraining a certain property is in relation to its parent class. As a consequence, this paper aims to compile the main existing formulas and the methodologies with which they have been derived. Additionally, we introduce some novel formulas for the number of smooth discrete aggregation functions with neutral element or absorbing element, idempotent conjunctions, and commutative and idempotent conjunctions.

In this article, an Interval Type-3 Fuzzy Logic System (IT3FLS) for enhancing the performance in Bee Colony Optimization (BCO) is outlined. The efficiency of the IT3FLS approach is verified with results on a set of benchmark mathematical functions. The IT3FLS provides an approach that helps to identify the optimal values in $\alpha$ and $\beta$ parameters that allows to improve the performance in the original BCO. The IT3FLS approach exhibits advantages in the optimization of the benchmark functions. It can be noted that a IT3FLS exhibits better results in the minimal values of the set of mathematical functions. The experimentation demostrates that the implementation of the IT3FLS approach enhances the performance of BCO when compared with respect to the variants utilizing Generalized Type-2 FLS (GT2FLS), Interval Type-2 FLS (IT2FLS) and Type-1 FLS (T1FLS).

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.