Fuzzy Sets and Systems最新文献

{"title":"General fractal dimensions of typical sets and measures","authors":"Rim Achour,&nbsp;Bilel Selmi","doi":"10.1016/j.fss.2024.109039","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109039","url":null,"abstract":"<div><p>Consider <span><math><mo>(</mo><mi>Y</mi><mo>,</mo><mi>ρ</mi><mo>)</mo></math></span> as a complete metric space and <span><math><mi>S</mi></math></span> as the space of probability Borel measures on <em>Y</em>. Let <span><math><msubsup><mrow><mover><mrow><mi>dim</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>B</mi></mrow><mrow><mi>Ψ</mi><mo>,</mo><mi>Φ</mi></mrow></msubsup><mo>(</mo><mi>E</mi><mo>)</mo></math></span> be the general upper box dimension of the set <span><math><mi>E</mi><mo>⊂</mo><mi>Y</mi></math></span>. We begin by proving that the general packing dimension of the typical compact set, in the sense of the Baire category, is at least <span><math><mi>inf</mi><mo>⁡</mo><mrow><mo>{</mo><msubsup><mrow><mover><mrow><mi>dim</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>B</mi></mrow><mrow><mi>Ψ</mi><mo>,</mo><mi>Φ</mi></mrow></msubsup><mo>(</mo><mi>B</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>r</mi><mo>)</mo><mo>)</mo><mspace></mspace><mo>|</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Y</mi><mo>,</mo><mi>r</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></mrow></math></span> where <span><math><mi>B</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>r</mi><mo>)</mo></math></span> is the closed ball in <em>Y</em> with center at <em>x</em> and radii <span><math><mi>r</mi><mo>&gt;</mo><mn>0</mn></math></span>. 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 <span><math><mi>S</mi></math></span> 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 <em>Y</em>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141323410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attribute implications with unknown information based on weak Heyting algebras","authors":"Pablo Cordero,&nbsp;Manuel Enciso,&nbsp;Ángel Mora,&nbsp;Francisco Pérez-Gámez","doi":"10.1016/j.fss.2024.109026","DOIUrl":"10.1016/j.fss.2024.109026","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001726/pdfft?md5=ee2ac4c6b8ecd2ed61b7fd43fe035028&pid=1-s2.0-S0165011424001726-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141280384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Towards the definition of spatial granules","authors":"Liquan Zhao,&nbsp;Yiyu Yao","doi":"10.1016/j.fss.2024.109027","DOIUrl":"10.1016/j.fss.2024.109027","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141278881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reduction of complexity using generators of pseudo-overlap and pseudo-grouping functions","authors":"Mikel Ferrero-Jaurrieta ,&nbsp;Rui Paiva ,&nbsp;Anderson Cruz ,&nbsp;Benjamín Bedregal ,&nbsp;Xiaohong Zhang ,&nbsp;Zdenko Takáč ,&nbsp;Carlos López-Molina ,&nbsp;Humberto Bustince","doi":"10.1016/j.fss.2024.109025","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109025","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001714/pdfft?md5=3ed86ab47bd97e1aac2a168c62d02481&pid=1-s2.0-S0165011424001714-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Legal fuzzy incidence blocks and legal flow reduction sets with application to water distribution networks","authors":"Gayathri G. ,&nbsp;Sunil Mathew ,&nbsp;J.N. Mordeson","doi":"10.1016/j.fss.2024.109024","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109024","url":null,"abstract":"<div><p>Directed fuzzy incidence graphs (DFIGs) are fuzzy incidence structures where each edge and incidence pair has a specific direction. In these graphs, the relationships are not symmetric, making it easier to identify the extent of interaction between nodes and arcs. The comprehensive investigation of connectivity in directed fuzzy incidence graphs holds the potential to provide solutions for a wide range of real-world problems including traffic flow optimization in one-way traffic networks and migration analysis of refugees across various countries. The main objective of this paper is to extend the connectivity concepts of directed fuzzy incidence graphs, which help to analyze various stochastic networks influenced by external factors. The major concepts discussed in this article are legal fuzzy incidence blocks, legal flow reduction sets, and the DFIG-version of Menger's theorem. Directed fuzzy incidence graphs having no legal flow reduction nodes are defined as legal fuzzy incidence blocks (LFI-blocks). Legal flow reduction nodes (LFR-nodes) are distinct elements, the elimination of which results in a reduction of the directed incidence connectivity between some other pair of nodes. Since LFI-blocks lack these elements, the removal of none of the nodes reduce the legal flow between other pair of nodes. Consequently, for each node under consideration, any other pair of nodes connected by at least one <em>di</em>-path must possess a widest legal <em>di</em>-path which avoids that specific node. LFI-blocks exhibit differing attributes in contrast to their counterparts in fuzzy graphs and fuzzy incidence graphs. This viewpoint motivated the authors to investigate these distinctions and assess the possibility of defining equivalent conditions for LFI-blocks, similar to the equivalent conditions established for fuzzy blocks and fuzzy incidence blocks. A key characteristic of legal fuzzy incidence blocks is their capacity to incorporate legal flow reduction links, even allowing for the presence of shared nodes among two legal flow reduction links. This contrasts with fuzzy graphs and fuzzy incidence graphs, where if two fuzzy bridges happen to share a common node, it results in that node being a fuzzy cutnode. Two equivalent conditions are proposed for a directed fuzzy incidence graph to become a legal fuzzy incidence block. It is shown that any two nodes in a legal fuzzy incidence block which are connected by at least one <em>di</em>-path, but not by a legal flow reduction link will have at least two internally disjoint widest legal <em>di</em>-paths joining them. To identify the maximum number of such internally disjoint widest legal <em>di</em>-paths, the notion of legal flow reduction set of nodes and arcs is introduced. These sets are characterized using widest legal <em>di</em>-paths. Moreover, the DFIG-version of Menger's theorem for nodes is established, which explains the relation between number of internally disjoint widest legal <em>d","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141249860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A survey on the enumeration of classes of logical connectives and aggregation functions defined on a finite chain, with new results","authors":"Marc Munar ,&nbsp;Miguel Couceiro ,&nbsp;Sebastia Massanet ,&nbsp;Daniel Ruiz-Aguilera","doi":"10.1016/j.fss.2024.109023","DOIUrl":"10.1016/j.fss.2024.109023","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001696/pdfft?md5=b68d5fcda92a3ef66deb2634bd618add&pid=1-s2.0-S0165011424001696-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141134216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Type-3 fuzzy dynamic adaptation of Bee colony optimization applied to mathematical functions","authors":"Leticia Amador-Angulo ,&nbsp;Oscar Castillo ,&nbsp;Patricia Melin ,&nbsp;Zong Woo Geem","doi":"10.1016/j.fss.2024.109014","DOIUrl":"10.1016/j.fss.2024.109014","url":null,"abstract":"<div><p>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 <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> 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).</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141139472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effectiveness of an ensemble technique based on the distributivity equation in detecting suspicious network activity","authors":"Ewa Rak ,&nbsp;Jaromir Sarzyński ,&nbsp;Rafał Rak","doi":"10.1016/j.fss.2024.109015","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109015","url":null,"abstract":"<div><p>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, <em>F</em>-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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141077980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disturbance rejections of polynomial fuzzy systems under equivalent-input-disturbance estimator approach","authors":"P. Selvaraj ,&nbsp;O.M. Kwon ,&nbsp;S.H. Lee ,&nbsp;R. Sakthivel","doi":"10.1016/j.fss.2024.109013","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109013","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141089736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of subjective policy reflection using the Choquet integral and its applications","authors":"Jacob Wood ,&nbsp;Dojin Kim ,&nbsp;Lee-Chae Jang","doi":"10.1016/j.fss.2024.109012","DOIUrl":"10.1016/j.fss.2024.109012","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141054699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}