Fuzzy Sets and SystemsPub Date : 2026-03-01Epub Date: 2025-11-17DOI: 10.1016/j.fss.2025.109683
Qian Hu , Jiapeng Bai , Jun Zhang , Yafei Song , Jusheng Mi
{"title":"FNCEOD: Fuzzy neighborhood combination entropy-based outlier detection","authors":"Qian Hu , Jiapeng Bai , Jun Zhang , Yafei Song , Jusheng Mi","doi":"10.1016/j.fss.2025.109683","DOIUrl":"10.1016/j.fss.2025.109683","url":null,"abstract":"<div><div>Outlier detection, as an important direction of data mining, aims to identify data objects that deviate from normal patterns and is widely used in fields such as financial fraud, network security, and medical diagnosis. Functioning as an essential tool in knowledge acquisition and data mining, granular computing provides a novel framework that emulates human cognitive patterns for resolving large-scale complex problems. However, traditional outlier detection methods based on granular computing are difficult to balance data diversity and fuzziness. Therefore, this article constructs an outlier detection model based on fuzzy neighborhood combination entropy using neighborhood fuzzy granules and combination entropy. Firstly, the fuzzy neighborhood combination entropy of the information system is defined, and the relative fuzzy neighborhood combination entropy of the object is defined by the change in neighborhood fuzzy entropy caused by the object. Secondly, the relative fuzzy cardinality of the object is defined by the difference degree between its fuzzy neighborhoods, and the anomaly factor of the object is measured by its relative fuzzy neighborhoods combination entropy and relative fuzzy cardinality. Then, an outlier detection model based on the combination entropy of fuzzy neighborhoods is constructed and the relevant algorithm is designed. Finally, the effectiveness and efficiency of the proposed method were verified through publicly available datasets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"526 ","pages":"Article 109683"},"PeriodicalIF":2.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580332","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}
Fuzzy Sets and SystemsPub Date : 2026-03-01Epub Date: 2025-11-11DOI: 10.1016/j.fss.2025.109675
Shengda Tang , Zihan Chen , Hai Wang , Jun Cheng
{"title":"Reinforcement learning-based stochastic structurally-sparse sliding mode control for IT-2 T-S fuzzy interconnected multi-area power system","authors":"Shengda Tang , Zihan Chen , Hai Wang , Jun Cheng","doi":"10.1016/j.fss.2025.109675","DOIUrl":"10.1016/j.fss.2025.109675","url":null,"abstract":"<div><div>This article develops a novel fuzzy stochastic structurally-sparse sliding mode control (FS<sup>4</sup>MC) scheme for the malicious attacks-injected interconnected multi-area power systems (IMAPSs). In response to the nonlinear characteristics of valve position deviation and the uncertain switching feature of the inter-area feedback communication network (FCN), an interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy IMAPS model with the Markov jump structurally-sparse FCN topology is established. Subsequently, FS<sup>4</sup>MC compensation strategy is developed for this model to counteract the impact of attack signals, ensuring the finite-time reachability of the ideal sliding surface and the stochastic stability of the IT-2 T-S fuzzy IMAPS with switching FCN topology. On the other hand, since the FS<sup>4</sup>MC scheme design relies on IMAPS dynamics, which is frequently unavailable, a data-centric algorithm is developed to compute this scheme without requiring either model information or an initially stabilizing policy pair. Finally, the case study on a three-area IMAPS demonstrates the effectiveness of the proposed method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"526 ","pages":"Article 109675"},"PeriodicalIF":2.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624363","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}
Fuzzy Sets and SystemsPub Date : 2026-03-01Epub Date: 2025-11-08DOI: 10.1016/j.fss.2025.109674
Dingxin He , Haoping Wang , Yang Tian , Minxuan Zha , Radu-Emil Precup
{"title":"Fractional-order ultra-local model-based direct adaptive fuzzy sliding mode control for mechatronic systems with mismatched disturbances and input nonlinearities","authors":"Dingxin He , Haoping Wang , Yang Tian , Minxuan Zha , Radu-Emil Precup","doi":"10.1016/j.fss.2025.109674","DOIUrl":"10.1016/j.fss.2025.109674","url":null,"abstract":"<div><div>Aiming at the trajectory tracking problem of the mechatronic systems in the presence of uncertainties, matched and mismatched disturbances, and input nonlinearities, a fractional-order <em>ultra-local model</em>-based direct adaptive fuzzy controller (FO-DAFC) is proposed in this paper. To reduce the difficulty of controller design, the fractional-order <em>ultra-local model</em> is constructed to reformulate the complex mechatronic system. Then, a global sliding surface is proposed to eliminates the reaching phase and ensures the global robustness. Furthermore, an ideal global sliding mode controller is designed to converge the tracking error. However, the unknown and unmeasured parameters are existed in the ideal controller. The fuzzy logic system is thus established to approximate the ideal control law. And the fuzzy weight adaptive law is designed by using gradient descent method. Correspondingly, the direct adaptive fuzzy controller is proposed. After that, the stability of the closed-loop system with the proposed FO-DAFC is analyzed through using Lyapunov theorem. Ultimately, the numerical simulation of 2-DOF robotic manipulator with different input nonlinearities and co-simulation of 4-DOF robotic manipulator compared with other controllers are completed. The obtained results demonstrate the effectiveness and superiority of the proposed controller.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"526 ","pages":"Article 109674"},"PeriodicalIF":2.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580335","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}
Fuzzy Sets and SystemsPub Date : 2026-03-01Epub Date: 2025-11-04DOI: 10.1016/j.fss.2025.109653
Weiling Bao , Shoucheng Yuan , Dian Zhang , Jun Cheng , Dan Zhang , Yu Fu
{"title":"Adaptive neural security control of fuzzy systems with sojourn-probability-Based multi-mode attacks","authors":"Weiling Bao , Shoucheng Yuan , Dian Zhang , Jun Cheng , Dan Zhang , Yu Fu","doi":"10.1016/j.fss.2025.109653","DOIUrl":"10.1016/j.fss.2025.109653","url":null,"abstract":"<div><div>This paper addresses the challenges of hybrid cyberattacks on fuzzy systems, focusing on observer-based security control strategies enhanced by adaptive neural networks. A generalized multi-mode denial-of-service (DoS) attack model is developed, utilizing a variable matrix to represent diverse attack ranges across multiple communication channels, with sojourn probabilities employed to describe attack stochasticity, thus offering an alternative to traditional Markov models. The study also investigates unknown deception attacks, incorporating an online weight-adjusting neural network to estimate and counteract the adverse effects of these malicious inputs. Furthermore, a dynamic mismatch model framework is introduced to accurately characterize the evolving discrepancies between actual and estimated DoS attack modes, addressing the limitations of prior fixed mismatch assumptions. The findings present a robust foundation for enhancing the resilience of fuzzy systems against hybrid cyberattacks, providing significant implications for future research in network security. On this basis, by using Lyapunov theory, sufficient criteria that guarantee the boundedness of the closed-loop fuzzy system are established. Finally, the effectiveness and the superiority of the designed control strategy are verified by the tunnel diode circuit model.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"526 ","pages":"Article 109653"},"PeriodicalIF":2.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624364","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-30DOI: 10.1016/j.fss.2025.109663
Amal Aarab , Aicha Driouch
{"title":"Uncertainty modelling of the nonlinear Black-Scholes equation and decision-making using fuzzy logic","authors":"Amal Aarab , Aicha Driouch","doi":"10.1016/j.fss.2025.109663","DOIUrl":"10.1016/j.fss.2025.109663","url":null,"abstract":"<div><div>In the financial world, particularly in option pricing, the price of underlying assets is often difficult to predict due to interest rate and volatility variations. In order to provide more accurate predictions, the fuzzy approach proves to be an effective tool for modelling the uncertainty inherent in financial markets. In this work, we propose a numerical approach for pricing European options using fuzzy-parameter partial differential equation. We analyse the extended nonlinear Black-Scholes problem of Barles-Soner’s model, leading to the computation of a range of European option prices. We determine the value for the fair price using the center of gravity method, along with its corresponding <span><math><mrow><mi>α</mi><mo>−</mo></mrow></math></span>level derived from an optimization problem to assess its plausibility. In addition, we quantify the vagueness of the fuzzy output by the 15–85 mid-percentile range, which provides a description of the spread around the defuzzified value. These results support prediction and decision-making purposes.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109663"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475788","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-22DOI: 10.1016/j.fss.2025.109654
Weili Yang , Weipeng Liu , Cailu Wang
{"title":"Global and approximate optimization for constrained max-min systems","authors":"Weili Yang , Weipeng Liu , Cailu Wang","doi":"10.1016/j.fss.2025.109654","DOIUrl":"10.1016/j.fss.2025.109654","url":null,"abstract":"<div><div>This paper focuses on the global optimization problem in max-min systems subject to non-negative affine equality constraints. By constructing the greatest lower bound, we establish a solvability criterion for the global optimization problem and derive a uniqueness criterion for globally optimal solutions. We construct the feasible max-plus projection set to determine the set of all globally optimal solutions. An algorithm is developed to verify the solvability of the global optimization problem and to find all globally optimal solutions. Furthermore, when the global optimization problem is unsolvable, we introduce approximate optimization to obtain the optimal feasible value by using the max-plus vector norm, and provide the set of all approximate optimal solutions. The effectiveness of the proposed method is demonstrated through illustrative examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109654"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475789","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-25DOI: 10.1016/j.fss.2025.109652
Diego García-Zamora , Antonio Fco Roldán López De Hierro , Humberto Bustince
{"title":"Extended dissimilarities and d-Choquet integral for fuzzy numbers","authors":"Diego García-Zamora , Antonio Fco Roldán López De Hierro , Humberto Bustince","doi":"10.1016/j.fss.2025.109652","DOIUrl":"10.1016/j.fss.2025.109652","url":null,"abstract":"<div><div><span><math><mi>d</mi></math></span>-Choquet integrals were introduced as a class of functions that generalize the classical Choquet integral by replacing the difference with a dissimilarity. This paper faces the problem of computing d-Choquet integrals when the information is imprecise/vague and, more specifically, when it is modeled as fuzzy numbers. We also study the main properties of such an extension and analyze how the features of the considered dissimilarity and fuzzy measure impact the extended <span><math><mi>d</mi></math></span>-Choquet integral.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109652"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145428798","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-27DOI: 10.1016/j.fss.2025.109644
Xin Liu, Yongjian Xie, Mengyuan Zhang
{"title":"A generalization of Stone duality of archimedean lattice effect algebras","authors":"Xin Liu, Yongjian Xie, Mengyuan Zhang","doi":"10.1016/j.fss.2025.109644","DOIUrl":"10.1016/j.fss.2025.109644","url":null,"abstract":"<div><div>Based on the sheaf representations of hyperarchimedean MV-algebras, we suggested the definition of a spectral presheaf on the context category of an Archimedean lattice effect algebra and proved that two Archimedean lattice effect algebras are isomorphic if and only if their spectral presheaves are isomorphic. The spectral presheaf representation of an Archimedean lattice effect algebra can be considered as a generalized Stone duality of the lattice effect algebra.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109644"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145428794","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-30DOI: 10.1016/j.fss.2025.109662
Chun Yong Wang , Lijuan Wan , Bo Zhang
{"title":"On the equivalence classes induced by L-fuzzy rough approximation operators","authors":"Chun Yong Wang , Lijuan Wan , Bo Zhang","doi":"10.1016/j.fss.2025.109662","DOIUrl":"10.1016/j.fss.2025.109662","url":null,"abstract":"<div><div>This paper studies the equivalence classes induced by <span><math><mi>L</mi></math></span>-fuzzy rough approximation operators from the theoretical point of view, where <span><math><mi>L</mi></math></span> is a doubly residuated lattice with an involutive negation. We examine the relationship between <span><math><mi>L</mi></math></span>-fuzzy rough approximation operators and the equivalence classes they induce. We point out the conditions, where a pair of <span><math><mi>L</mi></math></span>-fuzzy sets forms an <span><math><mi>L</mi></math></span>-fuzzy rough set and the family of all <span><math><mi>L</mi></math></span>-fuzzy rough sets induces a complete lattice, respectively. In particular, some results in this paper can be generalized into the equivalence classes induced by <span><math><mi>L</mi></math></span>-fuzzy rough approximation operators, where <span><math><mi>L</mi></math></span> is a residuated lattice.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109662"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475790","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}
Fuzzy Sets and SystemsPub Date : 2026-02-15Epub Date: 2025-10-27DOI: 10.1016/j.fss.2025.109657
Ting-hai Zhang , Feng Qin , Wenhuang Li , Zhihong Yi
{"title":"New types of ordinal sums of fuzzy Sheffer strokes and the induced pseudo (quasi)-overlap and grouping functions","authors":"Ting-hai Zhang , Feng Qin , Wenhuang Li , Zhihong Yi","doi":"10.1016/j.fss.2025.109657","DOIUrl":"10.1016/j.fss.2025.109657","url":null,"abstract":"<div><div>It is well-established that the Sheffer stroke can independently form a complete logical system, holding unique theoretical significance within classical logic. Recently, scholars have explored the structures and properties of the corresponding fuzzy Sheffer stroke (hereafter referred to as <span><math><mi>FSS</mi></math></span>) within the fuzzy logic framework. This paper introduces two novel types of ordinal sums of <span><math><mi>FSS</mi></math></span>s, which are defined based on whether the <span><math><mi>x</mi></math></span>-coordinate or <span><math><mi>y</mi></math></span>-coordinate of the function lies within the subintervals of the summands. We investigate several important properties of these sums and establish their equivalent characterizations. Furthermore, building upon these two classes of ordinal sum structures, we construct pseudo (quasi)-overlap and grouping functions (abbreviated as <span><math><mrow><mi>P</mi><mi>Q</mi><mi>O</mi><mi>F</mi></mrow></math></span> and <span><math><mrow><mi>P</mi><mi>Q</mi><mi>G</mi><mi>F</mi></mrow></math></span>), and present their associated properties. These constructions provide two effective methods for developing <span><math><mrow><mi>P</mi><mi>Q</mi><mi>O</mi><mi>F</mi></mrow></math></span> and <span><math><mrow><mi>P</mi><mi>Q</mi><mi>G</mi><mi>F</mi></mrow></math></span>, which have broad applications in fuzzy inference and multi-attribute decision-making.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"525 ","pages":"Article 109657"},"PeriodicalIF":2.7,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475791","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}