Fuzzy Sets and Systems最新文献

{"title":"Radon-Nikodým theorems for generalized fuzzy number measures","authors":"Sokol Bush Kaliaj","doi":"10.1016/j.fss.2025.109380","DOIUrl":"10.1016/j.fss.2025.109380","url":null,"abstract":"<div><div>In this paper we deal with generalized fuzzy number measures defined on Σ and taking values in the set <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, where <span><math><mo>(</mo><mi>Ω</mi><mo>,</mo><mi>Σ</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math></span> is a complete finite measure space, <span><math><mi>c</mi><mi>w</mi><mi>k</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the family of all non-empty convex weakly compact subsets of a Banach space <em>X</em> and <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is such that a fuzzy set <span><math><mi>u</mi><mo>:</mo><mi>X</mi><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> is a member of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> if and only if<span><span><span><math><mrow><msup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>α</mi></mrow></msup><mo>∈</mo><mi>c</mi><mi>w</mi><mi>k</mi><mo>(</mo><mi>X</mi><mo>)</mo><mspace></mspace><mtext> for all </mtext><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mspace></mspace><mo>(</mo><msup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>α</mi></mrow></msup><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>X</mi><mo>:</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mi>α</mi><mo>}</mo><mo>)</mo><mo>.</mo></mrow></math></span></span></span> We show two Radon-Nikodým theorems for such generalized fuzzy number measures in terms of Pettis integral of fuzzy mappings. The first theorem works for a <em>μ</em>-continuous generalized fuzzy number measure <span><math><mi>M</mi><mo>:</mo><mi>Σ</mi><mo>→</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of bounded variation in a Banach space <em>X</em> with the Radon-Nikodým property (RNP). The next theorem shows that if a generalized fuzzy number measure <span><math><mi>M</mi><mo>:</mo><mi>Σ</mi><mo>→</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is “dominated” by a generalized fuzzy number <span><math><mi>Q</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi><mi>w</mi><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> in terms of <em>α</em>-level sets, i.e.,<span><span><span><math><mrow><msup><mrow><mo>[</mo><mi>M</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>]</mo></mrow><mrow><mi>α</mi></mrow></msup><mo>⊂</mo><mi>μ</mi><mo>(</mo><mi>A</mi><mo>)</mo><msup><mrow><mo>[</mo><mi>Q</mi><mo>]</mo></mrow><mrow><mi>α</mi></mrow></msup><mspace></mspace><mtext> for all </mtext><mi>A</mi><mo>∈</mo><mi>Σ</mi><mo>,</mo><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>,</mo></mrow></math></sp","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109380"},"PeriodicalIF":3.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680187","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":"Asynchronous membership functions decoupling based event-triggered fuzzy networked control for nonlinear systems","authors":"Wen-Bo Xie ,&nbsp;Yong-Qi Wu ,&nbsp;Shi-Qi Zheng ,&nbsp;Yu-Long Wang","doi":"10.1016/j.fss.2025.109377","DOIUrl":"10.1016/j.fss.2025.109377","url":null,"abstract":"<div><div>This paper focuses on the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> robust control for a kind of nonlinear networked control systems depicted by T-S fuzzy form model. An event-triggered communication scheme is adopted to improve the utilization of network resources. A new fuzzy system model is derived by designing an asynchronous membership functions decoupling method, such that more information about the membership functions is involved in the process of stability and robustness analysis. Based on Lyapunov Krasovskii Functional (LKF) method, a series of convex stability and robustness conditions can be given. Finally, two benchmark examples are introduced to prove the effectiveness of the designed method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109377"},"PeriodicalIF":3.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704446","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":"Fuzzy neighborhood based variable-precision granular-ball rough sets with applications to feature selection","authors":"Yongxi Chen ,&nbsp;Zhehuang Huang ,&nbsp;Jinjin Li","doi":"10.1016/j.fss.2025.109382","DOIUrl":"10.1016/j.fss.2025.109382","url":null,"abstract":"<div><div>Granular-ball computing is an efficient, simple and scalable computing paradigm that has emerged in recent years. By sampling the data with multiple divisions, the knowledge on different granularity levels is obtained, so as to achieve the purpose of multi-granularity data analysis. As a representative model of granular-ball computing, granular ball neighborhood rough set model (GBNRS) offers greater generality and flexibility as it can adaptively generate different neighborhood radii for each object. However, GBNRS consistently sets the purity degree with 1 for all granular-balls, which may lead to poor fault tolerance in uncertain information systems. Additionally, GBNRS lacks effective approximation operators, making it hard to effectively characterize the differences among samples. For these reasons, a new variable-precision rough set model is set forth by combining granular-ball rough sets, fuzzy rough sets and neighborhood rough sets. To this end, a granular-ball fuzzy neighborhood is presented to reflect the similarity of the samples and a pair of variable-precision approximation operators is formulated to improve the noise-tolerant ability. On this basis, a new granular-ball rough set model i.e. fuzzy neighborhood based granular-ball rough sets (FNGBRS) is proposed. Furthermore, a variable-precision dependency function is introduced to evaluate the classification ability of a given feature sets at different granularity levels. The dimensionality reduction of decision systems is carried out under the condition of keeping the classification ability unchanged, and a feature selection algorithm is developed by using the variable-precision dependency function. Numerical experiments on 12 different types of datasets demonstrate that the proposed model outperforms some state-of-the-art feature learning algorithms in terms of classification accuracy and the number of selected features.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109382"},"PeriodicalIF":3.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696005","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":"Relational modifiers for interval valued fuzzy sets and lattice valued mappings","authors":"Mohammad Ojaghi ,&nbsp;Tofigh Allahviranloo ,&nbsp;Somayeh Ezadi ,&nbsp;Susana Montes","doi":"10.1016/j.fss.2025.109370","DOIUrl":"10.1016/j.fss.2025.109370","url":null,"abstract":"<div><div>In this paper, we introduce a new type of fuzzy modifiers (i.e., mappings that transform interval-valued fuzzy sets (IVFS) into modified Interval-valued fuzzy sets (MIVFS)). Also, mappings transform lattice-valued fuzzy sets (LVFS) into modified lattice-valued fuzzy sets (MLVFS) using the concept of implication and conjunction to preserve the monotonicity of mapping A: X → L. We showed these modifiers preserve strict monotonicity of mapping A.</div><div>Also, using the concept of aggregation functions, we introduced fuzzy modifiers of mapping A, which are a more general form of the previous modifiers. We show these modifiers preserve the strict monotonicity of A.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109370"},"PeriodicalIF":3.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680189","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":"Tracking control for nonlinear systems with time-varying delay using the fuzzy preview repetitive control approach","authors":"Li Li ,&nbsp;Jiang Wu ,&nbsp;Xiaohua Meng","doi":"10.1016/j.fss.2025.109378","DOIUrl":"10.1016/j.fss.2025.109378","url":null,"abstract":"<div><div>This paper investigates an innovative technology for fuzzy preview repetitive control (FPRC) in nonlinear systems with time-varying delay and uncertainties using the Takagi-Sugeno (T-S) fuzzy model. The proposed FPRC strategy considers time-changing delays and previewable, periodic target signals. The controller integrates a fuzzy output feedback controller, a fuzzy preview controller, and a repetitive controller to address the tracking control problem of periodic target signals. The research constructs a T-S fuzzy augmented error system using the error system method and state augmentation technique. Subsequetnly, the FPRC design challenge is transformed into a feedback stabilization problem of the augmented error system. Empolying fuzzy Lyapunov function and linear matrix inequality (LMI) techniques, the study derives sufficient conditions for the asymptotic stability of the augmented error system in the form of a set of LMIs, presenting the design method of the FPRC law. The validity of the results is demonstrated through numerical simulations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109378"},"PeriodicalIF":3.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696004","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":"State quasi-filters on state EQ-algebras","authors":"Bin Zhao,&nbsp;Jieqiong Shi","doi":"10.1016/j.fss.2025.109373","DOIUrl":"10.1016/j.fss.2025.109373","url":null,"abstract":"<div><div>In this paper, we focus on studying state quasi-filters of SEQ-algebras (that is, state EQ-algebras), and characterizing local SEQ-algebras with the help of state quasi-filters. To begin with, we introduce state quasi-filters and two special types of state quasi-filters, which are maximal state quasi-filters and prime state quasi-filters on SEQ-algebras, investigate their related properties and give some equivalent characterizations of them. Moreover, we prove that the set of all state quasi-filters on an SEQ-algebra is not only a Brouwerian algebraic lattice but also a coherent frame and obtain some conditions under which maximal state quasi-filters coincide with prime state quasi-filters. Then, we introduce and characterize local SEQ-algebras and some subclasses of local SEQ-algebras, such as perfect SEQ-algebras, locally finite SEQ-algebras and peculiar SEQ-algebras by use of some kinds of state quasi-filters. In the last, we discuss their other related properties and prove that each perfect good EQ-algebra admits a nontrivial internal state. In particular, we state a classification theorem of local SEQ-algebras and show that each local SEQ-algebra is either perfect or locally finite or peculiar.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109373"},"PeriodicalIF":3.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680188","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":"Packet loss compensation-based fault detection for fuzzy Markov jump systems: A zonotopic residual evaluation approach","authors":"Li-Xiang Feng ,&nbsp;Guang-Hong Yang","doi":"10.1016/j.fss.2025.109374","DOIUrl":"10.1016/j.fss.2025.109374","url":null,"abstract":"<div><div>This paper focuses on the fault detection problem for a class of nonlinear Markov jump systems with packet losses, in which the nonlinearity and uncertainty of the original system are captured by the interval type-2 fuzzy sets. To deal with the random packet losses, a single exponential smoothing technique-based compensation scheme is introduced to counteract the effect of missing measurements. On this basis, an asynchronous fuzzy filter is designed. Then, using the residual signals generated by the filter, a zonotopic-based detection strategy is proposed to calculate dynamic thresholds and detect actuator faults. By applying the information about the footprint of uncertainty and the Lyapunov functional approach, the membership-function-dependent filter design conditions are obtained, which can guarantee the stochastic stability and strict dissipativity of the fault detection system. Compared with the membership-function-independent filtering design conditions in the existing results, the given membership-function-dependent ones reduce the conservatism of the design. Finally, a tunnel diode circuit example is provided to validate the effectiveness of the proposed approach, which shows that the zonotopic threshold analysis-based detection method shortens the fault response time more than the one using the constant threshold.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"512 ","pages":"Article 109374"},"PeriodicalIF":3.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680190","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":"Characterizations of some classes of generated implication solutions to the cross-migrativity","authors":"Tianlong Zhang ,&nbsp;Kuanyun Zhu ,&nbsp;Jingru Wang ,&nbsp;Deng Pan","doi":"10.1016/j.fss.2025.109375","DOIUrl":"10.1016/j.fss.2025.109375","url":null,"abstract":"<div><div>This paper focuses on the cross-migrativity between grouping functions and the (<em>g</em>, min)-implications generated by additive generators of continuous Archimedean t-conorms and the <span><math><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-implications introduced by generalized additive generators of representable uninorms. In addition, we show that (<span><math><mi>g</mi><mo>,</mo><mi>min</mi></math></span>)-implications and <span><math><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-implications do not belong to any of the classes known <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>N</mi><mo>)</mo><mo>−</mo><mo>,</mo><mi>R</mi><mo>−</mo><mo>,</mo><mi>Q</mi><mi>L</mi><mo>−</mo></math></span>, generalized-<em>h</em>, <em>h</em>-generated, Yager's <em>f</em>- and <em>g</em>-implications. In particular, we establish a series of necessary and sufficient conditions for the cross-migrativity of the grouping functions and several particular types of generated implications (i.e., <em>h</em>-generated implications, <em>k</em>-generated implications, (<span><math><mi>g</mi><mo>,</mo><mi>min</mi></math></span>)-implications and <span><math><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-implications) by using the multiplicative (additive) generators and ordinal sums of grouping functions, the distributive laws and contraction law between grouping functions and fuzzy implications, and study a broader connection between grouping functions and generated implications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"511 ","pages":"Article 109375"},"PeriodicalIF":3.2,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644551","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":"Interpretable Forex trading models based on new technical analysis indicators and fuzzy multi-criteria optimization","authors":"Pavel Sevastjanov ,&nbsp;Krzysztof Kaczmarek ,&nbsp;Ludmila Dymova ,&nbsp;Leszek Rutkowski","doi":"10.1016/j.fss.2025.109371","DOIUrl":"10.1016/j.fss.2025.109371","url":null,"abstract":"<div><div>New technical analysis indicators based on the use of complete information about Candles (Opening, Low, High, Closing prices and Volumes) and mathematical tools of fuzzy set theory have been developed and tested. They were directly focused on profit forecasting and returning the relative strength of trading signals. Using them, a set of new technical analysis indicators was developed and studied, based on a fuzzy multi-criteria aggregation of developed particular indicators. Based on these results, a set of highly profitable and reliable new interpretable Forex trading models based on fuzzy multi-criteria aggregation of model output parameters and new technical analysis indicators was developed and tested. It is shown that these models are significantly superior to the traditional ones based on a single-criteria approach. The results obtained provide an opportunity to develop trading models based on a portfolio based approach in the Forex market. The article may be of interest mainly to researchers and Automatic Trading Systems developers, especially using the most popular Meta Trader 4 platform with about 16 million users (traders) in 2024 year.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"511 ","pages":"Article 109371"},"PeriodicalIF":3.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644549","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":"On counting and constructing all admissible orders of the non-empty intervals in any finite chain","authors":"Peter Sussner ,&nbsp;Felipe Scherer Vicentin","doi":"10.1016/j.fss.2025.109372","DOIUrl":"10.1016/j.fss.2025.109372","url":null,"abstract":"<div><div>In many fields, there is a need to process data that only includes a finite number of values. To express the uncertainty regarding these values, one can use non-empty intervals, called epistemic, that are usually ordered in terms of the product, aka marginal, order. However, a partial order of this form is often insufficient in applications such as decision making, optimization, image segmentation, and edge detection. To this end, the given partial order of the non-empty intervals in a finite chain must be extended to a linear order, known as an admissible order. In this paper, we determine the number of all of these linear extensions and present an algorithm for generating them.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"511 ","pages":"Article 109372"},"PeriodicalIF":3.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644552","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}