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Properties of fuzzy set spaces with Lp metrics
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-31 DOI: 10.1016/j.fss.2024.109256
Huan Huang
{"title":"Properties of fuzzy set spaces with Lp metrics","authors":"Huan Huang","doi":"10.1016/j.fss.2024.109256","DOIUrl":"10.1016/j.fss.2024.109256","url":null,"abstract":"<div><div>This paper discusses the properties of the spaces of fuzzy sets in a metric space with <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-type <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics, <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>. The <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics are well-defined if and only if the corresponding Haudorff distance functions are measurable. In this paper, we give several fundamental conclusions on the measurability of these Haudorff distance functions. Then we give some characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics. At last we present the completions of fuzzy set spaces with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109256"},"PeriodicalIF":3.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158903","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}
引用次数: 0
Fixed-time adaptive fuzzy control for stochastic MEME gyroscopes with optimized transient behaviors and limited communication resources
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-27 DOI: 10.1016/j.fss.2024.109255
Yu Xia , Junyang Li , Cheng Wang
{"title":"Fixed-time adaptive fuzzy control for stochastic MEME gyroscopes with optimized transient behaviors and limited communication resources","authors":"Yu Xia ,&nbsp;Junyang Li ,&nbsp;Cheng Wang","doi":"10.1016/j.fss.2024.109255","DOIUrl":"10.1016/j.fss.2024.109255","url":null,"abstract":"<div><div>This study expands the existing model for microelectromechanical system (MEMS) gyroscopes by transitioning from a deterministic model to a stochastic nonlinear model and proposes an adaptive fuzzy control scheme that is triggered by events and ensures prescribed performance for stochastic MEMS gyroscopes. Unlike current control schemes for MEMS gyroscopes, the scheme guarantees full control over output overshoot and input vibration, while eliminating the need for design parameters to meet feasibility conditions in event-triggered mechanisms. Additionally, it introduces a type-3 fuzzy system with improved modeling capabilities to approximate unknown nonlinear terms. By incorporating command filtering techniques, the scheme effectively addresses issues related to complexity explosion and filtering errors in backstepping designs. Through the application of fixed-time Lyapunov stability theory on stochastic systems, it is demonstrated that all closed-loop signals are fixed-time bounded in probability. Moreover, the tracking error consistently remains within predefined performance boundaries. Simulation experiments validate both the effectiveness and superiority of the scheme.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109255"},"PeriodicalIF":3.2,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158902","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}
引用次数: 0
⁎-betweenness induced by fuzzy metrics
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-24 DOI: 10.1016/j.fss.2024.109254
Zhenyu Jin , Conghua Yan
{"title":"⁎-betweenness induced by fuzzy metrics","authors":"Zhenyu Jin ,&nbsp;Conghua Yan","doi":"10.1016/j.fss.2024.109254","DOIUrl":"10.1016/j.fss.2024.109254","url":null,"abstract":"<div><div>Motivated by Zhang et al. <span><span>[28]</span></span>, <span><span>[38]</span></span>, <span><span>[39]</span></span>, we aim to make a further discussion of ⁎-betweenness relations. In this paper, we provide the method to construct the ⁎-betweenness by GV fuzzy metrics. After considering the description of ⁎-equivalence with respect to strong fuzzy metrics, we investigate the construction of ⁎-<em>E</em>-betweenness. Some properties of ⁎-betweenness and ⁎-<em>E</em>-betweenness are discussed and some conclusions or conditions in <span><span>[28]</span></span> are verified. This paper is also a supplement of <span><span>[28]</span></span>. Finally, the relationship between fuzzifying convex structures and ⁎-betweenness relations has been studied.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109254"},"PeriodicalIF":3.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159873","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}
引用次数: 0
Discrete imprecise copulas
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-24 DOI: 10.1016/j.fss.2024.109251
Tomaž Košir , Elisa Perrone
{"title":"Discrete imprecise copulas","authors":"Tomaž Košir ,&nbsp;Elisa Perrone","doi":"10.1016/j.fss.2024.109251","DOIUrl":"10.1016/j.fss.2024.109251","url":null,"abstract":"<div><div>In this paper, we study discrete quasi-copulas associated with imprecise copulas. We focus on discrete imprecise copulas that are in correspondence with the Alternating Sign Matrices and provide some construction techniques of dual pairs. Additionally, we show how to obtain (full-domain) self-dual imprecise copulas through patchwork techniques. We further investigate the properties of the constructed dual pairs and prove that they are coherent and avoid sure loss.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109251"},"PeriodicalIF":3.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159871","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}
引用次数: 0
Fuzzy-model-based bipartite synchronization for nonlinear cooperation-competition networks with semi-Markov switching topologies under FDI attacks
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-20 DOI: 10.1016/j.fss.2024.109252
Liangyao Shi , Feng Li , Hao Shen , Ju H. Park
{"title":"Fuzzy-model-based bipartite synchronization for nonlinear cooperation-competition networks with semi-Markov switching topologies under FDI attacks","authors":"Liangyao Shi ,&nbsp;Feng Li ,&nbsp;Hao Shen ,&nbsp;Ju H. Park","doi":"10.1016/j.fss.2024.109252","DOIUrl":"10.1016/j.fss.2024.109252","url":null,"abstract":"<div><div>This paper addresses the bipartite synchronization issue for a class of continuous-time nonlinear cooperation-competition networks, in which the relationships between network systems coexist with coordination and antagonism with the network topology switching obeys a semi-Markov jump process. First, the Takagi-Sugeno fuzzy method is employed to modify the nonlinear function in the networks to deal with this complexity. Then, a fuzzy security control law is devised for the networks to ensure that systems enable bipartite synchronization when communication channels are vulnerable to false data injection attacks. In addition, sufficient conditions are provided to guarantee that the resulting closed-loop system is stochastically stable with a prescribed passive performance index by constructing suitable Lyapunov functions. Lastly, the correctness of the proposed controller is validated by a numerical example and a single-link robot arm model example.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109252"},"PeriodicalIF":3.2,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180842","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}
引用次数: 0
On the centroid of a general type-2 fuzzy set with monotonically increasing second membership functions 关于具有单调递增第二成员函数的一般第二类模糊集的中心点
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-19 DOI: 10.1016/j.fss.2024.109247
Xianliang Liu , Zhihuan Hu , Weidong Zhang
{"title":"On the centroid of a general type-2 fuzzy set with monotonically increasing second membership functions","authors":"Xianliang Liu ,&nbsp;Zhihuan Hu ,&nbsp;Weidong Zhang","doi":"10.1016/j.fss.2024.109247","DOIUrl":"10.1016/j.fss.2024.109247","url":null,"abstract":"<div><div>In a type-2 fuzzy logic system, the centroid computation of a general type-2 fuzzy set (T2 FS) is one of the most important type reduction methods. Nearly all of the existing algorithms are based on the <em>α</em>-plane representation or <em>z</em>-slice representation. Therefore, all of these algorithms can only approximately compute the centroid of a general T2 FS and cannot obtain the analytic expression of the centroid of a general T2 FS. The main objective of this study is to obtain the analytic expression of the centroid of a general T2 FS with monotonically increasing second membership functions based on a discrete universe of discourse. First, assuming that the second membership functions of a general T2 FS is linear and monotonically increasing, a method is proposed to compute its centroid. Second, an approach to calculate the centroid of a general T2 FS is also analyzed, if the second membership functions are only monotonically increasing. Finally, two numerical examples are given to demonstrate the calculation processes of the proposed method in this study. Notably, the proposed method can also be employed to obtain the analytic expression of the centroid of a general T2 FS with monotonically decreasing second membership functions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109247"},"PeriodicalIF":3.2,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180843","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}
引用次数: 0
On some types of reduction for families of fuzzy sets
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-18 DOI: 10.1016/j.fss.2024.109248
Guilong Liu
{"title":"On some types of reduction for families of fuzzy sets","authors":"Guilong Liu","doi":"10.1016/j.fss.2024.109248","DOIUrl":"10.1016/j.fss.2024.109248","url":null,"abstract":"<div><div>A covering is a family of sets. This paper studies the generalization of rough set models via a generalization of the concept of neighborhoods when considering a general family of sets instead of a partition of a set. Given the notion of neighborhood, we propose four different rough set models based on a family of sets and study the reduction problem for such sets. The reduction relationship between rough sets and formal contexts is established. Three reduction algorithms are obtained and applied to identify all reducts. We extend these results to fuzzy sets. Using a family of fuzzy sets to replace a fuzzy covering or a fuzzy <em>β</em> covering, we define set-based fuzzy rough sets and consider three types of reduction. Finally, we give reduction algorithms that are required to identify all reducts.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109248"},"PeriodicalIF":3.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180979","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}
引用次数: 0
Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-18 DOI: 10.1016/j.fss.2024.109249
Deli Zhang , Radko Mesiar , Endre Pap
{"title":"Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making","authors":"Deli Zhang ,&nbsp;Radko Mesiar ,&nbsp;Endre Pap","doi":"10.1016/j.fss.2024.109249","DOIUrl":"10.1016/j.fss.2024.109249","url":null,"abstract":"<div><div>As a generalization of Choquet integrals, the generalized Choquet type set-valued integral of functions w.r.t. set multifunctions and <em>σ</em>-additive measures has been performed in our previous paper <span><span>[66]</span></span>. The present paper is its continuation and it brings a novel set-valued type Choquet integral, named double set function multi-valued Choquet integral (DSMVCI), where the <em>σ</em>-additive measure is replaced by a fuzzy measure. Various kinds of its properties and convergence theorems are obtained, and set-valued type Jensen's and Markov's type inequalities are proved. Its application in multi-attribute decision-making with hesitant fuzzy information is given.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109249"},"PeriodicalIF":3.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180844","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}
引用次数: 0
An efficient algorithm for estimating profust failure probability function under the assumption of probable input and fuzzy state
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-18 DOI: 10.1016/j.fss.2024.109250
Xiaomin Wu, Zhenzhou Lu, Yizhou Chen, Kaixuan Feng
{"title":"An efficient algorithm for estimating profust failure probability function under the assumption of probable input and fuzzy state","authors":"Xiaomin Wu,&nbsp;Zhenzhou Lu,&nbsp;Yizhou Chen,&nbsp;Kaixuan Feng","doi":"10.1016/j.fss.2024.109250","DOIUrl":"10.1016/j.fss.2024.109250","url":null,"abstract":"<div><div>Under the assumption of <strong>pro</strong>bable input and <strong>fu</strong>zzy <strong>st</strong>ate (profust), profust (also named as generalized) failure probability function (G-FPF), which varies with random input distribution parameters (DP) in the interested region, can reflect the effect of DP on structure safety and decouples the generalized reliability-based design optimization. The direct double-loop analysis of G-FPF, which repeatedly estimates the G-FPF values at different DP realizations, is time-consuming. Thus, this paper proposes a single-loop importance sampling (IS) method to estimate G-FPF by combining a variance reduction technique with a sample information-sharing strategy. The proposed method has two innovations. The first is constructing an optimal unified IS density (ISD), which is independent of the DP and envelops the interested DP region. By sharing the sample of the unified ISD, the double-loop analysis for G-FPF can be avoided, and by fusing the IS variance reduction technique, the efficiency of estimating G-FPF can be improved further. The second is designing an adaptive strategy to update the Kriging model of performance function, so that the computational cost, which is measured by the number of performance function evaluations while ensuring the acceptable precision of G-FPF estimation, can be reduced in approaching and sampling the optimal unified ISD as well as predicting the performance function at the sample of the optimal unified ISD. Moreover, the proposed method has wide applicability, and it has no restriction on the nonlinearity of the performance function and the size of the interested DP region, which is sufficiently verified by the presented examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109250"},"PeriodicalIF":3.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159872","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}
引用次数: 0
Algebraic representations of (fuzzy) completely distributive lattices
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-17 DOI: 10.1016/j.fss.2024.109245
Xiaowei Wei , Yueli Yue
{"title":"Algebraic representations of (fuzzy) completely distributive lattices","authors":"Xiaowei Wei ,&nbsp;Yueli Yue","doi":"10.1016/j.fss.2024.109245","DOIUrl":"10.1016/j.fss.2024.109245","url":null,"abstract":"<div><div>Choosing completely distributive lattices as lattice-valued environment, this paper introduces the strong <em>L</em>-upper set monad <span><math><mi>S</mi></math></span>, studies Eilenberg-Moore algebras, Kleisli monoids and its applications of <span><math><mi>S</mi></math></span>. Concretely, we give the monad <span><math><mi>S</mi></math></span> by adjoints. Then we characterize fuzzy completely distributive lattices by its Eilenberg-Moore algebras and study Kleisli monoids of the monad. Moreover, we investigate the necessary and sufficient conditions for the establishment of <span><math><mi>S</mi></math></span>. Finally, we construct two monads, study the relationships between these two monads and <span><math><mi>S</mi></math></span>, moreover verify the rationality of the selection of lattice-valued environment by those relationships.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109245"},"PeriodicalIF":3.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180980","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}
引用次数: 0
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