Fuzzy Sets and Systems最新文献

{"title":"Estimation of the domain of attraction for continuous-time saturated positive polynomial fuzzy systems based on novel analysis and convexification strategies","authors":"Meng Han ,&nbsp;Yongjie Huang ,&nbsp;Ge Guo ,&nbsp;H.K. Lam ,&nbsp;Zhengsong Wang","doi":"10.1016/j.fss.2024.109155","DOIUrl":"10.1016/j.fss.2024.109155","url":null,"abstract":"<div><div>In this paper, the domain of attraction (DOA) of the continuous-time positive polynomial fuzzy systems subject to input saturation is estimated by using the level set of the linear copositive Lyapunov function. To relax the estimation of DOA, the restriction on the level set is removed by embedding the expression of the level set into the stability conditions and positivity conditions. Referring to the nonconvex terms caused by above novel analysis strategy, some polynomial inequality lemmas are proposed to handle them; the nonconvex terms caused by imperfect premise matching (IPM) nonlinear membership functions are dealt with by sector nonlinear methods and advanced Chebyshev membership-function-dependent (MFD) methods. In this advanced MFD method, the state space segmentation and polynomial order selection of the Chebyshev approximation method are improved based on breakpoints of the first derivative and curvature, respectively, which is helpful to reduce the conservatism and computational burden of the result. Thus, this advanced Chebyshev MFD method not only optimizes the convexification strategy, but also can further be extended to estimate the DOA when it is used to introduce the membership functions information for convex stability and positivity conditions. Finally, a numerical example and the lipoprotein metabolism and potassium ion transfer nonlinear model are presented to validate the effectiveness and feasibility of the aforementioned analysis and convexification strategies in the expansion of DOA estimation.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560572","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":"Uncertainty merging with basic uncertain information in probability environment","authors":"LeSheng Jin ,&nbsp;Yi Yang ,&nbsp;Zhen-Song Chen ,&nbsp;Muhammet Deveci ,&nbsp;Radko Mesiar","doi":"10.1016/j.fss.2024.109153","DOIUrl":"10.1016/j.fss.2024.109153","url":null,"abstract":"<div><div>Basic uncertain information is a recently introduced and significant type of uncertainty that proves particularly valuable in decision-making environments with inherent uncertainties. In this study, we propose the concept of uncertainty cognition merging, which effectively combines basic uncertain information granules with probability measures to generate new probability measures within the same probability space. Additionally, we present a degenerated method that merges basic uncertain information granules with unit intervals to create new subintervals. We introduce four distinct uncertainty cognition merging methods and thoroughly compare and analyze their respective properties, limitations, and advantages. To demonstrate the practical application potential of our proposals, we provide numerical examples alongside further mathematical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532657","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":"New results on α-cuts of type-2 fuzzy sets","authors":"Wei Zhang ,&nbsp;Bao Qing Hu","doi":"10.1016/j.fss.2024.109152","DOIUrl":"10.1016/j.fss.2024.109152","url":null,"abstract":"<div><div>The <em>α</em>-cut (i.e., <em>α</em>-plane) of type-2 fuzzy sets is a very useful tool for computation. However, there are some theoretical mistakes in type-2 fuzzy sets literature discussing the topic of <em>α</em>-cuts. This paper will illustrate these mistakes through examples and specifically address the two new questions induced by them: (1) Taking the <em>α</em>-cut (resp. <em>α</em>-strong cut) of the result obtained by performing a <em>T</em>-extension operation of ⁎ (i.e., t-norm extension operation of a general binary operation) on two type-2 fuzzy sets is equal to what? (2) What conditions are required for taking the <em>α</em>-cut (resp. <em>α</em>-strong cut) of the result obtained by performing a <em>T</em>-extension operation of ⁎ on two type-2 fuzzy sets to be equal to performing the ⁎ operation on the <em>α</em>-cuts (resp. <em>α</em>-strong cuts) of these two type-2 fuzzy sets? Finally, we will get a comprehensive answer to these two questions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445642","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 differentiability and mass distributions of typical bivariate copulas","authors":"Nicolas Pascal Dietrich,&nbsp;Wolfgang Trutschnig","doi":"10.1016/j.fss.2024.109150","DOIUrl":"10.1016/j.fss.2024.109150","url":null,"abstract":"<div><div>Despite the fact that copulas are commonly considered as analytically smooth/regular objects, derivatives of copulas have to be handled with care. Triggered by a recently published result characterizing multivariate copulas via <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-increasingness of their partial derivative we study the bivariate setting in detail and show that the set of non-differentiability points of a copula may be quite large. We first construct examples of copulas <em>C</em> whose first partial derivative <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mn>1</mn></mrow></msub><mi>C</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> is pathological in the sense that for almost every <span><math><mi>x</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> it does not exist on a dense subset of <span><math><mi>y</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, and then show that the family of these copulas is dense. Since in commonly considered subfamilies more regularity might be typical, we then focus on bivariate Extreme Value copulas (EVCs) and show that a topologically typical EVC is not absolutely continuous but has degenerated discrete component, implying that in this class typically <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mn>1</mn></mrow></msub><mi>C</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> exists in full <span><math><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div><div>Considering that regularity of copulas is closely related to their mass distributions we then study mass distributions of topologically typical copulas and prove the surprising fact that topologically typical bivariate copulas are mutually completely dependent with full support. Furthermore, we use the characterization of EVCs in terms of their associated Pickands dependence measures <em>ϑ</em> on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, show that regularity of <em>ϑ</em> carries over to the corresponding EVC and prove that the subfamily of all EVCs whose absolutely continuous, discrete and singular component has full support is dense in the class of all EVCs.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445721","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":"Invariant idempotent ⁎-measures generated by iterated function systems","authors":"Natalia Mazurenko ,&nbsp;Khrystyna Sukhorukova ,&nbsp;Mykhailo Zarichnyi","doi":"10.1016/j.fss.2024.109151","DOIUrl":"10.1016/j.fss.2024.109151","url":null,"abstract":"<div><div>It is known that every continuous t-norm ⁎ generates a functor of the so-called ⁎-measures in the category of compact Hausdorff spaces. Similarly to the case of the hyperspace functor and the probability measure functors one can define the notion of invariant ⁎-measure for iterated function systems of contractions on compact metric spaces.</div><div>We provide a simple proof of existence and uniqueness of invariant ⁎-measures. Some examples of invariant ⁎-measures, for different t-norms ⁎, are presented.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533115","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":"Optimality results for a class of nonconvex fuzzy optimization problems with granular differentiable objective functions","authors":"Tadeusz Antczak","doi":"10.1016/j.fss.2024.109147","DOIUrl":"10.1016/j.fss.2024.109147","url":null,"abstract":"<div><div>There is the growing use in practice of optimization models with uncertain data related to human activity in which hypotheses are not verified in a way specific for classical optimization. Fuzzy optimization problems have been introduced and developed for formulating and solving such real-world extremum problems which are usually not well defined. In most works devoted to fuzzy optimization problems, fuzzy numbers are characterized by their vertical membership functions which causes some difficulties in calculations and is the reason for arithmetic paradoxes. In the paper, therefore, fuzzy numbers are characterized by their horizontal membership functions and the concept of a <em>gr</em>-derivative of a fuzzy function is used which is based on the horizontal membership function and the granular difference. Although the convexity notion is a very important property of optimization models, there are real-world processes and systems with uncertainty that cannot be modeled with convex fuzzy optimization problems. Therefore, new concepts of granular generalized convexity notions, that is, the concepts of granular pre-invexity and <em>gr</em>-differentiable invexity are introduced to fuzzy analysis and some properties of the aforesaid granular generalized convexity concepts are investigated. Further, the class of nonconvex smooth optimization problems with <em>gr</em>-differentiable fuzzy-valued objective function and differentiable inequality constraint functions is considered as an application of the concept of <em>gr</em>-differentiable invexity. Then, the Karush-Kuhn-Tucker necessary optimality conditions are established for a global fuzzy minimizer with regard to the distinct fuzzy numbers in the analyzed fuzzy extremum problem. Further, the sufficiency of the aforesaid necessary optimality conditions of a Karush-Kuhn-Tucker type is also proved.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532658","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":"Information fusion in order-2 fuzzy environments: A matrix transformation perspective","authors":"Li Zhu ,&nbsp;Qianli Zhou ,&nbsp;Yong Deng ,&nbsp;Witold Pedrycz","doi":"10.1016/j.fss.2024.109146","DOIUrl":"10.1016/j.fss.2024.109146","url":null,"abstract":"<div><div>Order-2 information granules, as a representation of multi-layer structured information, have recently rekindled discussions. It is usually generated by abstracting order-1 information granules. When the dependence relationship and corresponding membership function of the order-1 information granules (reference information granules) are known, Pedrycz et al. used a method based on gradient optimization to complete the aggregation of the order-2 information granules. In this paper, we discuss a more specific scenario: not only the dependencies between reference information granules are captured, but also the order-1 information granules can be expressed as specific fuzzy information distributions. For this, we propose a fusion scheme of order-2 fuzzy sets based on matrix transformation called CQRP. To our knowledge, it is the first method that completely integrates the structural information of the order-2 environment into the fusion of order-2 fuzzy sets. In the process, we also creatively proposed the attraction and exclusion of structural information, deepening the understanding of structural information. Through sufficient comparison and analysis, we prove that it makes fuller use of information in the order-2 environment and is more reasonable and effective in tasks such as classification and identification.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432498","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 r→-Sheffer strokes: A new class of directionally monotone functions","authors":"Yifan Zhao,&nbsp;Hua-Wen Liu","doi":"10.1016/j.fss.2024.109149","DOIUrl":"10.1016/j.fss.2024.109149","url":null,"abstract":"<div><div>Recently, Baczyński et al. introduced the axiomatic definition of fuzzy Sheffer strokes and incorporated the Sheffer stroke operation into the fuzzy logic framework [Fuzzy Sets Syst. 431 (2022) 110-128]. In this paper, we introduce a new class of directionally monotone functions, called <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes. Firstly, we propose the notion of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes by relaxing the monotonicity of fuzzy Sheffer strokes to the directional monotonicity. And then, we discuss some vital properties of such functions as well as its relationship between fuzzy Sheffer strokes. Subsequently, we give a representation of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes by means of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-pre-conjunctions and fuzzy negations. Meanwhile, we give a characterization of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-(constant) Sheffer strokes. Besides, we provide several construction methods of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes. Interestingly, we show that <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-pre-conjunctions, <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-pre-disjunctions, (light) <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-pre-t-norms, (light) <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-pre-t-conorms, <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-(quasi-)overlap and grouping functions, and <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-implication functions can be obtained through adequate combinations of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes. Finally, we present an example of a potential application of <span><math><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span>-Sheffer strokes in fire detectors.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432615","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 prime filter theorem in multilattices","authors":"Luc Éméry Diékouam Fotso ,&nbsp;Carole Pierre Kengne ,&nbsp;Daquin Cédric Awouafack","doi":"10.1016/j.fss.2024.109148","DOIUrl":"10.1016/j.fss.2024.109148","url":null,"abstract":"<div><div>This paper mainly focuses on building the fuzzy prime filter theorem for multilattices. Firstly, we introduce the notion of a fuzzy filter generated by a fuzzy subset of a multilattice and we give a characterization. Also, we define four types of fuzzy prime filters and establish some relationships between them. Finally, we state and prove the fuzzy prime filter theorem in distributive multilattices.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531222","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 fuzzy inner products constructed by fuzzy numbers in linear spaces","authors":"Jian-Zhong Xiao ,&nbsp;Chen-Ying Wang","doi":"10.1016/j.fss.2024.109144","DOIUrl":"10.1016/j.fss.2024.109144","url":null,"abstract":"<div><div>In this paper a new definition for fuzzy inner product spaces is presented. Just as the set of real numbers can be embedded in a set of fuzzy numbers, a crisp inner product space can be considered as a special case of fuzzy inner product spaces. An example is given to demonstrate that, the new definition is a nontrivial generalization for the crisp inner product spaces. Under certain restrictions, a fuzzy inner product space can become a fuzzy normed space. Based on some elementary properties for the families of semi-inner products of endpoints, the linearly topological structure of new spaces is discussed. Moreover, the orthogonality between two vectors is considered and a fuzzy version of Pythagorean theorem is given.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420975","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}