Pub Date : 2024-11-16DOI: 10.1016/j.fss.2024.109192
Bilel Selmi
The main objective of this paper is to investigate the average general fractal dimensions of typical compact metric spaces within the Gromov-Hausdorff space, using the Gromov-Hausdorff metric. As an application of the main results, we demonstrate that a typical compact metric space Σ exhibits such irregularity that the lower and upper average general Hewitt-Stromberg dimensions, as well as the general box dimensions corresponding to all higher-order Hölder and Cesàro averages, diverge significantly.
{"title":"Average general fractal dimensions of typical compact metric spaces","authors":"Bilel Selmi","doi":"10.1016/j.fss.2024.109192","DOIUrl":"10.1016/j.fss.2024.109192","url":null,"abstract":"<div><div>The main objective of this paper is to investigate the average general fractal dimensions of typical compact metric spaces within the Gromov-Hausdorff space, using the Gromov-Hausdorff metric. As an application of the main results, we demonstrate that a typical compact metric space Σ exhibits such irregularity that the lower and upper average general Hewitt-Stromberg dimensions, as well as the general box dimensions corresponding to all higher-order Hölder and Cesàro averages, diverge significantly.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109192"},"PeriodicalIF":3.2,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663939","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}
Pub Date : 2024-11-15DOI: 10.1016/j.fss.2024.109190
Xiangjie Fang, Kuanyun Zhu
In 2022, Zhu et al. [14] studied the α-cross-migrativity between uninorms and overlap (grouping) functions, and mainly characterized in detail the corresponding cross-migrativity property when uninorms belong to five general classes (i.e., , , , and ), respectively. However, the results obtained by Zhu et al. have some defects, such as lengthy (or unclear) proofs, false proofs and faulty conclusions. Therefore, this paper indicates the defects and reasons, and the corresponding correction. In addition, some further conclusions are given, which relates the α-cross-migrativity between uninorms and overlap (grouping) functions to α-cross-migrativity between t-norms (t-conorms) and overlap (grouping) functions.
{"title":"A note on the cross-migrativity between uninorms and overlap (grouping) functions","authors":"Xiangjie Fang, Kuanyun Zhu","doi":"10.1016/j.fss.2024.109190","DOIUrl":"10.1016/j.fss.2024.109190","url":null,"abstract":"<div><div>In 2022, Zhu et al. <span><span>[14]</span></span> studied the <em>α</em>-cross-migrativity between uninorms and overlap (grouping) functions, and mainly characterized in detail the corresponding cross-migrativity property when uninorms belong to five general classes (i.e., <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>min</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>max</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi><mi>d</mi><mi>e</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>r</mi><mi>e</mi><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>cos</mi></mrow></msub></math></span>), respectively. However, the results obtained by Zhu et al. have some defects, such as lengthy (or unclear) proofs, false proofs and faulty conclusions. Therefore, this paper indicates the defects and reasons, and the corresponding correction. In addition, some further conclusions are given, which relates the <em>α</em>-cross-migrativity between uninorms and overlap (grouping) functions to <em>α</em>-cross-migrativity between t-norms (t-conorms) and overlap (grouping) functions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109190"},"PeriodicalIF":3.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663948","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}
This study emanates from a simple observation: as specified by Vapnik [37] in his study, an artificial neural network cannot generate a universal approximator if the aggregation function chosen to design the artificial neuron does not include non-linearity. The usual option is to follow a linear aggregation by a non-linear function, or so-called activation function. We wonder if this approach could be replaced by one using a natively non-linear aggregation function.
Among all of the available non-linear aggregation functions, here we are interested in aggregations based on weighted minimum and weighted maximum operations [8]. As these operators were originally developed within a possibility theory and fuzzy rule framework, such operators cannot be easily integrated into a neural network because the values that are usually considered belong to . For gradient descent based learning, a neuron must be an aggregation function derivable with respect to its inputs and synaptic weights, whose variables (synaptic weights, inputs and outputs) must all be signed real values. We thus propose an extension of weighted maximum based aggregation to enable this learning process. We show that such an aggregation can be seen as a combination of four Sugeno integrals. Finally, we compare this type of approach with the classical one.
{"title":"Combining thresholded real values for designing an artificial neuron in a neural network","authors":"Olivier Strauss , Agnès Rico , Jérôme Pasquet , Lionel Pibre","doi":"10.1016/j.fss.2024.109191","DOIUrl":"10.1016/j.fss.2024.109191","url":null,"abstract":"<div><div>This study emanates from a simple observation: as specified by Vapnik <span><span>[37]</span></span> in his study, an artificial neural network cannot generate a universal approximator if the aggregation function chosen to design the artificial neuron does not include non-linearity. The usual option is to follow a linear aggregation by a non-linear function, or so-called activation function. We wonder if this approach could be replaced by one using a natively non-linear aggregation function.</div><div>Among all of the available non-linear aggregation functions, here we are interested in aggregations based on weighted minimum and weighted maximum operations <span><span>[8]</span></span>. As these operators were originally developed within a possibility theory and fuzzy rule framework, such operators cannot be easily integrated into a neural network because the values that are usually considered belong to <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. For gradient descent based learning, a neuron must be an aggregation function derivable with respect to its inputs and synaptic weights, whose variables (synaptic weights, inputs and outputs) must all be signed real values. We thus propose an extension of weighted maximum based aggregation to enable this learning process. We show that such an aggregation can be seen as a combination of four Sugeno integrals. Finally, we compare this type of approach with the classical one.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109191"},"PeriodicalIF":3.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663949","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}
Pub Date : 2024-11-12DOI: 10.1016/j.fss.2024.109176
Feiyue Shen , Haoyi Zhang , Wenhai Qi , Ju H. Park , Jun Cheng , Kaibo Shi
This paper studies the nonfragile anti-transitional-asynchrony fault tolerant control for discrete interval type-2 fuzzy semi-Markov jump systems with bounded dwell time. In contrast to the traditional Takagi-Sugeno (T-S) fuzzy model, this paper utilises the interval 2-type fuzzy model to represent the nonlinear discrete semi-Markov jump systems. The main novelty is to design an anti-transitional-asynchrony fault-tolerant control mechanism with controller gain fluctuations under the framework of IT2 fuzzy, fault-tolerant control, and transitional asynchrony, which reduces the conservatism to a certain extent. The transitional asynchrony is adopted, i.e., the controller switching lags behind the plant switching, and this lag is associated with the transition between the current mode and the next mode. By virtue of semi-Markov kernel method, the mean-square stability of the underlying system is achieved, overcoming the difficulties caused by the transitional asynchrony. In addition, taking into account that the actuator may encounter random faults during system operation, this paper applies a fault tolerant method in the design of nonfragile anti-transitional-asynchrony control to improve the fault tolerance of the system. Finally, a tunnel circuit model verifies the effectiveness of the designed control method.
{"title":"Nonfragile anti-transitional-asynchrony fault tolerant control for IT2 fuzzy semi-Markov jump systems with actuator failures","authors":"Feiyue Shen , Haoyi Zhang , Wenhai Qi , Ju H. Park , Jun Cheng , Kaibo Shi","doi":"10.1016/j.fss.2024.109176","DOIUrl":"10.1016/j.fss.2024.109176","url":null,"abstract":"<div><div>This paper studies the nonfragile anti-transitional-asynchrony fault tolerant control for discrete interval type-2 fuzzy semi-Markov jump systems with bounded dwell time. In contrast to the traditional Takagi-Sugeno (T-S) fuzzy model, this paper utilises the interval 2-type fuzzy model to represent the nonlinear discrete semi-Markov jump systems. The main novelty is to design an anti-transitional-asynchrony fault-tolerant control mechanism with controller gain fluctuations under the framework of IT2 fuzzy, fault-tolerant control, and transitional asynchrony, which reduces the conservatism to a certain extent. The transitional asynchrony is adopted, i.e., the controller switching lags behind the plant switching, and this lag is associated with the transition between the current mode and the next mode. By virtue of semi-Markov kernel method, the mean-square stability of the underlying system is achieved, overcoming the difficulties caused by the transitional asynchrony. In addition, taking into account that the actuator may encounter random faults during system operation, this paper applies a fault tolerant method in the design of nonfragile anti-transitional-asynchrony control to improve the fault tolerance of the system. Finally, a tunnel circuit model verifies the effectiveness of the designed control method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109176"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663944","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}
Pub Date : 2024-11-12DOI: 10.1016/j.fss.2024.109171
Siyu Guo, Yingnan Pan, Zhechen Zhu
This paper considers the prescribed performance fuzzy adaptive tracking control problem of multiagent systems under a chaos-based privacy-preserving mechanism and a learning-enabled event-triggered mechanism. Initially, a chaos-based mask function is constructed, which is related to the chaotic states in the Lorentz system. The utilization of chaos adds unpredictability and full randomness to the mask function, which greatly reduces the risk of privacy leakage. Additionally, two value functions are designed as inputs of the fully connected neural network, and the fully connected neural network is used to predict the parameter value in the event-triggered mechanism, which effectively enhances the flexibility of the proposed learning-enabled event-triggered mechanism. Furthermore, in the process of controller design, by employing an error transformed function, the system errors are stabilized within the prescribed performance boundaries. Finally, a simulation example is provided to validate the effectiveness of the proposed control scheme.
{"title":"Learning-enabled event-triggered fuzzy adaptive control of multiagent systems with prescribed performance: A chaos-based privacy-preserving method","authors":"Siyu Guo, Yingnan Pan, Zhechen Zhu","doi":"10.1016/j.fss.2024.109171","DOIUrl":"10.1016/j.fss.2024.109171","url":null,"abstract":"<div><div>This paper considers the prescribed performance fuzzy adaptive tracking control problem of multiagent systems under a chaos-based privacy-preserving mechanism and a learning-enabled event-triggered mechanism. Initially, a chaos-based mask function is constructed, which is related to the chaotic states in the Lorentz system. The utilization of chaos adds unpredictability and full randomness to the mask function, which greatly reduces the risk of privacy leakage. Additionally, two value functions are designed as inputs of the fully connected neural network, and the fully connected neural network is used to predict the parameter value in the event-triggered mechanism, which effectively enhances the flexibility of the proposed learning-enabled event-triggered mechanism. Furthermore, in the process of controller design, by employing an error transformed function, the system errors are stabilized within the prescribed performance boundaries. Finally, a simulation example is provided to validate the effectiveness of the proposed control scheme.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109171"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663946","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}
Pub Date : 2024-11-12DOI: 10.1016/j.fss.2024.109189
Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou
We give the concept of subdifferentiability for a fuzzy n-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.
我们给出了模糊 n 单元数值函数的次微分性概念。然后，我们根据新定义阐述了与次微分性相关的一些定理。最后，我们介绍了优化问题的一些应用，包括拉格朗日对偶问题和复合最小化问题。
{"title":"Subdifferential of fuzzy n-cell number-valued functions and its applications in optimization problems","authors":"Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou","doi":"10.1016/j.fss.2024.109189","DOIUrl":"10.1016/j.fss.2024.109189","url":null,"abstract":"<div><div>We give the concept of subdifferentiability for a fuzzy <em>n</em>-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109189"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663947","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}
Pub Date : 2024-11-08DOI: 10.1016/j.fss.2024.109180
Yang Wu, Lianjun Hu, Qi Chen, Yong Zhang, Libing Wu
This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.
{"title":"Dynamic event-triggered fault-tolerant control for nonaffine systems with asymmetric error constraint","authors":"Yang Wu, Lianjun Hu, Qi Chen, Yong Zhang, Libing Wu","doi":"10.1016/j.fss.2024.109180","DOIUrl":"10.1016/j.fss.2024.109180","url":null,"abstract":"<div><div>This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109180"},"PeriodicalIF":3.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663943","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}
Pub Date : 2024-11-08DOI: 10.1016/j.fss.2024.109188
Bin Pang , Xiu-Yun Wu , Bernard De Baets
Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.
{"title":"Geometric properties of ternary fuzzy relations","authors":"Bin Pang , Xiu-Yun Wu , Bernard De Baets","doi":"10.1016/j.fss.2024.109188","DOIUrl":"10.1016/j.fss.2024.109188","url":null,"abstract":"<div><div>Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that <em>axiomatic properties</em> of ternary fuzzy relations seem to be ideally suited to capture <em>geometric characteristics</em> of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as <em>geometric properties</em>. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109188"},"PeriodicalIF":3.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663945","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}
Pub Date : 2024-11-07DOI: 10.1016/j.fss.2024.109165
Ali Dastbaravarde, Ali Dolati
A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.
{"title":"Quantile dependence: A generalization of upper and lower tail dependence","authors":"Ali Dastbaravarde, Ali Dolati","doi":"10.1016/j.fss.2024.109165","DOIUrl":"10.1016/j.fss.2024.109165","url":null,"abstract":"<div><div>A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109165"},"PeriodicalIF":3.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663940","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}
Pub Date : 2024-11-07DOI: 10.1016/j.fss.2024.109169
Wojciech Sałabun
This paper introduces Asymmetric Interval Numbers , a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity. incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for , discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for . Several illustrative examples demonstrate the practical application of . Although challenges remain, such as exploring performance with different distributions and reducing overestimation, present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of , paving the way for further research and application in diverse scientific and industrial contexts.
本文介绍了非对称区间数 (AIN)，这是一种新型区间数，它结合了经典区间数的直接识别特性和模糊集的先进不确定性建模能力，同时又保持了简洁性。AIN 包含区间内的期望值，与经典区间数相比，能更准确地表示数据的不确定性。我们定义了 AIN 的基本算术运算，讨论了它们的特性，并提供了证明。此外，我们还提出了基本二元和一元运算的对称性和不对称性定理，从而加强了 AIN 的数学框架。几个示例展示了 AIN 的实际应用。尽管仍存在一些挑战，如探索不同分布的性能和减少高估，但 AINs 是区间运算中一个很有前途的进步。本研究强调了 AINs 的实践和理论意义，为进一步研究 AINs 并将其应用于各种科学和工业领域铺平了道路。
{"title":"Asymmetric interval numbers: A new approach to modeling uncertainty","authors":"Wojciech Sałabun","doi":"10.1016/j.fss.2024.109169","DOIUrl":"10.1016/j.fss.2024.109169","url":null,"abstract":"<div><div>This paper introduces Asymmetric Interval Numbers <span><math><mo>(</mo><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi><mo>)</mo></math></span>, a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity. <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span> incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span>, discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span>. Several illustrative examples demonstrate the practical application of <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span>. Although challenges remain, such as exploring performance with different distributions and reducing overestimation, <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span> present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of <span><math><mi>A</mi><mi>I</mi><mi>N</mi><mi>s</mi></math></span>, paving the way for further research and application in diverse scientific and industrial contexts.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109169"},"PeriodicalIF":3.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663942","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}
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