This paper studies a class of credibilistic optimization (CO) problems, in which a convex objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to discuss the robust counterpart approximations of ambiguous credibilistic constraints. Under mild assumptions, the closed property about the feasible region of credibilistic constraint is discussed. Using the obtained results, this paper deals with the robust counterpart approximations of credibilistic constraints under two types of ambiguity sets of possibility distributions. The first type is exponential function-based ambiguity set of possibility distribution, while the second type of ambiguity set is a particular case of the first one, and it is based on range and expectation information of fuzzy variables. The developed approximation techniques are capable to utilize the knowledge of ambiguity sets of possibility distributions when building distribution uncertainty-immunized solutions. As a result, the obtained safe approximations of ambiguous credibilistic constraints are computationally tractable convex/linear constraints. To apply the proposed approximation approach, a portfolio optimization problem is addressed, in which the investor is to find a portfolio to maximize the value-at-risk of his total return under the support and expectation information of uncertain returns. We use two types of robust counterpart approximations to credibilistic constraints. The computational results support our arguments.
{"title":"(2003-5785) Approximating credibilistic constraints by robust counterparts of uncertain linear inequality","authors":"N. Liu, Y. J. Chen, Yankui Liu","doi":"10.22111/IJFS.2021.6075","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6075","url":null,"abstract":"This paper studies a class of credibilistic optimization (CO) problems, in which a convex objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to discuss the robust counterpart approximations of ambiguous credibilistic constraints. Under mild assumptions, the closed property about the feasible region of credibilistic constraint is discussed. Using the obtained results, this paper deals with the robust counterpart approximations of credibilistic constraints under two types of ambiguity sets of possibility distributions. The first type is exponential function-based ambiguity set of possibility distribution, while the second type of ambiguity set is a particular case of the first one, and it is based on range and expectation information of fuzzy variables. The developed approximation techniques are capable to utilize the knowledge of ambiguity sets of possibility distributions when building distribution uncertainty-immunized solutions. As a result, the obtained safe approximations of ambiguous credibilistic constraints are computationally tractable convex/linear constraints. To apply the proposed approximation approach, a portfolio optimization problem is addressed, in which the investor is to find a portfolio to maximize the value-at-risk of his total return under the support and expectation information of uncertain returns. We use two types of robust counterpart approximations to credibilistic constraints. The computational results support our arguments.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81489594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article presents a new, multidimensional arithmetic of type 2 fuzzy numbers (M-IT2-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type 2 standard fuzzy arithmetic (IT2-SF arithmetic). The proposed M-IT2-F arithmetic has mathematical properties that IT2-SF arithmetic does not have. Thanks to these properties, it provides accurate calculation results that are not over- or under-estimated in terms of uncertainty. The paper contains comparisons of both types of arithmetic in application to two problems. Fuzzy arithmetic is not a finished work and is in a phase of continuous improvement and development. M-IT2-F arithmetic is a higher form of M-IT2 (non-fuzzy) arithmetic.
{"title":"(2008-6074) Multidimensional interval type 2 epistemic fuzzy arithmetic","authors":"A. Piegat, M. Landowski","doi":"10.22111/IJFS.2021.6076","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6076","url":null,"abstract":"The article presents a new, multidimensional arithmetic of type 2 fuzzy numbers (M-IT2-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type 2 standard fuzzy arithmetic (IT2-SF arithmetic). The proposed M-IT2-F arithmetic has mathematical properties that IT2-SF arithmetic does not have. Thanks to these properties, it provides accurate calculation results that are not over- or under-estimated in terms of uncertainty. The paper contains comparisons of both types of arithmetic in application to two problems. Fuzzy arithmetic is not a finished work and is in a phase of continuous improvement and development. M-IT2-F arithmetic is a higher form of M-IT2 (non-fuzzy) arithmetic.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75010525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multiple twin support vector machine (MTSVM) which evaluates all the training data into a ``one-versus-rest'' structure is a multi-class classification algorithm. It has extensive applications in the multi-class classification problems. Like twin support vector machine (TSVM), MTSVM treats all sample points equally because it lacks the ability to judge the importance of different sample points. In order to improve the classification performance of MTSVM, a new method of adding interval-valued fuzzy membership degree to sample points is proposed. In this way, a novel interval-valued fuzzy multiple twin support vector machine (IVF-MTSVM) is established in this paper. Previous methods of adding fuzzy membership degree to sample points are totally based on their importance to the class, while the method in this paper emphasizes the importance of sample points to the classification model, and takes into account the importance to the class to some extent. This is a new perspective to establish fuzzy membership degree to sample points in support vector machines since it is different from the previous methods in thinking. Then the solution to IVF-MTSVM is derived. Experiments on UCI datasets show that this new method has certain advantages over other multi-class twin support vector machine methods in ``one-versus-rest'' structure and other fuzzy multiple twin support vector machine established by some previous methods. Finally, Friedman test and Benferroni-Dunn test are used to verify the statistical significance of this new method.
多孪生支持向量机(Multiple twin support vector machine, MTSVM)是一种多类分类算法，它将所有训练数据评估为“一对余”结构。它在多类分类问题中有着广泛的应用。与双支持向量机(TSVM)一样，由于缺乏判断不同样本点重要性的能力，MTSVM对所有样本点一视同仁。为了提高MTSVM的分类性能，提出了在样本点上加入区间值模糊隶属度的新方法。在此基础上，建立了一种新的区间值模糊多孪生支持向量机。以往对样本点添加模糊隶属度的方法完全是基于样本点对类的重要性，而本文的方法强调了样本点对分类模型的重要性，并在一定程度上考虑了样本点对类的重要性。在思路上不同于以往的方法，为支持向量机中样本点模糊隶属度的建立提供了一个新的视角。然后推导了IVF-MTSVM的解。在UCI数据集上的实验表明，该方法在“one- against -rest”结构和其他一些方法建立的模糊多类双胞胎支持向量机方面，比其他多类双胞胎支持向量机方法具有一定的优势。最后利用Friedman检验和Benferroni-Dunn检验验证了新方法的统计显著性。
{"title":"A novel interval-valued fuzzy multiple twin support vector machine","authors":"H. Ju, W. Qiang, Ling Jing","doi":"10.22111/IJFS.2021.5916","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5916","url":null,"abstract":"Multiple twin support vector machine (MTSVM) which evaluates all the training data into a ``one-versus-rest'' structure is a multi-class classification algorithm. It has extensive applications in the multi-class classification problems. Like twin support vector machine (TSVM), MTSVM treats all sample points equally because it lacks the ability to judge the importance of different sample points. In order to improve the classification performance of MTSVM, a new method of adding interval-valued fuzzy membership degree to sample points is proposed. In this way, a novel interval-valued fuzzy multiple twin support vector machine (IVF-MTSVM) is established in this paper. Previous methods of adding fuzzy membership degree to sample points are totally based on their importance to the class, while the method in this paper emphasizes the importance of sample points to the classification model, and takes into account the importance to the class to some extent. This is a new perspective to establish fuzzy membership degree to sample points in support vector machines since it is different from the previous methods in thinking. Then the solution to IVF-MTSVM is derived. Experiments on UCI datasets show that this new method has certain advantages over other multi-class twin support vector machine methods in ``one-versus-rest'' structure and other fuzzy multiple twin support vector machine established by some previous methods. Finally, Friedman test and Benferroni-Dunn test are used to verify the statistical significance of this new method.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73110714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fuzzy random partial differential equations (PDEs) present a connection between random dynamical systems with nonstatistical inexactness data. These blended models could be efficiently used in modeling dynamical systems working in vagueness and ambiguity environments such as fuzzy random adaptive control, fuzzy random financial prediction, fuzzy random biological modeling, etc. In this article, we study Goursat problem for fuzzy random wave equations in the framework of generalized complete metric spaces in the sense of Luxemburg. We consider equations under generalized Hukuhara differentiability. The force functions are constrained by generalized Lipschitz conditions, that makes the range of PDEs types wider than using unbounded and locally Lipschitz conditions. The existence, uniqueness and boundedness of fuzzy solutions are investigated by employing Picard successive approximation method and Luxemburg fixed point theorem. Some illustrated examples are given to demonstrate for theoretical results.
{"title":"On Goursat problem for fuzzy random partial differential equations under generalized Lipschitz conditions","authors":"N. T. K. Son, H. Long, N. P. Dong","doi":"10.22111/IJFS.2021.5912","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5912","url":null,"abstract":"Fuzzy random partial differential equations (PDEs) present a connection between random dynamical systems with nonstatistical inexactness data. These blended models could be efficiently used in modeling dynamical systems working in vagueness and ambiguity environments such as fuzzy random adaptive control, fuzzy random financial prediction, fuzzy random biological modeling, etc. In this article, we study Goursat problem for fuzzy random wave equations in the framework of generalized complete metric spaces in the sense of Luxemburg. We consider equations under generalized Hukuhara differentiability. The force functions are constrained by generalized Lipschitz conditions, that makes the range of PDEs types wider than using unbounded and locally Lipschitz conditions. The existence, uniqueness and boundedness of fuzzy solutions are investigated by employing Picard successive approximation method and Luxemburg fixed point theorem. Some illustrated examples are given to demonstrate for theoretical results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76785326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article aimed to investigate the problem of global dissipativity of Fuzzy Bidirectional Associative Memory Neural Networks (FBAMNNs- for short) with proportional delays. Via Lyapunov Functionals (LFs- for short) and Linear Matrix Inequality (LMI- for short) approach, we obtained new sufficient conditions to guarantee the global dissipativity and global exponential dissipativity of the proposed model. In addition, two different types of activation functions are considered, including general bounded and Lipschitz-type activation functions. Moreover, the globally attractive and globally exponentially attractive sets are presented. Lastly, two numerical examples are given to illustrate the effectiveness of the developed results.
{"title":"Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays","authors":"C. Aouiti, R. Sakthivel, F. Touati","doi":"10.22111/IJFS.2021.5914","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5914","url":null,"abstract":"This article aimed to investigate the problem of global dissipativity of Fuzzy Bidirectional Associative Memory Neural Networks (FBAMNNs- for short) with proportional delays. Via Lyapunov Functionals (LFs- for short) and Linear Matrix Inequality (LMI- for short) approach, we obtained new sufficient conditions to guarantee the global dissipativity and global exponential dissipativity of the proposed model. In addition, two different types of activation functions are considered, including general bounded and Lipschitz-type activation functions. Moreover, the globally attractive and globally exponentially attractive sets are presented. Lastly, two numerical examples are given to illustrate the effectiveness of the developed results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74086580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, Fang and Hu introduced the definition of semi-t-operators on bounded lattices. In this study, we propose several construction methods to obtain such a semi-t-operator from a given semi-t-conorm and semi-t-norm on bounded lattices. Furthermore, we discuss the presence of idempotent semi-t-operators on bounded lattices, and show several different methods for construction of idempotent semi-t-operators on bounded lattices with additional constraints.
{"title":"Semi-t-operators and idempotent semi-t-operators on bounded lattices","authors":"Yan Wang, Z. Li, Huaxiang Liu","doi":"10.22111/IJFS.2021.5918","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5918","url":null,"abstract":"Recently, Fang and Hu introduced the definition of semi-t-operators on bounded lattices. In this study, we propose several construction methods to obtain such a semi-t-operator from a given semi-t-conorm and semi-t-norm on bounded lattices. Furthermore, we discuss the presence of idempotent semi-t-operators on bounded lattices, and show several different methods for construction of idempotent semi-t-operators on bounded lattices with additional constraints.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79111918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the existence of solutions to first-order interval-valued differential equations with length constraints under gH-differentiability. By using the fixed point theory of compact maps on metric spaces, we provide some sufficient conditions for the existence of solutions. At the end of this paper, we show some examples to illustrate our results.
{"title":"On the existence of solutions to interval-valued differential equations with length constraints","authors":"H. Wang, R. Rodríguez-López","doi":"10.22111/IJFS.2021.5909","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5909","url":null,"abstract":"In this paper, we consider the existence of solutions to first-order interval-valued differential equations with length constraints under gH-differentiability. By using the fixed point theory of compact maps on metric spaces, we provide some sufficient conditions for the existence of solutions. At the end of this paper, we show some examples to illustrate our results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83409865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to the large use of fuzzy numbers, the ranking of these numbers is very important.In this paper, we propose a new method for ranking generalized fuzzy numbers with different left and right heights.The proposed method, at first obtains the centers of gravity of fuzzy numbers and left and right side crisp numbers; then by computing left and right areas associated with them, ranks the fuzzy numbers. The proposed method can overcome the flaws and defects of some ranking methods, and the provided examples are evidence of this. Finally this method is applied to the fuzzy risk analysis problem.
{"title":"A novel method for ranking generalized fuzzy numbers with two different heights and its application in fuzzy risk analysis","authors":"Y. Barazandeh, B. Ghazanfari","doi":"10.22111/IJFS.2021.5915","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5915","url":null,"abstract":"Due to the large use of fuzzy numbers, the ranking of these numbers is very important.In this paper, we propose a new method for ranking generalized fuzzy numbers with different left and right heights.The proposed method, at first obtains the centers of gravity of fuzzy numbers and left and right side crisp numbers; then by computing left and right areas associated with them, ranks the fuzzy numbers. The proposed method can overcome the flaws and defects of some ranking methods, and the provided examples are evidence of this. Finally this method is applied to the fuzzy risk analysis problem.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89399735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Farlie-Gumble-Morgenstren (FGM) family and archimedean family are the most popular parametric families of copulas. In the present paper, we propose an extension of archimedean copulas with concave multiplicative generators in the style of FGM family. In particular, our method allows the modelling of higher positive dependence than the other FGM extensions in the literature. The construction and characteristics of the proposed model along with some examples of parametric subfamilies are provided. A numerical study is used to illustrate the methodology.
{"title":"FGM generated archimedean copulas with concave multiplicative generators","authors":"N. Doodman, M. Amini, H. Jabbari, A. Dolati","doi":"10.22111/IJFS.2021.5911","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5911","url":null,"abstract":"The Farlie-Gumble-Morgenstren (FGM) family and archimedean family are the most popular parametric families of copulas. In the present paper, we propose an extension of archimedean copulas with concave multiplicative generators in the style of FGM family. In particular, our method allows the modelling of higher positive dependence than the other FGM extensions in the literature. The construction and characteristics of the proposed model along with some examples of parametric subfamilies are provided. A numerical study is used to illustrate the methodology.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77923372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a new separated design of adaptive observer-based fault estimator (FE) and fault-tolerant control (FTC) is introduced for nonlinear systems along with sensor and actuator faults in the presence of external disturbance and parametric modeling uncertainty by T-S fuzzy modeling, which can easily challenge integrated design strategies. Firstly, a new fuzzy adaptive FE estimates actuator/sensor faults, and the system states simultaneously and also can automatically estimate and compensates bi-directional uncertainties between FE function and control system. Secondly, a fuzzy state feedback FTC controller is designed based on these estimations. Then the proposed separated FE/FTC design presented which is solved by linear matrix inequality via $H_infty$ optimization. Finally, a tutorial example of an inverted pendulum on a cart demonstrates the validity and effectiveness of the proposed design.
{"title":"A new separated fault estimator and fault-tolerant control design strategy for uncertain nonlinear systems using T-S fuzzy modeling","authors":"M. Cheraghiyan","doi":"10.22111/IJFS.2021.5919","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5919","url":null,"abstract":"In this paper, a new separated design of adaptive observer-based fault estimator (FE) and fault-tolerant control (FTC) is introduced for nonlinear systems along with sensor and actuator faults in the presence of external disturbance and parametric modeling uncertainty by T-S fuzzy modeling, which can easily challenge integrated design strategies. Firstly, a new fuzzy adaptive FE estimates actuator/sensor faults, and the system states simultaneously and also can automatically estimate and compensates bi-directional uncertainties between FE function and control system. Secondly, a fuzzy state feedback FTC controller is designed based on these estimations. Then the proposed separated FE/FTC design presented which is solved by linear matrix inequality via $H_infty$ optimization. Finally, a tutorial example of an inverted pendulum on a cart demonstrates the validity and effectiveness of the proposed design.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76664558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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