This paper aims to establish the existence and uniqueness results for two kinds of implicit uncertain fractional integral equations with the fuzzy concept via the fixed point theorem and successive approximation method. Besides, we also present various Ulam-Hyers stability and Ulam-Hyers-Rassias stability results of two kinds of implicit fuzzy fractional integral equations. Finally, some examples are given to illustrate our main results.
{"title":"On the stability for implicit uncertain fractional integral equations with fuzzy concept","authors":"N. Hoa","doi":"10.22111/IJFS.2021.5882","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5882","url":null,"abstract":"This paper aims to establish the existence and uniqueness results for two kinds of implicit uncertain fractional integral equations with the fuzzy concept via the fixed point theorem and successive approximation method. Besides, we also present various Ulam-Hyers stability and Ulam-Hyers-Rassias stability results of two kinds of implicit fuzzy fractional integral equations. Finally, some examples are given to illustrate our main results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82188859","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 purpose of this study is to develop a dairy global supply chain planning model in which operational and financial dimensions are appropriately integrated in order to adjust the credit sale strategy. In order to evaluate the financial performance of the dairy supply chain, economic value-added index and some financial ratios are used. The proposed model is compared to traditional approaches, which usually use the profit maximization as an objective function. Also, the amount of credit sales is considered as a decision variable for the first time in this research. The developed model utilized a new risk measure, i.e., the fuzzy CVaR, to cope with the uncertainty of the exchange rate and the quality and quantity of returned products. The effectiveness and efficiency of the proposed model are analyzed and assessed using the data of a real dairy supply chain. The analysis of results obtained from the developed fuzzy mathematical model shows an increase in profit and a reduction in semi-variance compared to previously developed models. Also, some numerical experiments analyses index and the impact of credit sales strategy.
{"title":"Adjusting the credit sales using CVaR-based robust possibilistic programming approach","authors":"A. Yousefi, M. Pishvaee, E. Teimoury","doi":"10.22111/IJFS.2021.5877","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5877","url":null,"abstract":"The purpose of this study is to develop a dairy global supply chain planning model in which operational and financial dimensions are appropriately integrated in order to adjust the credit sale strategy. In order to evaluate the financial performance of the dairy supply chain, economic value-added index and some financial ratios are used. The proposed model is compared to traditional approaches, which usually use the profit maximization as an objective function. Also, the amount of credit sales is considered as a decision variable for the first time in this research. The developed model utilized a new risk measure, i.e., the fuzzy CVaR, to cope with the uncertainty of the exchange rate and the quality and quantity of returned products. The effectiveness and efficiency of the proposed model are analyzed and assessed using the data of a real dairy supply chain. The analysis of results obtained from the developed fuzzy mathematical model shows an increase in profit and a reduction in semi-variance compared to previously developed models. Also, some numerical experiments analyses index and the impact of credit sales strategy.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78011082","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 presents a new robust adaptive sliding mode controller for a class of uncertain nonlinear systems whereas only the system output is measurable. Firstly, a robust adaptive fuzzy observer is designed for the system in order to estimate its state variables. The robust asymptotic convergence of the proposed observer is proven by Lyapunov direct method. Then based on the observation states, a robust adaptive sliding mode controller is suggested such that the closed loop system to be asymptotically stable. Robust asymptotic stability of the overall system suggested by the controller is also confirmed based on Lyapunov theory. Simulation results illustrate practicality and effectiveness of the proposed technique for controlling uncertain nonlinear systems.
{"title":"Robust output feedback adaptive sliding mode control for a class of uncertain nonlinear systems using robust adaptive fuzzy observer","authors":"A. A. Kalat, V. Mokhtari","doi":"10.22111/IJFS.2021.5881","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5881","url":null,"abstract":"This article presents a new robust adaptive sliding mode controller for a class of uncertain nonlinear systems whereas only the system output is measurable. Firstly, a robust adaptive fuzzy observer is designed for the system in order to estimate its state variables. The robust asymptotic convergence of the proposed observer is proven by Lyapunov direct method. Then based on the observation states, a robust adaptive sliding mode controller is suggested such that the closed loop system to be asymptotically stable. Robust asymptotic stability of the overall system suggested by the controller is also confirmed based on Lyapunov theory. Simulation results illustrate practicality and effectiveness of the proposed technique for controlling uncertain nonlinear systems.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79398515","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}
Nowadays, some burgeoning issues occurring in green and sustainable supply chain face an increasing number of tackles, including uncertain factors and unobserved data, which makes it even more complicated to assess supply chain efficiency. To address this issue, this paper applies uncertainty theory to two-stage network DEA intending to deal with inaccurate data. Moreover, the bi-echelon supply chain generally suffers asymmetric power among involved members. Therefore, this paper proposes attrition rate (D) and fulfillment rate (G) in the first and second stages respectively so as to reveal the bi-echelon supply chain within different leader-follower patterns. The first two models assume the upstream firm is the leader while the last two models regard the downstream firm as the leader. We find out that the results of the evaluation vary under divergent patterns accordingly by running a numerical example. Adopting proposed models can help decision-makers of the multistage supply chain make decisions more effectively and avoid possible mistakes.
{"title":"Uncertain network DEA models for evaluating efficiencies of Bi-echelon supply chain with asymmetric power","authors":"Bao Jiang, L. Peng, Jian Li, Waichon Lio","doi":"10.22111/IJFS.2021.5874","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5874","url":null,"abstract":"Nowadays, some burgeoning issues occurring in green and sustainable supply chain face an increasing number of tackles, including uncertain factors and unobserved data, which makes it even more complicated to assess supply chain efficiency. To address this issue, this paper applies uncertainty theory to two-stage network DEA intending to deal with inaccurate data. Moreover, the bi-echelon supply chain generally suffers asymmetric power among involved members. Therefore, this paper proposes attrition rate (D) and fulfillment rate (G) in the first and second stages respectively so as to reveal the bi-echelon supply chain within different leader-follower patterns. The first two models assume the upstream firm is the leader while the last two models regard the downstream firm as the leader. We find out that the results of the evaluation vary under divergent patterns accordingly by running a numerical example. Adopting proposed models can help decision-makers of the multistage supply chain make decisions more effectively and avoid possible mistakes.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78868679","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 deals with the problem H∞ control under network T-S fuzzy system with random packet dropouts for the synchronous machine. In the control design, the intermittent data loss existing in the closed-loop system is taken into account. Two main approaches adopted in this paper to design the fuzzy controller. First, a new version of the T-S fuzzy state-feedback controller is constructed to guarantee the resulting closed-loop system to be stochastically stable. Furthermore, in this regard, by taking into account a new version of fuzzy Lyapunov-Krasovskii functional (LKF) in conjunction with free weighting matrices, containing mode-dependent non-integral term such that the resulting system is stochastically stable with the desired performance. Second, to establish the pole place method (PPM) with the membership function. Furthermore, to make the controller design more convenient, the designed controller does not need to share the number of fuzzy rules and membership functions with the model. Synchronous machine parameters are used for the simulation results which are provided to show the usefulness of the proposed algorithm.
{"title":"Stability and stabilization of network T-S fuzzy systems with random packet-loss for Synchronous machine","authors":"M. S. Aslam, X. Dai, T. Zhao","doi":"10.22111/IJFS.2021.5870","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5870","url":null,"abstract":"This article deals with the problem H∞ control under network T-S fuzzy system with random packet dropouts for the synchronous machine. In the control design, the intermittent data loss existing in the closed-loop system is taken into account. Two main approaches adopted in this paper to design the fuzzy controller. First, a new version of the T-S fuzzy state-feedback controller is constructed to guarantee the resulting closed-loop system to be stochastically stable. Furthermore, in this regard, by taking into account a new version of fuzzy Lyapunov-Krasovskii functional (LKF) in conjunction with free weighting matrices, containing mode-dependent non-integral term such that the resulting system is stochastically stable with the desired performance. Second, to establish the pole place method (PPM) with the membership function. Furthermore, to make the controller design more convenient, the designed controller does not need to share the number of fuzzy rules and membership functions with the model. Synchronous machine parameters are used for the simulation results which are provided to show the usefulness of the proposed algorithm.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78218184","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 Hyers-Ulam-Rassias stability of theimpulsive fuzzy nonlinear difference equations in the multidimensional fuzzy quaternion space.Some sufficient conditions of the Hyers-Ulam-Rassias stability are established for the quaternion multidimensional fuzzy nonlinear difference equations with impulses and several examples are demonstrated to show the feasibility of our obtained results.
{"title":"(2005-5867) Hyers-Ulam-Rassias stability of quaternion multidimensional fuzzy nonlinear difference equations with impulses","authors":"Z. Li, Chao Wang, R. Agarwal, R. Sakthivel","doi":"10.22111/IJFS.2021.5950","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5950","url":null,"abstract":"In this paper, we consider the Hyers-Ulam-Rassias stability of theimpulsive fuzzy nonlinear difference equations in the multidimensional fuzzy quaternion space.Some sufficient conditions of the Hyers-Ulam-Rassias stability are established for the quaternion multidimensional fuzzy nonlinear difference equations with impulses and several examples are demonstrated to show the feasibility of our obtained results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79302876","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}
To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analysed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.
{"title":"(2002-5686) Milstein method for solving fuzzy differential equation","authors":"L. Ji, C. L. You","doi":"10.22111/IJFS.2021.5946","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5946","url":null,"abstract":"To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analysed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80624112","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}
M. Ghaffari, T. Allahviranloo, S. Abbasbandy, M. Azhini
The main purpose of this paper is to obtain an analytical solution for the time-fractional fuzzy equation. To do this, the time-fractional equation is transformed into an algebraic equation using the fuzzy Laplace and Fourier transforms. The fractional derivatives are described in the Caputo gH-differentiability. In addition, to demonstrate the efficiency of the method some various examples are solved.
本文的主要目的是得到时间分数型模糊方程的解析解。为此，使用模糊拉普拉斯变换和傅立叶变换将时间分数方程转换为代数方程。分数阶导数用Caputo h -可微性来描述。此外，为了证明该方法的有效性，还求解了一些不同的算例。
{"title":"(2004-5828) On the fuzzy solutions of time-fractional problems","authors":"M. Ghaffari, T. Allahviranloo, S. Abbasbandy, M. Azhini","doi":"10.22111/IJFS.2021.5935","DOIUrl":"https://doi.org/10.22111/IJFS.2021.5935","url":null,"abstract":"The main purpose of this paper is to obtain an analytical solution for the time-fractional fuzzy equation. To do this, the time-fractional equation is transformed into an algebraic equation using the fuzzy Laplace and Fourier transforms. The fractional derivatives are described in the Caputo gH-differentiability. In addition, to demonstrate the efficiency of the method some various examples are solved.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76795054","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}
We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular, 2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.
{"title":"(2009-6152) 2-set-based extended functions","authors":"R. Mesiar, A. Kolesárová, S. Borkotokey","doi":"10.22111/IJFS.2020.5816","DOIUrl":"https://doi.org/10.22111/IJFS.2020.5816","url":null,"abstract":"We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular, 2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74362529","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 reliability of a warm standby series-parallel system without adequate samples is studied based on the uncertainty theory. It is assumed that the lifetimes of system elements follow independent uncertainty distributions with uncertain parameters. Three different switch models, including absolutely reliable mode, discrete mode and continuous mode, are developed for the warm standby series-parallel system. Besides, the cold standby series-parallel system is discussed as a special case. The reliability function and mean time to failure of each developed model are analyzed. A numerical example for the system with different switches is implemented to illustrate the application and efficiency of the proposed models.
{"title":"(1912-5631) Reliability analysis of a warm standby series-parallel system with different switches and bi-uncertain lifetimes","authors":"Zhaocai Liu, Linmin Hu, Sijia Liu, Youzheng Wang","doi":"10.22111/IJFS.2020.5811","DOIUrl":"https://doi.org/10.22111/IJFS.2020.5811","url":null,"abstract":"The reliability of a warm standby series-parallel system without adequate samples is studied based on the uncertainty theory. It is assumed that the lifetimes of system elements follow independent uncertainty distributions with uncertain parameters. Three different switch models, including absolutely reliable mode, discrete mode and continuous mode, are developed for the warm standby series-parallel system. Besides, the cold standby series-parallel system is discussed as a special case. The reliability function and mean time to failure of each developed model are analyzed. A numerical example for the system with different switches is implemented to illustrate the application and efficiency of the proposed models.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83016396","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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