T. Allahviranloo, M. R. Balooch Shahryari, O. Sedaghatfar, M. R. Shahriari, R. Saadati, S. Noeiaghdam, U. Fernandez-Gamiz
In this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values −∞˜ and +∞˜ at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concepts such as fuzzy indicator function and fuzzy infimal convolution for extended fuzzy-valued functions. Finally, we introduce the concept of directional generalized derivative for extended above functions and its properties. Eventually, we give a practical example that will illustrate well the directional g-derivative for the extended fuzzy-valued convex function.
{"title":"The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications","authors":"T. Allahviranloo, M. R. Balooch Shahryari, O. Sedaghatfar, M. R. Shahriari, R. Saadati, S. Noeiaghdam, U. Fernandez-Gamiz","doi":"10.1155/2024/8335864","DOIUrl":"https://doi.org/10.1155/2024/8335864","url":null,"abstract":"In this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values −∞˜ and +∞˜ at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concepts such as fuzzy indicator function and fuzzy infimal convolution for extended fuzzy-valued functions. Finally, we introduce the concept of directional generalized derivative for extended above functions and its properties. Eventually, we give a practical example that will illustrate well the directional g-derivative for the extended fuzzy-valued convex function.","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140717975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we examine the numerical solutions of nonlinear fuzzy fractional partial differential equations under the Caputo derivative utilizing the technique of fuzzy Adomian decomposition. This technique is used as an alternative method for obtaining approximate fuzzy solutions to various types of fractional differential equations and also investigated some new existence and uniqueness results of fuzzy solutions. Some examples are given to support the effectiveness of the proposed technique. We present the numerical results in graphical form for different values of fractional order and uncertainty γ∈0,1.
{"title":"Usage of the Fuzzy Adomian Decomposition Method for Solving Some Fuzzy Fractional Partial Differential Equations","authors":"Nagwa A. Saeed, D. Pachpatte","doi":"10.1155/2024/8794634","DOIUrl":"https://doi.org/10.1155/2024/8794634","url":null,"abstract":"In this study, we examine the numerical solutions of nonlinear fuzzy fractional partial differential equations under the Caputo derivative utilizing the technique of fuzzy Adomian decomposition. This technique is used as an alternative method for obtaining approximate fuzzy solutions to various types of fractional differential equations and also investigated some new existence and uniqueness results of fuzzy solutions. Some examples are given to support the effectiveness of the proposed technique. We present the numerical results in graphical form for different values of fractional order and uncertainty γ∈0,1.","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cutter planning and control are the crucial problems in machining processes. The current literature indicates that the issue of cutter planning and control problem was not adequately researched in the past in a metal-cutting process. Usually, cutter planning and control problems were addressed using different optimization, simulation, and computer-aided planning (CAP) methods. To bridge this knowledge gap, this study proposed a decision support system (DSS) that can integrate fuzzy case-based reasoning (F-CBR) and fuzzy analytic hierarchy process (F-AHP) methods. This integration was applied to determine hybrid similarity measures between new and prior cases. The study provides new insights into the integration of fuzzy set theory (FST), CBR, and AHP for solving machining cutter planning and control problems. Our proposed system retrieves the best similar prior cases to reuse and adapt them to new order arrivals. A numerical example was illustrated to validate the soundness of the researched DSS.
{"title":"Application of Fuzzy Case-Based Reasoning and Fuzzy Analytic Hierarchy Process for Machining Cutter Planning and Control","authors":"Fentahun Moges Kasie, Glen Bright","doi":"10.1155/2023/8072930","DOIUrl":"https://doi.org/10.1155/2023/8072930","url":null,"abstract":"Cutter planning and control are the crucial problems in machining processes. The current literature indicates that the issue of cutter planning and control problem was not adequately researched in the past in a metal-cutting process. Usually, cutter planning and control problems were addressed using different optimization, simulation, and computer-aided planning (CAP) methods. To bridge this knowledge gap, this study proposed a decision support system (DSS) that can integrate fuzzy case-based reasoning (F-CBR) and fuzzy analytic hierarchy process (F-AHP) methods. This integration was applied to determine hybrid similarity measures between new and prior cases. The study provides new insights into the integration of fuzzy set theory (FST), CBR, and AHP for solving machining cutter planning and control problems. Our proposed system retrieves the best similar prior cases to reuse and adapt them to new order arrivals. A numerical example was illustrated to validate the soundness of the researched DSS.","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135917936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the process of composite resin prepreg tape winding, the presence of pores or voids among the layers of composite can result in reduced strength of winding. To alleviate this problem, it is required that the composite tape winding machines be designed such that the layers of composite are evenly wound on the previous one. The paper presents a novel design of flexible winding system for composite tape winding. Based on the analysis of errors in winding process, the novel winding system eliminates winding point error and winding angle error based on the speed controlled flexible roller. This paper also presents the kinetic analysis of the novel system and its controller design. Experiments are conducted on the novel winding system. The experimental results illustrate that the novel flexible winding system has a good performance in winding accuracy.
{"title":"Research on fuzzy control based flexible composite winding system","authors":"Xiaodong He, Yaoyao Shi, K. Chao","doi":"10.1155/2016/7181706","DOIUrl":"https://doi.org/10.1155/2016/7181706","url":null,"abstract":"In the process of composite resin prepreg tape winding, the presence of pores or voids among the layers of composite can result in reduced strength of winding. To alleviate this problem, it is required that the composite tape winding machines be designed such that the layers of composite are evenly wound on the previous one. The paper presents a novel design of flexible winding system for composite tape winding. Based on the analysis of errors in winding process, the novel winding system eliminates winding point error and winding angle error based on the speed controlled flexible roller. This paper also presents the kinetic analysis of the novel system and its controller design. Experiments are conducted on the novel winding system. The experimental results illustrate that the novel flexible winding system has a good performance in winding accuracy.","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2016/7181706","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64509172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tsallis entropy is a q-parameter extension of Shannon entropy. By extremizing the Tsallis entropy within the framework of fuzzy c-means clustering (FCM), a membership function similar to the statistical mechanical distribution function is obtained. The Tsallis entropy-based DA-FCM algorithm was developed by combining it with the deterministic annealing (DA) method. One of the challenges of this method is to determine an appropriate initial annealing temperature and a q value, according to the data distribution. This is complex, because the membership function changes its shape by decreasing the temperature or by increasing q. Quantitative relationships between the temperature and q are examined, and the results showthat, in order to change uikq equally, inverse changes must be made to the temperature and q. Accordingly, in this paper, we propose and investigate two kinds of combinatorial methods for q-incrementation and the reduction of temperature for use in the Tsallis entropy-based FCM. In the proposed methods, q is defined as a function of the temperature. Experiments are performed using Fisher's iris dataset, and the proposed methods are confirmed to determine an appropriate q value in many cases.
{"title":"Quantitative analyses and development of a q -incrementation algorithm for FCM with tsallis entropy maximization","authors":"M. Yasuda","doi":"10.1155/2015/404510","DOIUrl":"https://doi.org/10.1155/2015/404510","url":null,"abstract":"Tsallis entropy is a q-parameter extension of Shannon entropy. By extremizing the Tsallis entropy within the framework of fuzzy c-means clustering (FCM), a membership function similar to the statistical mechanical distribution function is obtained. The Tsallis entropy-based DA-FCM algorithm was developed by combining it with the deterministic annealing (DA) method. One of the challenges of this method is to determine an appropriate initial annealing temperature and a q value, according to the data distribution. This is complex, because the membership function changes its shape by decreasing the temperature or by increasing q. Quantitative relationships between the temperature and q are examined, and the results showthat, in order to change uikq equally, inverse changes must be made to the temperature and q. Accordingly, in this paper, we propose and investigate two kinds of combinatorial methods for q-incrementation and the reduction of temperature for use in the Tsallis entropy-based FCM. In the proposed methods, q is defined as a function of the temperature. Experiments are performed using Fisher's iris dataset, and the proposed methods are confirmed to determine an appropriate q value in many cases.","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2015/404510","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64945758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1007/978-81-322-2119-7_85
D. Deenadayalan, I. A. Beski
{"title":"Fuzzy-Based Torque Ripple Optimization and Digitalized Sector Selection in DTC Scheme","authors":"D. Deenadayalan, I. A. Beski","doi":"10.1007/978-81-322-2119-7_85","DOIUrl":"https://doi.org/10.1007/978-81-322-2119-7_85","url":null,"abstract":"","PeriodicalId":45308,"journal":{"name":"Advances in Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87738065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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