Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms.To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem.The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models.Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem.Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model.We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study.The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved.
{"title":"A multi-attribute assessment of fuzzy regression models","authors":"J. Chachi, A. Kazemifard, M. Jalalvand","doi":"10.22111/IJFS.2021.6181","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6181","url":null,"abstract":"Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms.To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem.The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models.Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem.Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model.We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study.The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86482818","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}
A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) methodis put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.
提出了一种新的模糊推理方法SQI(对称五元组蕴涵)方法，它是对五元组蕴涵原理方法的推广。首先，提出了与QIP方法不同的对称五元组隐含原理。在此基础上，得到了模糊模量(FMP)和模糊模量(FMT)的SQI方法的统一最优解，并验证了其可逆性。此外，针对多规则情况，给出了SQI方法的最优解，该方法涉及两种通用方法，即FITA (first- inter -then-aggregate)和FATI (first-aggregate-then-infer)。分析了在SQI方法环境下，FITA和FATI的连续性和插值的等价关系。最后，给出了基于FATI的SQI方法在情感计算领域中出现的一个计算实例。结果表明，SQI方法保留了与QIP方法相同的特性。
{"title":"On the symmetric quintuple implicational method of fuzzy reasoning","authors":"Yiming Tang, G. Bao, J. Chen, W. Pedrycz","doi":"10.22111/IJFS.2021.6180","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6180","url":null,"abstract":"A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) methodis put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72712815","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}
Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.The probabilistic hesitant fuzzy preference relations can more effectively express thehesitant preference information of decision makers.But in the existing research, all of them are based on discrete probability distribution.In order to give decision maker more evaluation space,continuous probability distribution is necessary to be considered.Therefore, in this paper, the continuous probability-interval valued fuzzy setis defined and its probability is represented by a probability density function.A method of converting probabilistic hesitant fuzzy set into continuous probability-interval valued fuzzy setis developed to transform discrete data into continuous data.Then, the continuous probability-interval valued fuzzy preference relations is presented.In order to consider the consistency of continuous probability-interval valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed.The individual consistency index and group consensus index are also presented to determine the consistency level.And then, an algorithm is introduced for checking and improving the individual consistency level andgroup consensus level.Finally, a numerical example is shown to the effectiveness of proposed algorithm,the comparative analysis is given with the existing methods toshow the superiority of this algorithm.
{"title":"Continuous probability-interval valued fuzzy preference relations and its application in group decision making","authors":"J. Mo, H. L. Huang","doi":"10.22111/IJFS.2021.6184","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6184","url":null,"abstract":"Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.The probabilistic hesitant fuzzy preference relations can more effectively express thehesitant preference information of decision makers.But in the existing research, all of them are based on discrete probability distribution.In order to give decision maker more evaluation space,continuous probability distribution is necessary to be considered.Therefore, in this paper, the continuous probability-interval valued fuzzy setis defined and its probability is represented by a probability density function.A method of converting probabilistic hesitant fuzzy set into continuous probability-interval valued fuzzy setis developed to transform discrete data into continuous data.Then, the continuous probability-interval valued fuzzy preference relations is presented.In order to consider the consistency of continuous probability-interval valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed.The individual consistency index and group consensus index are also presented to determine the consistency level.And then, an algorithm is introduced for checking and improving the individual consistency level andgroup consensus level.Finally, a numerical example is shown to the effectiveness of proposed algorithm,the comparative analysis is given with the existing methods toshow the superiority of this algorithm.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73277592","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}
Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices $ C_{pm} $ and $ C_{pmk} $ have been developed to consider customers' ideal value that called target value ($ T $). Although, these indices have similar features of the well-known indices $ C_{p} $ and $ C_{pk} $, one of the most important differences is to consider textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices $ C_{pm} $ and $ C_{pmk} $ have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) $ widetilde{dddot{C}}_{pm}$ and $ widetilde{dddot{C}}_{pmk} $ have been obtained and the main formulas of them have been produced. Additionally, the proposed $ widetilde{dddot{C}}_{pm} $ and $ widetilde{dddot{C}}_{pmk} $ have been applied on real case studies from manufacturing industry. The obtained results show that the indices $ widetilde{dddot{C}}_{pm} $ and $ widetilde{dddot{C}}_{pmk} $ include more informative and flexible results to evaluate capability of process.
{"title":"(2011-6272) Design and analysis of process capability indices cpm and cpmk by neutrosophic sets","authors":"S. Yalçın, I. Kaya","doi":"10.22111/IJFS.2021.6251","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6251","url":null,"abstract":"Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices $ C_{pm} $ and $ C_{pmk} $ have been developed to consider customers' ideal value that called target value ($ T $). Although, these indices have similar features of the well-known indices $ C_{p} $ and $ C_{pk} $, one of the most important differences is to consider textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices $ C_{pm} $ and $ C_{pmk} $ have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) $ widetilde{dddot{C}}_{pm}$ and $ widetilde{dddot{C}}_{pmk} $ have been obtained and the main formulas of them have been produced. Additionally, the proposed $ widetilde{dddot{C}}_{pm} $ and $ widetilde{dddot{C}}_{pmk} $ have been applied on real case studies from manufacturing industry. The obtained results show that the indices $ widetilde{dddot{C}}_{pm} $ and $ widetilde{dddot{C}}_{pmk} $ include more informative and flexible results to evaluate capability of process.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73016912","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 arithmetic performed with the product t-norm is the focus of this paper. The subject is handled from both practical and theoretical perspectives. Explicit formulas for product-sum and product-multiplication of triangular fuzzy numbers are obtained. These formulas can effectively replace the computational methods proposed so far. The issue that these operations are not shape preserving is solved by the presentation of appropriate approximations. Finally, the product arithmetic is compared in detail to the arithmetic performed with the boundary t-norms, namely the minimum and drastic sum.
{"title":"(2102-6503) Fuzzy arithmetic with product t-norm","authors":"G. Soylu, M. Aslan","doi":"10.22111/IJFS.2021.6250","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6250","url":null,"abstract":"Fuzzy arithmetic performed with the product t-norm is the focus of this paper. The subject is handled from both practical and theoretical perspectives. Explicit formulas for product-sum and product-multiplication of triangular fuzzy numbers are obtained. These formulas can effectively replace the computational methods proposed so far. The issue that these operations are not shape preserving is solved by the presentation of appropriate approximations. Finally, the product arithmetic is compared in detail to the arithmetic performed with the boundary t-norms, namely the minimum and drastic sum.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88528600","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 paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.
{"title":"(2008-6132) A novel fuzzy sliding mode control approach for chaotic systems","authors":"R. Amirabadi, O. S. Fard, A. Mansoori","doi":"10.22111/IJFS.2021.6248","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6248","url":null,"abstract":"The purpose of this paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73094064","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}
Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kind of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.
{"title":"(2012-6338) Design and Analysis of Acceptance Sampling Plans Based on Intuitionistic Fuzzy Linguistic Terms","authors":"G. Işık, I. Kaya","doi":"10.22111/IJFS.2021.6211","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6211","url":null,"abstract":"Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kind of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73468778","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}
Shivam Shreevastava, Shivani Singh, A. K. Tiwari, T. Som
In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.
{"title":"( 2005-5897) Different classes ratio and Laplace summation operator based intuitionistic fuzzy rough attribute selection","authors":"Shivam Shreevastava, Shivani Singh, A. K. Tiwari, T. Som","doi":"10.22111/IJFS.2021.6212","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6212","url":null,"abstract":"In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77308520","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":"On the fuzzy solutions of time-fractional problems","authors":"M. Ghaffari, T. Allahviranloo, S. Abbasbandy, M. Azhini","doi":"10.22111/IJFS.2021.6081","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6081","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":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89885580","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 introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(oplus,otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and v{S}trboja cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], sup, otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.
{"title":"Jensen's inequalities for pseudo-integrals","authors":"Deli Zhang, E. Pap","doi":"10.22111/IJFS.2021.6084","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6084","url":null,"abstract":"In this paper, we introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(oplus,otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and v{S}trboja cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], sup, otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87001929","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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