In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. And some illustrative examples are given.
{"title":"Construction methods for triangular norms and triangular conorms on appropriate bounded lattices","authors":"Emel Asici","doi":"10.22111/IJFS.2021.6083","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6083","url":null,"abstract":"In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. And some illustrative examples are given.","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":"79347226","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}
Always the decision of the government to the private sector is faced with the challenges and high level of importance, because these decisions should be taken at the meeting of standards and functional requirements to overcome investors' interests. These decisions include education, and due to the governance nature of education and the governments' strategies in this area, the private sectors who act in it, have been affected by the consequences of different decisions. In this paper, our motivation is to propose a system to decide on how to develop applied academic educations at the Applied ScienceEducation Centers (ASEC's) which are supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is theFuzzy Inference System (FIS) to reach this goal. The model performed in this study consists of a two-part FIS for two purposes straight ahead.The first concerns the quantitative development of higher applied education, including the number of Course Request (CR) for each ASEC with 4 inputs and 242 rules. The latter, is related to the qualitative development of higher applied education, including the assessment of the capability and competence of each ASEC for specific CR with the course and student admission background, specialty, committee's and council’s opinion, and frequency of course in city or province with 9 inputs, 350 rules, and an output. Each section has its inputs and rules that are determined and used by experts in this domain. Our results show that using this method, provides some cost and time savings. This model analyzes in less than 2 minutes, while in practice it could be gain within 1650 person /hours work in different committees that all of them have their costs. Also, results are very close to reality with the advantage that there is no way to apply personal preferences, which largely meets the needs of research.
{"title":"Using a fuzzy expert system as a decision support system to decrease time consumption in the UAST development process: A case study","authors":"A. A. Esboei, M. Gavareshki","doi":"10.22111/IJFS.2021.6079","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6079","url":null,"abstract":"Always the decision of the government to the private sector is faced with the challenges and high level of importance, because these decisions should be taken at the meeting of standards and functional requirements to overcome investors' interests. These decisions include education, and due to the governance nature of education and the governments' strategies in this area, the private sectors who act in it, have been affected by the consequences of different decisions. In this paper, our motivation is to propose a system to decide on how to develop applied academic educations at the Applied ScienceEducation Centers (ASEC's) which are supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is theFuzzy Inference System (FIS) to reach this goal. The model performed in this study consists of a two-part FIS for two purposes straight ahead.The first concerns the quantitative development of higher applied education, including the number of Course Request (CR) for each ASEC with 4 inputs and 242 rules. The latter, is related to the qualitative development of higher applied education, including the assessment of the capability and competence of each ASEC for specific CR with the course and student admission background, specialty, committee's and council’s opinion, and frequency of course in city or province with 9 inputs, 350 rules, and an output. Each section has its inputs and rules that are determined and used by experts in this domain. Our results show that using this method, provides some cost and time savings. This model analyzes in less than 2 minutes, while in practice it could be gain within 1650 person /hours work in different committees that all of them have their costs. Also, results are very close to reality with the advantage that there is no way to apply personal preferences, which largely meets the needs of research.","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":"90662404","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 analyzed. 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":"Milstein method for solving fuzzy differential equation","authors":"L. Y. Ji, C. L. You","doi":"10.22111/IJFS.2021.6086","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6086","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 analyzed. 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":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84885693","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 fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers. To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance. Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.
{"title":"A bilateral fuzzy support vector machine hybridizing the Gaussian mixture model","authors":"M. Mohammadi, M. Sarmad","doi":"10.22111/IJFS.2021.6088","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6088","url":null,"abstract":"The fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers. To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance. Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.","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":"75476948","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 develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.The main results are: (1) The set of all C-compact elements of a completeQ-ordered set is irreducible complete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, evenC-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.
{"title":"C-continuous fuzzy posets","authors":"Y. Zhang, Bin Zhao","doi":"10.22111/IJFS.2021.6082","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6082","url":null,"abstract":"In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.The main results are: (1) The set of all C-compact elements of a completeQ-ordered set is irreducible complete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, evenC-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.","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":"77660759","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}
Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. That the migrativity equation as a kind of restricted general associative equation have been proven to be useful in a wide range of fields like decision making, aggregation of information, image processing and so on. In the literature, the already existing results concerning the migrativity equation between overlap (grouping) functions and uninorms are based on the assumption that uninorms belong to one of the most studied classes. In this study we will explore it involving uninorms in a more general setting. To be specific, we investigate the migrativity properties between overlap (grouping) functions and uninorms in the case when uninorms have continuous underlying operators. We will show along the paper that many new solutions to the equation are characterized from this new point of view.
{"title":"New results on the migrativity properties for overlap (grouping) functions and uninorms","authors":"W. Li, F. Qin","doi":"10.22111/IJFS.2021.6085","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6085","url":null,"abstract":"Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. That the migrativity equation as a kind of restricted general associative equation have been proven to be useful in a wide range of fields like decision making, aggregation of information, image processing and so on. In the literature, the already existing results concerning the migrativity equation between overlap (grouping) functions and uninorms are based on the assumption that uninorms belong to one of the most studied classes. In this study we will explore it involving uninorms in a more general setting. To be specific, we investigate the migrativity properties between overlap (grouping) functions and uninorms in the case when uninorms have continuous underlying operators. We will show along the paper that many new solutions to the equation are characterized from this new point of view.","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":"87030605","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 consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. For a suitably defined function $hat{v}$ assigning to each formula $varphi$ some object of $C$, the hom-object $C(hat{v} (varphi),hat{v}(psi))$ represents the degree of derivability of $psi$ from $varphi$. We reformulate completeness result for intuitionistic propositional logic, as well as H' ajek's completeness results concerning the product, G" odel and L ukasiewicz fuzzy logic in the context of enriched category theory.
{"title":"Fuzzy logic and enriched categories","authors":"S. Dautovic, M. Zekic","doi":"10.22111/IJFS.2021.6077","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6077","url":null,"abstract":"We consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. For a suitably defined function $hat{v}$ assigning to each formula $varphi$ some object of $C$, the hom-object $C(hat{v} (varphi),hat{v}(psi))$ represents the degree of derivability of $psi$ from $varphi$. We reformulate completeness result for intuitionistic propositional logic, as well as H' ajek's completeness results concerning the product, G\" odel and L ukasiewicz fuzzy logic in the context of enriched category theory.","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":"74513724","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}
Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two the generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.
{"title":"(2007-6024) Ranking of generalized fuzzy numbers based on accuracy of comparison","authors":"M. A. Firozja, F. R. Balf, B. Agheli, R. Chutia","doi":"10.22111/IJFS.2021.6164","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6164","url":null,"abstract":"Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two the generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91282383","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}
Several fuzzy topologies are defined and studied by different authors. In this article, we unify five of the most common fuzzy topologies existing in the literature, as well as the standard topology. This is done by introducing the notion of structural topology on objects in a category and proving that topologies on a set as well as fuzzy topologies on fuzzy sets and fuzzy topologies on fuzzy subsets are all structural topologies. We also introduce the notion of structural continuity and we show that the fuzzy continuity defined in the literature in all the above mentioned cases, as well as the standard continuity are structural.
{"title":"(2011-6279) Structural topology in a category","authors":"S. Hosseini, R. Amini","doi":"10.22111/IJFS.2021.6167","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6167","url":null,"abstract":"Several fuzzy topologies are defined and studied by different authors. In this article, we unify five of the most common fuzzy topologies existing in the literature, as well as the standard topology. This is done by introducing the notion of structural topology on objects in a category and proving that topologies on a set as well as fuzzy topologies on fuzzy sets and fuzzy topologies on fuzzy subsets are all structural topologies. We also introduce the notion of structural continuity and we show that the fuzzy continuity defined in the literature in all the above mentioned cases, as well as the standard continuity are structural.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84719518","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 research, a Type 2 adaptive fuzzy controller approach is formulated and designed to be applied to variable speed doubly fed induction generator-based wind turbines directly connected to the grid. It brings this study to evaluate the whole operation of the system to capture the highest rate of power in the wind turbines. The controlling approach is considered to keep the stator reactive power to the ideal value. In contrast to the other researches, here the controlling technique is developed through the nonlinear systems. By the aim of making progress in system operation, in contrast with the Type 1 adaptive fuzzy system, type two adaptive fuzzy theory is proposed to approximate a large number of uncertainties and the dynamic nonlinearities, exists in tracking errors which may limit the system performance. Feedback linearization control approach helps us to algebraically alter the system into a linearized plant. Thanks to the Lyapunov theorem, the introduced type two adaptive fuzzy approach is proved to meet the uniformly ultimately boundness (UUB) property. On the other hand, it results better tracking function. The simulation outputs represent that the proposed technique is robust enough in presence of parameter variations and unstructured uncertainties.
{"title":"(1912-5600) Type 2 adaptive fuzzy control approach applied to variable speed DFIG based wind turbines with MPPT algorithm","authors":"S. Hosseini, M. Manthouri","doi":"10.22111/IJFS.2021.6166","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6166","url":null,"abstract":"In this research, a Type 2 adaptive fuzzy controller approach is formulated and designed to be applied to variable speed doubly fed induction generator-based wind turbines directly connected to the grid. It brings this study to evaluate the whole operation of the system to capture the highest rate of power in the wind turbines. The controlling approach is considered to keep the stator reactive power to the ideal value. In contrast to the other researches, here the controlling technique is developed through the nonlinear systems. By the aim of making progress in system operation, in contrast with the Type 1 adaptive fuzzy system, type two adaptive fuzzy theory is proposed to approximate a large number of uncertainties and the dynamic nonlinearities, exists in tracking errors which may limit the system performance. Feedback linearization control approach helps us to algebraically alter the system into a linearized plant. Thanks to the Lyapunov theorem, the introduced type two adaptive fuzzy approach is proved to meet the uniformly ultimately boundness (UUB) property. On the other hand, it results better tracking function. The simulation outputs represent that the proposed technique is robust enough in presence of parameter variations and unstructured uncertainties.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77212270","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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