In general, agents always face an increasing need to focus on multiple aims efficiently under their operational processes. However, agents might take different activity levels to participate and might represent administrative areas of different scales. Therefore, this paper proposes a normalized index considering multi-criteria situations and supreme-utilities among fuzzy activity level (decision, strategy) vectors. Three existing notions of traditional game theory are reinterpreted in the framework of multi-criteria fuzzy transferable utility games. First, the normalized index could be represented as an alternative formulation in terms of excess functions. Second, an axiomatic result is proposed to present the rationality of this normalized index based on the reduced game and related consistency. Finally, two dynamic processes are introduced to illustrate that this normalized index could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.
{"title":"A normalized distribution mechanism under multi-criteria situations and fuzzy behavior","authors":"Y. Liao","doi":"10.22111/IJFS.2021.6337","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6337","url":null,"abstract":"In general, agents always face an increasing need to focus on multiple aims efficiently under their operational processes. However, agents might take different activity levels to participate and might represent administrative areas of different scales. Therefore, this paper proposes a normalized index considering multi-criteria situations and supreme-utilities among fuzzy activity level (decision, strategy) vectors. Three existing notions of traditional game theory are reinterpreted in the framework of multi-criteria fuzzy transferable utility games. First, the normalized index could be represented as an alternative formulation in terms of excess functions. Second, an axiomatic result is proposed to present the rationality of this normalized index based on the reduced game and related consistency. Finally, two dynamic processes are introduced to illustrate that this normalized index could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76737459","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}
S. Hasanzadeh, Seyyed Mostafa Fakhrahmad, M. Taheri
In the design of recommender systems, it is believed that the set of reviews written by a user can somehow reveal his/her interests, and the content of an item can also be implied from its corresponding reviews. The present study attempts to model both the users and the items via extracting key information from the existing textual reviews. Based on this information, a fuzzy rule-based classifier is designed and tuned, which aims to predict whether a typical user will be interested in a typical item or not. For this purpose, the set of all reviews belonging to a user are mapped to a vector representing the user's interests. Similarly, the set of reviews written by different users over an item are merged and mapped to a vector representing the item. By conjoining these two vectors, a longer vector is obtained which will be used as the input of the classifier. To optimize the classifier, an adaptive approach is suggested and rule-weight learning is carried out, accordingly. The performance of the proposed fuzzy recommender system was evaluated on the Amazon dataset. Experimental results narrate from the promising classification ability of the proposed recommender system compared to state of the art.
{"title":"A fuzzy approach to review-based recommendation: Design and optimization of a fuzzy classification scheme based on implicit features of textual reviews","authors":"S. Hasanzadeh, Seyyed Mostafa Fakhrahmad, M. Taheri","doi":"10.22111/IJFS.2021.6335","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6335","url":null,"abstract":"In the design of recommender systems, it is believed that the set of reviews written by a user can somehow reveal his/her interests, and the content of an item can also be implied from its corresponding reviews. The present study attempts to model both the users and the items via extracting key information from the existing textual reviews. Based on this information, a fuzzy rule-based classifier is designed and tuned, which aims to predict whether a typical user will be interested in a typical item or not. For this purpose, the set of all reviews belonging to a user are mapped to a vector representing the user's interests. Similarly, the set of reviews written by different users over an item are merged and mapped to a vector representing the item. By conjoining these two vectors, a longer vector is obtained which will be used as the input of the classifier. To optimize the classifier, an adaptive approach is suggested and rule-weight learning is carried out, accordingly. The performance of the proposed fuzzy recommender system was evaluated on the Amazon dataset. Experimental results narrate from the promising classification ability of the proposed recommender system compared to state of the art.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76162700","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":"Fuzzy arithmetic with product t-norm","authors":"G. Soylu, M. Aslan","doi":"10.22111/IJFS.2021.6341","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6341","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":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77410149","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}
People's demand for the decision-making space of opinion expression is getting higher, and the methods to determine the threshold value of current consensus still remain elusive. To deal with large and diverse information of users and discuss deeply the threshold in social networks, we establish a new consistency model with a new preference structure. In this paper, the Pythagorean fuzzy numbers (PFNs) are introduced into social network group decision-making for the expression of decision-makers' preference (DMs) and the concepts definition of the distance measurements, consensus index, and threshold indifference curves, respectively. In addition, we establish a Pythagorean fuzzy group consensus model with minimum adjustment through determining the setting rule of threshold value before reaching the consensus. Finally, we use the proposed model to solve the selection of square cabin hospitals.
{"title":"A visual social network group consensus approach with minimum adjustment based on Pythagorean fuzzy set","authors":"Y. Liu, W. Diao, J. Yang, J. Yi","doi":"10.22111/IJFS.2021.6340","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6340","url":null,"abstract":"People's demand for the decision-making space of opinion expression is getting higher, and the methods to determine the threshold value of current consensus still remain elusive. To deal with large and diverse information of users and discuss deeply the threshold in social networks, we establish a new consistency model with a new preference structure. In this paper, the Pythagorean fuzzy numbers (PFNs) are introduced into social network group decision-making for the expression of decision-makers' preference (DMs) and the concepts definition of the distance measurements, consensus index, and threshold indifference curves, respectively. In addition, we establish a Pythagorean fuzzy group consensus model with minimum adjustment through determining the setting rule of threshold value before reaching the consensus. Finally, we use the proposed model to solve the selection of square cabin hospitals.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82302760","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":"A novel fuzzy sliding mode control approach for chaotic systems","authors":"R. Amirabadi, O. S. Fard, A. Mansoori","doi":"10.22111/IJFS.2021.6338","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6338","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":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75255880","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":"Structural topology in a category","authors":"S. Hosseini, R. Amini","doi":"10.22111/IJFS.2021.6332","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6332","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":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88986491","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}
Positive homogeneity is represented as a constraint 0-homogeneity and generalized into z-homogeneity, called also z-end point linearity. Several special z-homogeneous aggregation functions are studied, in particular semicopulas, quasi-copulas, copulas, overlap functions, etc.
{"title":"End-point linear functions","authors":"A. Stupňanová, Y. Su, R. Mesiar","doi":"10.22111/IJFS.2021.6329","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6329","url":null,"abstract":"Positive homogeneity is represented as a constraint 0-homogeneity and generalized into z-homogeneity, called also z-end point linearity. Several special z-homogeneous aggregation functions are studied, in particular semicopulas, quasi-copulas, copulas, overlap functions, etc.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86149775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a new definition of a fuzzy $k$-pseudo metric is introduced and its induced fuzzifying structures are constructed, such as a fuzzifying neighborhood system, a fuzzifying topology, a fuzzifying closure operator, a fuzzifying uniformity.Besides, it is shown that there is a one-to-one correspondence between fuzzy $k$-pseudo metrics and nests of crisp $k$-pseudo metrics.
{"title":"A new definition of fuzzy k-pseudo metric and its induced fuzzifying structures","authors":"Yu Zhong, A. Sostak","doi":"10.22111/IJFS.2021.6333","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6333","url":null,"abstract":"In this paper, a new definition of a fuzzy $k$-pseudo metric is introduced and its induced fuzzifying structures are constructed, such as a fuzzifying neighborhood system, a fuzzifying topology, a fuzzifying closure operator, a fuzzifying uniformity.Besides, it is shown that there is a one-to-one correspondence between fuzzy $k$-pseudo metrics and nests of crisp $k$-pseudo metrics.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83057218","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, the conception of centroid of $n$-dimensional fuzzy number is introduced viaregarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional fuzzy number. Therefore, it can approximate (characterize) the fuzzy number more objectively and reasonably than using the mean of the multi dimensional fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional fuzzy numbers (fuzzy $n$-cell numbers and fuzzy $n$-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional fuzzy number on the unit interval $[0,1]$, rather than the multiple integral of the membership function of the multi dimensional fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy $n$-cell number and fuzzy $n$-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional fuzzy number, we define a fuzzy order on $n$-dimensional fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.
{"title":"Calculation of centroid of high dimensional fuzzy number and application","authors":"G. Wang, Y. Xu","doi":"10.22111/IJFS.2021.6331","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6331","url":null,"abstract":"In this paper, the conception of centroid of $n$-dimensional fuzzy number is introduced viaregarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional fuzzy number. Therefore, it can approximate (characterize) the fuzzy number more objectively and reasonably than using the mean of the multi dimensional fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional fuzzy numbers (fuzzy $n$-cell numbers and fuzzy $n$-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional fuzzy number on the unit interval $[0,1]$, rather than the multiple integral of the membership function of the multi dimensional fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy $n$-cell number and fuzzy $n$-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional fuzzy number, we define a fuzzy order on $n$-dimensional fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86166885","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}
Unlike other mathematical models, soft set theory provides a parameterization tool contribution. However, in this theory, since membership degrees are expressed as 0 and 1, for (0; 1), we cannot determine whether any object belongs to a parameter or not. Researchers have tried to overcome this situation by ensuring that the decision maker expresses these values. However, we cannot know the accuracy of the data provided to us by the decision maker. Therefore, inthis study, we introduced the concepts of relational membership function, relational non-membership function, inverse relational membership function and inverse relational non-membership function and examined the related properties of these concepts. Then, we propose two new approaches so that uncertainty can be expressed in an ideal way and canbe used in decision-making. Finally, the approaches given and some of the important approaches in the literature are compared and analyzed.
{"title":"(2102-6461) Two novel approaches that reduce the effectiveness of the decision maker in decision making under uncertainty environments","authors":"O. Dalkl","doi":"10.22111/IJFS.2021.6430","DOIUrl":"https://doi.org/10.22111/IJFS.2021.6430","url":null,"abstract":"Unlike other mathematical models, soft set theory provides a parameterization tool contribution. However, in this theory, since membership degrees are expressed as 0 and 1, for (0; 1), we cannot determine whether any object belongs to a parameter or not. Researchers have tried to overcome this situation by ensuring that the decision maker expresses these values. However, we cannot know the accuracy of the data provided to us by the decision maker. Therefore, inthis study, we introduced the concepts of relational membership function, relational non-membership function, inverse relational membership function and inverse relational non-membership function and examined the related properties of these concepts. Then, we propose two new approaches so that uncertainty can be expressed in an ideal way and canbe used in decision-making. Finally, the approaches given and some of the important approaches in the literature are compared and analyzed.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89707224","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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