Pub Date : 2020-04-02DOI: 10.1080/16168658.2020.1751405
M. Touqeer
ABSTRACT As an extension of the applications of soft sets in α-ideals of BCI-algebras, we have defined the idea of ‘intuitionistic fuzzy soft α-ideals’ and proved their basic properties. ‘Intuitionistic fuzzy soft BCI-algebras' and ‘intuitionistic fuzzy soft ideals' have been described with the help of concrete examples. We proved that any IFSI of a BCK-algebra is an ‘intuitionistic fuzzy soft BCK-algebra' (IFSBCKA). Afterwards we have proceeded towards the detail discussion of IFSαIs. The notion of intuitionistic fuzzy soft α-ideals in BCI-algebras is presented, the corresponding properties are proved and concrete applications are given. Connections between various types of intuitionistic fuzzy soft α-ideals and intuitionistic fuzzy soft ideals are described. Intuitionistic fuzzy soft α-ideals are characterised using the idea of soft (δ, η)-level set.
{"title":"Intuitionistic Fuzzy Soft Set Theoretic Approaches to α-ideals in BCI-algebras","authors":"M. Touqeer","doi":"10.1080/16168658.2020.1751405","DOIUrl":"https://doi.org/10.1080/16168658.2020.1751405","url":null,"abstract":"ABSTRACT As an extension of the applications of soft sets in α-ideals of BCI-algebras, we have defined the idea of ‘intuitionistic fuzzy soft α-ideals’ and proved their basic properties. ‘Intuitionistic fuzzy soft BCI-algebras' and ‘intuitionistic fuzzy soft ideals' have been described with the help of concrete examples. We proved that any IFSI of a BCK-algebra is an ‘intuitionistic fuzzy soft BCK-algebra' (IFSBCKA). Afterwards we have proceeded towards the detail discussion of IFSαIs. The notion of intuitionistic fuzzy soft α-ideals in BCI-algebras is presented, the corresponding properties are proved and concrete applications are given. Connections between various types of intuitionistic fuzzy soft α-ideals and intuitionistic fuzzy soft ideals are described. Intuitionistic fuzzy soft α-ideals are characterised using the idea of soft (δ, η)-level set.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"46 1","pages":"150 - 180"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91050256","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 : 2020-04-02DOI: 10.1080/16168658.2020.1824397
M. Niksirat
This paper deals with multi-depot bus scheduling (MDBS) problem. Depot workload balancing constraints are introduced. In this case, the problem can be stated as a two-objective multi-commodity flow problem with soft constraints. Two state-of-the-art heuristics are developed including schedule-based and cluster-based heuristics, both of them extend auction algorithm. Also three different approaches are proposed to satisfy depot workload balancing constraints. The convergence of each algorithm is investigated and its complexity obtained. To illustrate the main concepts and results, a small example is solved. Also, to demonstrate the performance of the proposed algorithms, some benchmark examples are considered and CPU-time and optimality gap are compared. The results show a great improvement in the CPU time and quality of the solution of the proposed algorithms. Also the extension of the proposed algorithms under ε-scaling approach is analysed.
{"title":"State-of-the-Art Auction Algorithms for Multi-depot Bus Scheduling Problem Considering Depot Workload Balancing Constraints","authors":"M. Niksirat","doi":"10.1080/16168658.2020.1824397","DOIUrl":"https://doi.org/10.1080/16168658.2020.1824397","url":null,"abstract":"This paper deals with multi-depot bus scheduling (MDBS) problem. Depot workload balancing constraints are introduced. In this case, the problem can be stated as a two-objective multi-commodity flow problem with soft constraints. Two state-of-the-art heuristics are developed including schedule-based and cluster-based heuristics, both of them extend auction algorithm. Also three different approaches are proposed to satisfy depot workload balancing constraints. The convergence of each algorithm is investigated and its complexity obtained. To illustrate the main concepts and results, a small example is solved. Also, to demonstrate the performance of the proposed algorithms, some benchmark examples are considered and CPU-time and optimality gap are compared. The results show a great improvement in the CPU time and quality of the solution of the proposed algorithms. Also the extension of the proposed algorithms under ε-scaling approach is analysed.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"18 1","pages":"253 - 273"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81498817","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 : 2020-04-02DOI: 10.1080/16168658.2020.1804040
K. Teimourzadeh, J. Pourmahmoud, S. Kordrostami
Road safety problem is an important issue which is always considered as one of the main benchmarks to assess growth and development in many countries. Many factors influence in calculating the road safety index. In the past, for calculating the road safety index, all factors affecting road safety were considered as desirable indicators. In this paper, the road safety factors are considered in two categories: desirable and undesirable indicators. Moreover, the observed values of the factors affecting the road safety index in practice are sometimes uncertain. In this study, fuzzy data envelopment analysis method is applied to calculate and evaluate road safety index. A generalised fuzzy index-maximising model is proposed to obtain an optimal road safety index, in which the optimal index is obtained as the maximum value of sum of weighted desirable–undesirable factors. In addition, the problem of ranking of the roads is investigated with regard to the optimal composite index. In order to rank the roads, a new index is suggested that discriminates the efficient roads. Finally, the proposed method is applied to evaluate the safety problem for a case study on the roads of East Azarbaijan Province in Iran.
{"title":"A New Estimation of Road Safety Index in Transportation Systems with Fuzzy-DEA Method: A Case Study on Roads of East Azarbaijan Province in Iran","authors":"K. Teimourzadeh, J. Pourmahmoud, S. Kordrostami","doi":"10.1080/16168658.2020.1804040","DOIUrl":"https://doi.org/10.1080/16168658.2020.1804040","url":null,"abstract":"Road safety problem is an important issue which is always considered as one of the main benchmarks to assess growth and development in many countries. Many factors influence in calculating the road safety index. In the past, for calculating the road safety index, all factors affecting road safety were considered as desirable indicators. In this paper, the road safety factors are considered in two categories: desirable and undesirable indicators. Moreover, the observed values of the factors affecting the road safety index in practice are sometimes uncertain. In this study, fuzzy data envelopment analysis method is applied to calculate and evaluate road safety index. A generalised fuzzy index-maximising model is proposed to obtain an optimal road safety index, in which the optimal index is obtained as the maximum value of sum of weighted desirable–undesirable factors. In addition, the problem of ranking of the roads is investigated with regard to the optimal composite index. In order to rank the roads, a new index is suggested that discriminates the efficient roads. Finally, the proposed method is applied to evaluate the safety problem for a case study on the roads of East Azarbaijan Province in Iran.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"30 1","pages":"223 - 237"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84406123","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 : 2020-04-02DOI: 10.1080/16168658.2020.1792610
Priscila de Jesus Freitas Pinto, C. H. dos Santos Grecco, Carlos Alberto Nunes Cosenza
The shipbuilding industry has evolved in recent years. Some quantitative and qualitative factors influence competitiveness of shipyards. The development of shipbuilding processes depends on evolution of manufacturing techniques, planning, organization and external environment. In general, regarding performance, quantitative variables are analyzed through mathematical and linear models. However, the qualitative variables, due to its subjectivity because it deals with human perceptions, it is not common for organizations to work on the performance of these factors. Then, this is the objective of the research, to analyze qualitative factors in shipbuilding in context with the Brazilian industry. The chosen that compose the proposed model are technology and industrial location. This research presents a prioritizing evaluation model of qualitative performance variables. So, presents as original the treatment by the fuzzy sets of qualitative critical factors expressed in linguistic terms by specialists working in the Brazilian sector, resulting in the prioritization of these factors. After result, the model was applied at specific shipyard. The results converge Brazil's real scenario and show that the proposed fuzzy model might be a good qualitative performance factor evaluation tool. Finally, to identify real the distance of a specific shipyard for to this research's model prioritization pattern by brazilian specialists.
{"title":"Fuzzy Model for the Priorization Analysis of Variable Quality Performance: An Approach in Shipbuilding","authors":"Priscila de Jesus Freitas Pinto, C. H. dos Santos Grecco, Carlos Alberto Nunes Cosenza","doi":"10.1080/16168658.2020.1792610","DOIUrl":"https://doi.org/10.1080/16168658.2020.1792610","url":null,"abstract":"The shipbuilding industry has evolved in recent years. Some quantitative and qualitative factors influence competitiveness of shipyards. The development of shipbuilding processes depends on evolution of manufacturing techniques, planning, organization and external environment. In general, regarding performance, quantitative variables are analyzed through mathematical and linear models. However, the qualitative variables, due to its subjectivity because it deals with human perceptions, it is not common for organizations to work on the performance of these factors. Then, this is the objective of the research, to analyze qualitative factors in shipbuilding in context with the Brazilian industry. The chosen that compose the proposed model are technology and industrial location. This research presents a prioritizing evaluation model of qualitative performance variables. So, presents as original the treatment by the fuzzy sets of qualitative critical factors expressed in linguistic terms by specialists working in the Brazilian sector, resulting in the prioritization of these factors. After result, the model was applied at specific shipyard. The results converge Brazil's real scenario and show that the proposed fuzzy model might be a good qualitative performance factor evaluation tool. Finally, to identify real the distance of a specific shipyard for to this research's model prioritization pattern by brazilian specialists.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"53 1","pages":"181 - 203"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82265685","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 : 2020-04-02DOI: 10.1080/16168658.2021.1943877
Bingyu Cao
{"title":"Thanks to the Journals of Exchanged Agreement and Supports","authors":"Bingyu Cao","doi":"10.1080/16168658.2021.1943877","DOIUrl":"https://doi.org/10.1080/16168658.2021.1943877","url":null,"abstract":"","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"29 1","pages":"274 - 275"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88813362","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 : 2020-04-02DOI: 10.1080/16168658.2020.1794498
S. Rivaz, S. H. Nasseri, M. Ziaseraji
The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal programming is suggested. Different solutions are obtained according to the priorities of the decision maker in the proposed model. With respect to its properties, at least a weakly efficient solution is yielded by solving the new model. To demonstrate the validity and strengths of the suggested model, some numerical examples are given. Further, a comparison is made with different existing methods.
{"title":"A Fuzzy Goal Programming Approach to Multiobjective Transportation Problems","authors":"S. Rivaz, S. H. Nasseri, M. Ziaseraji","doi":"10.1080/16168658.2020.1794498","DOIUrl":"https://doi.org/10.1080/16168658.2020.1794498","url":null,"abstract":"The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal programming is suggested. Different solutions are obtained according to the priorities of the decision maker in the proposed model. With respect to its properties, at least a weakly efficient solution is yielded by solving the new model. To demonstrate the validity and strengths of the suggested model, some numerical examples are given. Further, a comparison is made with different existing methods.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"38 1","pages":"139 - 149"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75869279","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 : 2020-04-02DOI: 10.1080/16168658.2020.1817658
M. Javaid, Agha Kashif, T. Rashid
In this article, the notion of hesitant fuzzy graph is introduced. It an extended structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with the system that is designed using fuzzy graphs. Several operations on hesitant fuzzy graphs are defined, namely Cartesian product, composition, tensor product and normal product. Furthermore, the relationship between the degree of vertices of the hesitant fuzzy graphs and the hesitant fuzzy graph obtained by their different products is developed. These operations are highly used in computer science, geometry, algebra, operations research, etc.
{"title":"Hesitant Fuzzy Graphs and Their Products","authors":"M. Javaid, Agha Kashif, T. Rashid","doi":"10.1080/16168658.2020.1817658","DOIUrl":"https://doi.org/10.1080/16168658.2020.1817658","url":null,"abstract":"In this article, the notion of hesitant fuzzy graph is introduced. It an extended structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with the system that is designed using fuzzy graphs. Several operations on hesitant fuzzy graphs are defined, namely Cartesian product, composition, tensor product and normal product. Furthermore, the relationship between the degree of vertices of the hesitant fuzzy graphs and the hesitant fuzzy graph obtained by their different products is developed. These operations are highly used in computer science, geometry, algebra, operations research, etc.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"33 1","pages":"238 - 252"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76296220","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 : 2020-04-02DOI: 10.1080/16168658.2020.1747162
A. Golmohammadi, Mahnoobeh Honarvar, H. Hosseini-nasab, R. Tavakkoli-Moghaddam
In this paper, a bi-objective optimization model is developed to integrate the cell formation and inter/intra-cell layouts in continuous space by considering fuzzy conditions to minimize the total cost of parts relocations as well as cells reconfigurations. The intra- and inter-cell movements for both parts and machines using batch sizes for transferring parts are related to the distance traveled through a rectilinear distance in a fuzzy environment. To solve the proposed problem as a bi-objective mixed-integer non-linear programming model is NP-hard, four meta-heuristic algorithms based on a multi-objective optimization structure are tackled to address the problem. In this regard, not only Genetic Algorithm (GA), Keshtel Algorithm (KA) and Red Deer Algorithm (RDA) are employed to solve the problem, but also a novel hybrid meta-heuristic algorithm based on the benefits of aforementioned algorithms is developed. Finally, by considering some efficient assessment metrics of Pareto-based algorithms, the results indicate that the proposed hybrid algorithm not only is more appropriate than the exact solver but it also outperforms the performance of individual ones particularly in medium- and large-sized problems.
{"title":"A bi-objective Optimization Model for a Dynamic Cell Formation Integrated with Machine and Cell Layouts in a Fuzzy Environment","authors":"A. Golmohammadi, Mahnoobeh Honarvar, H. Hosseini-nasab, R. Tavakkoli-Moghaddam","doi":"10.1080/16168658.2020.1747162","DOIUrl":"https://doi.org/10.1080/16168658.2020.1747162","url":null,"abstract":"In this paper, a bi-objective optimization model is developed to integrate the cell formation and inter/intra-cell layouts in continuous space by considering fuzzy conditions to minimize the total cost of parts relocations as well as cells reconfigurations. The intra- and inter-cell movements for both parts and machines using batch sizes for transferring parts are related to the distance traveled through a rectilinear distance in a fuzzy environment. To solve the proposed problem as a bi-objective mixed-integer non-linear programming model is NP-hard, four meta-heuristic algorithms based on a multi-objective optimization structure are tackled to address the problem. In this regard, not only Genetic Algorithm (GA), Keshtel Algorithm (KA) and Red Deer Algorithm (RDA) are employed to solve the problem, but also a novel hybrid meta-heuristic algorithm based on the benefits of aforementioned algorithms is developed. Finally, by considering some efficient assessment metrics of Pareto-based algorithms, the results indicate that the proposed hybrid algorithm not only is more appropriate than the exact solver but it also outperforms the performance of individual ones particularly in medium- and large-sized problems.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"2 5 1","pages":"204 - 222"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84101465","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 : 2020-01-02DOI: 10.1080/16168658.2020.1775332
I. Emovon, W. O. Aibuedefe
In this paper, a Multi-Criteria Decision-Making (MCDM) tool which combines Fuzzy Set Theory (FST) with TOPSIS (Fuzzy TOPSIS) is presented for selecting optimal material for the different components of the cashew juice extractor. The technique proposed utilise a broad multiple criteria methodology in finding optimal material from among alternative materials. The alternative materials are mild steel, stainless steel, galvanised steel, and alloy steel. To illustrate the applicability of the technique, a case study of the Auger material selection problem was used. The Auger was applied for the demonstration of the proposed method because it is the most critical component of the cashew juice extractor. The result of the analysis indicated that galvanised steel is the optimal material for the Auger. To validate the FUZZY TOPSIS method, the results obtained from it were compared with results obtained from FUZZY MOORA and FUZZY SAW methods. The comparative analysis indicated that FUZZY TOPSIS produces completely same result with the FUZZY SAW method and very similar results with the FUZZY MOORA method. This is an indication of the suitability of the proposed technique in resolving the material selection problem of the cashew juice extractor.
{"title":"FUZZY TOPSIS Application in Materials Analysis for Economic Production of Cashew Juice Extractor","authors":"I. Emovon, W. O. Aibuedefe","doi":"10.1080/16168658.2020.1775332","DOIUrl":"https://doi.org/10.1080/16168658.2020.1775332","url":null,"abstract":"In this paper, a Multi-Criteria Decision-Making (MCDM) tool which combines Fuzzy Set Theory (FST) with TOPSIS (Fuzzy TOPSIS) is presented for selecting optimal material for the different components of the cashew juice extractor. The technique proposed utilise a broad multiple criteria methodology in finding optimal material from among alternative materials. The alternative materials are mild steel, stainless steel, galvanised steel, and alloy steel. To illustrate the applicability of the technique, a case study of the Auger material selection problem was used. The Auger was applied for the demonstration of the proposed method because it is the most critical component of the cashew juice extractor. The result of the analysis indicated that galvanised steel is the optimal material for the Auger. To validate the FUZZY TOPSIS method, the results obtained from it were compared with results obtained from FUZZY MOORA and FUZZY SAW methods. The comparative analysis indicated that FUZZY TOPSIS produces completely same result with the FUZZY SAW method and very similar results with the FUZZY MOORA method. This is an indication of the suitability of the proposed technique in resolving the material selection problem of the cashew juice extractor.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"327 2","pages":"1 - 18"},"PeriodicalIF":1.2,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/16168658.2020.1775332","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72388525","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 : 2020-01-02DOI: 10.1080/16168658.2020.1778829
YU Peng, Xiaogang An, Xiaohong Zhang
By introducing the concepts of intuitionistic L-fuzzy β-covering and intuitionistic L-fuzzy β-neighborhood, we define three kinds of intuitionistic L-fuzzy β-covering rough set models. The basic properties of those intuitionistic L-fuzzy β-covering rough set models are investigated. Moreover, we define the other three kinds of intuitionistic L-fuzzy β-covering rough set models by using the former three models. Finally, we present the matrix representations of the newly defined lower and upper approximation operators so that the calculation of lower and upper approximations of subsets can be converted into operations on matrices.
{"title":"Intuitionistic L-fuzzy β-covering Rough Set","authors":"YU Peng, Xiaogang An, Xiaohong Zhang","doi":"10.1080/16168658.2020.1778829","DOIUrl":"https://doi.org/10.1080/16168658.2020.1778829","url":null,"abstract":"By introducing the concepts of intuitionistic L-fuzzy β-covering and intuitionistic L-fuzzy β-neighborhood, we define three kinds of intuitionistic L-fuzzy β-covering rough set models. The basic properties of those intuitionistic L-fuzzy β-covering rough set models are investigated. Moreover, we define the other three kinds of intuitionistic L-fuzzy β-covering rough set models by using the former three models. Finally, we present the matrix representations of the newly defined lower and upper approximation operators so that the calculation of lower and upper approximations of subsets can be converted into operations on matrices.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"14 1","pages":"19 - 37"},"PeriodicalIF":1.2,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89011222","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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