Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes

Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed by Yao is based on rough set theory and is a natural extension of the classical two-way decision approach. In this paper, we introduce the ide...

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Vydáno v:	International journal of approximate reasoning Ročník 81; s. 87 - 102
Hlavní autoři:	Sun, Bingzhen, Ma, Weimin, Xiao, Xia
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.02.2017
Témata:	Approximation Decision making Decision theory Decision-theoretic rough set Fuzzy rough set Fuzzy set theory Fuzzy sets Group decision making Mathematical analysis Mathematical models Multigranulation Risk Rough set over two universes Three-way decisions Multigranulation Three-way decisions Group decision making Decision-theoretic rough set Rough set over two universes Fuzzy rough set
ISSN:	0888-613X, 1873-4731
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Abstract	Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed by Yao is based on rough set theory and is a natural extension of the classical two-way decision approach. In this paper, we introduce the idea of decision-theoretic rough set into multigranulation approximation space and explore the rough approximation of a fuzzy decision object under the framework of two universes. We construct a variable precision multigranulation fuzzy decision-theoretic rough set over two universes by using the concept of an arbitrary binary fuzzy relation class between two different universes and the probability measurement of a fuzzy event. Several interesting properties of the proposed model are addressed and the decision rules are also deduced using the concept of three-way decision-making over two universes. Moreover, two special types of optimistic and pessimistic models are given by using different precision parameters. We then present a new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes. Meanwhile, we establish a cost-based method for sorting among all alternatives of group decision-making problems. Finally, an example of handling a medical diagnosis problem illustrates this approach. •A new multigranulation fuzzy decision-theoretic rough set over two universes was defined.•The relationship between the proposed model with the existing decision-theoretic rough set models was established.•The three-way decision was deduced based on the multigranulation fuzzy decision-theoretic rough set over two universes.•Multigranulation fuzzy decision-theoretic rough set-based three-way group decision making method was established over two universes.
AbstractList	Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed by Yao is based on rough set theory and is a natural extension of the classical two-way decision approach. In this paper, we introduce the idea of decision-theoretic rough set into multigranulation approximation space and explore the rough approximation of a fuzzy decision object under the framework of two universes. We construct a variable precision multigranulation fuzzy decision-theoretic rough set over two universes by using the concept of an arbitrary binary fuzzy relation class between two different universes and the probability measurement of a fuzzy event. Several interesting properties of the proposed model are addressed and the decision rules are also deduced using the concept of three-way decision-making over two universes. Moreover, two special types of optimistic and pessimistic models are given by using different precision parameters. We then present a new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes. Meanwhile, we establish a cost-based method for sorting among all alternatives of group decision-making problems. Finally, an example of handling a medical diagnosis problem illustrates this approach. Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed by Yao is based on rough set theory and is a natural extension of the classical two-way decision approach. In this paper, we introduce the idea of decision-theoretic rough set into multigranulation approximation space and explore the rough approximation of a fuzzy decision object under the framework of two universes. We construct a variable precision multigranulation fuzzy decision-theoretic rough set over two universes by using the concept of an arbitrary binary fuzzy relation class between two different universes and the probability measurement of a fuzzy event. Several interesting properties of the proposed model are addressed and the decision rules are also deduced using the concept of three-way decision-making over two universes. Moreover, two special types of optimistic and pessimistic models are given by using different precision parameters. We then present a new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes. Meanwhile, we establish a cost-based method for sorting among all alternatives of group decision-making problems. Finally, an example of handling a medical diagnosis problem illustrates this approach. •A new multigranulation fuzzy decision-theoretic rough set over two universes was defined.•The relationship between the proposed model with the existing decision-theoretic rough set models was established.•The three-way decision was deduced based on the multigranulation fuzzy decision-theoretic rough set over two universes.•Multigranulation fuzzy decision-theoretic rough set-based three-way group decision making method was established over two universes.
Author	Sun, Bingzhen Ma, Weimin Xiao, Xia
Author_xml	– sequence: 1 givenname: Bingzhen surname: Sun fullname: Sun, Bingzhen email: bzsun@xidian.edu.cn organization: School of Economics and Management, Xidian University, Xi'an, Shaanxi 710071, China – sequence: 2 givenname: Weimin surname: Ma fullname: Ma, Weimin email: mawm@tongji.edu.cn organization: School of Economics and Management, Tongji University, Shanghai 200092, China – sequence: 3 givenname: Xia surname: Xiao fullname: Xiao, Xia organization: School of Economics and Management, Tongji University, Shanghai 200092, China
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Snippet	Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed...
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SubjectTerms	Approximation Decision making Decision theory Decision-theoretic rough set Fuzzy rough set Fuzzy set theory Fuzzy sets Group decision making Mathematical analysis Mathematical models Multigranulation Risk Rough set over two universes Three-way decisions
Title	Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes
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