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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Bibliographic Details
Published in:International journal of approximate reasoning Vol. 81; pp. 87 - 102
Main Authors: Sun, Bingzhen, Ma, Weimin, Xiao, Xia
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2017
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2016.11.001