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Mathematical Problems in Engineering Volume 2019 ,2019-10-03
Three-Way Decisions with Single-Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis
Research Article
Peide Liu 1 Hongyu Yang 1
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DOI:10.1155/2019/3258018
Received 2019-04-28, accepted for publication 2019-08-31, Published 2019-08-31
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摘要

The single-valued neutrosophic set (SVNS) can not only depict imperfect information in the real decision system but also handle undetermined and inconformity information flexibly and effectively. Three-way decisions (3WDs) are often used as an effective method to deal with uncertainties, but the conditional probability is given by the decision maker subjectively, which makes the decision result too subjective. This paper proposes a novel model based on 3WDs to settle the multiattribute decision-making (MADM) problems, where the attribute values are described by SVNS, and the attribute weights are entirely unknown. At first, we build a single-valued neutrosophic decision theory rough set (SVNDTRS) model based on Bayesian decision process. Then, we use the analytic hierarchy process (AHP) approach to calculate the subjective weight of each attribute, the information entropy to obtain the attribute’s objective weight, and the minimum total deviation approach to determine the combined weight of the attributes. After obtaining the standard weight, the grey relational analysis (GRA) method is utilized to calculate the grey correlation closeness with the ideal solution, and the conditional probability is estimated by it. In addition, we develop a decision-making method in view of the ideal solution of 3WDs with the SVNS. This approach not only considers the lowest cost but also gives a corresponding semantic explanation for the decision result of each alternative, which can supplement the decision results of GRA. At last, we illustrate the feasibility and effectiveness of 3WDs through an example of supplier selection and compare it with other methods to verify the advantages of our approach.

授权许可

Copyright © 2019 Peide Liu and Hongyu Yang. 2019
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

通讯作者

Peide Liu.School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong 250014, China, sdufe.edu.cn.peide.liu@gmail.com

推荐引用方式

Peide Liu,Hongyu Yang. Three-Way Decisions with Single-Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis. Mathematical Problems in Engineering ,Vol.2019(2019)

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