Multi-stage group risk decision making with grey numbers based on grey target and prospect theory
Abstract
Purpose
With respect to multi-stage group risk decision-making problems in which all the attribute values take the form of grey number, and the weights of stages and decision makers are unknown, the purpose of this paper is to propose a new decision-making method based on grey target and prospect theory.
Design/methodology/approach
First, the sequencing and distance between two grey numbers are introduced. Then, a linear operator with the features of the “rewarding good and punishing bad” is presented based on the grey target given by decision maker, and the prospect value function of each attribute based on the zero reference point is defined. Next, weight models of stages and decision makers are suggested, which are based on restriction of stage fluctuation, the maximum differences of alternatives and the maximum entropy theory. Furthermore, the information of alternatives is aggregated by WA operator, the alternatives are selected by their prospect values.
Findings
The comprehensive cumulative prospect values are finally aggregated by WA operator, alternatives are selected or not are judged by the sign of the comprehensive prospect theory, if the prospect value of alternative is negative, the corresponding alternative misses the group decision makers’ grey target, on the contrary, if the prospect value of alternative is positive, the corresponding alternative is dropped into the group decision makers’ grey target, the alternative with positive prospect value whose value is the maximum is selected.
Originality/value
Compared with the traditional decision-making methods using expected utility theory which suppose the decision makers are all completely rational, the proposed method is based on irrational which is more in line with the decision maker’s psychology. And this method considers the decision maker’s psychological expectation values about every attribute, different satisfactory grey target about attributes will directly affect decision-making result.
Keywords
Acknowledgements
The authors are very grateful to the editor and the anonymous referees for their insightful and constructive comments on this paper. This research was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Grant No. FP7-PIIF-GA-2013-629051), the National Natural Science Foundation of China (91324003, 71401051, 71171112, 71171113, 71503103 and 71271226), the joint research project of both the NSFC (71111130211) and the RS of UK, the youth foundation of Humanities and Social Science of The Education Department Henan province of China (2015-QN-020), the youth science foundation of Henan university of science and technology (2015QN027), the scientific research foundation of Henan university of science and technology, the major project and key project of Social Science Foundation of China (10zd & 014, 12AZD102),the National Special Major Project for large Aircraft (2009ZX1102), natural science foundation of Jiangsu Province (BK20150157); Jiangsu Province Social Science Fund Project (14GLC008).
Citation
Yan, S. and Liu, S. (2016), "Multi-stage group risk decision making with grey numbers based on grey target and prospect theory", Grey Systems: Theory and Application, Vol. 6 No. 1, pp. 64-79. https://doi.org/10.1108/GS-09-2015-0062
Publisher
:Emerald Group Publishing Limited
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