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The result of group decision-making is always unstable, influenced by some uncertain factors. It is necessary to measure and analyse the stability of the result. A measurement based on the inclined angle of two vectors is proposed in this paper, in order to measure the stabilities of the results of weighted scoring rules. The concepts of stability degree and stability angle are given, whose geometric interpretations are displayed in the case of three candidates. Then an extended measurement called the relative stability degree is discussed to analyse the comparability of stability measurements for different numbers of candidates. Furthermore, this measurement and its extension are used to aid the decision-making of new project development in a software company.
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Wu et al. (2015) studied this question.
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