Abstract: The proposed single-valued neutrosophic sets make up for the shortcomings of fuzzy sets that cannot handle inconsistent and discontinuous information. The study regards three parameters of single-valued neutrosophic sets as three coordinates to generate a 3D dimension, and extends VIKOR method to single-valued neutrosophic sets environment. The ranking of original VIKOR method is based on the closeness between alternatives and the positive ideal solution(PIS). Namely the optimal compromise solution is the closest to PIS. However, in the 3D space consists of single-valued neutrosophic sets, the closest distance between the alternative and PIS does not mean that it is the farthest from the negative ideal solution(NIS). That is, the ranking and the optimal compromise solution are different when take the closeness between alternatives and PIS as baseline compared with the closeness between alternatives and NIS. Different preference of decision makers for reference standard lead to different results which cause confusion in the decision making. The existing research does not propose some advices to solve the problem. For this reason, the concept of reference coefficient(RC) is proposed and the closeness between alternatives and NIS is introduced into original VIKOR method and the influence of different RC is explored on the ranking and the optimal compromise solution. In order to verify the effectiveness of the improved method, the result of the paper are compared with those of the existing literature. The result shows that the changes of RC have an impact on the ranking and the optimal compromise solution. It is more reasonable for decision makers to consider the results of different RC comprehensively. VIKOR method based on the reference coefficient amends the use of original VIKOR method under the imprecision environment which is an extension of VIKOR method. The research result shows that it is a reasonable ranking method.

Key words: VIKOR, single-valued neutrosophic sets, reference coefficient, relative distance weights