Picture fuzzy sets are an extension of intuitionistic fuzzy set which can model the situations involving more answers of these types: yes, abstain, no, refusal. It is a powerful tool to deal with multiple attribute decision-making (MADM) problems. In this paper, we initiate a new axiomatic definition of picture fuzzy distance measure, which is presented by the picture fuzzy number (PFN) that will reduce the information loss and keep more original information. Meanwhile, the comparison method is proposed. Then, the objective weights of various attributes are determined via gray systems theory. Combing objective weights with subjective weights, we introduce the combined weights. Later, we give an algorithm to solve the MADM problem based on distance measure. Finally, the effectiveness and feasibility of the algorithm is demonstrated by a numerical example.
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Peng et al. (2017) studied this question.