As an extension of the intuitionistic fuzzy set, the Pythagorean fuzzy set can depict uncertain information more effectively, so it has been well applied in multiple criteria decision making problems. At present, the multiple criteria decision making methods using the Pythagorean fuzzy set are generally ranked based on the aggregation operator or the distance measure, ignoring the important tool of the similarity measure. Therefore, this paper proposes several new similarity measures of the Pythagorean fuzzy set and applies them to multiple criteria decision making problems. Firstly, several new similarity measures of the Pythagorean fuzzy set are proposed, and their properties are discussed. Then, based on the weighted similarity measures, the multiple criteria decision making method is proposed. Finally, the accuracy and reliability of the new similarity measures and the proposed multiple criteria decision making method are verified by the simulation cases.
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