A Novel Method for Multiattribute Decision Making with Interval-Valued Pythagorean Fuzzy Linguistic Information

Pythagorean fuzzy set (PFS), proposed by Yager (2013), is a generalization of the notion of Atanassov's intuitionistic fuzzy set, which has received more and more attention. In this paper, first, we define the weighted Minkowski distance with interval-valued PFSs. Second, inspired by the idea of the Pythagorean fuzzy linguistic variables, we define a new fuzzy variable called interval-valued Pythagorean fuzzy linguistic variable set (IVPFLVS), and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Third, some aggregation operators are presented for aggregating the interval-valued Pythagorean fuzzy linguistic information such as the interval-valued Pythagorean fuzzy linguistic weighted averaging (IVPFLWA), interval-valued Pythagorean fuzzy linguistic ordered weighted averaging (IVPFLOWA) , interval-valued Pythagorean fuzzy linguistic hybrid averaging, and generalized interval-valued Pythagorean fuzzy linguistic ordered weighted average operators. Fourth, some desirable properties of the IVPFLWA and IVPFLOWA operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, based on the IVPFLWA or interval-valued Pythagorean fuzzy linguistic geometric weighted operator, a practical example is provided to illustrate the application of the proposed approach and demonstrate its practicality and effectiveness. (C) 2017 Wiley Periodicals, Inc.