Abstract: In view of the multi-attribute decision problem in which attribute weights are completely unknown or partially known and attribute values are in the form of interval-valued Pythagorean hesitant fuzzy numbers, ELECTRE II decision making method is proposed based on interval-valued Pythagorean hesitant fuzzy entropy and cross entropy. Firstly, new interval score function and interval accuracy function of interval-valued Pythagorean hesitant fuzzy number are defined, and a new distance measure is defined. Secondly, the entropy and cross entropy formula are given based on the fuzzy factor, intuitive factor and amplitude factor of interval-valued Pythagorean hesitant fuzzy number, and their properties are proved. A method to determine attribute weights based on entropy and cross entropy is proposed. Finally, interval-valued Pythagorean hesitation fuzzy ELECTRE II method is proposed, and comprehensive precedence value is used to rank alternatives. The feasibility and effectiveness of the proposed method are verified by numerical example and comparative analysis.

Key words: multi-attribute decision making, interval-valued Pythagorean hesitant fuzzy sets, entropy, cross entropy, ELECTRE II method