Abstract: Since the Pythagorean fuzzy information aggregation operators are very rare,theresearch into Hamacher integration operator under Pythagorean fuzzy environment has certain theoretical value. Firstly, the Pythagoreanfuzzy operational laws are defined, which is based on the Hamacher t-norm and s-norm. Secondly, the Pythagorean fuzzy Hamacher weighted average (PFHWA) operator and the Pythagorean fuzzyHamacher weighted geometric (PFHWG) operator are proposed, and some properties of these operators such as monotonicity,idempotency and boundednessare discussed in detail,and some special cases of these operators are given. Moreover,two new approaches to Pythagorean fuzzy multi-attribute group decision making are presented based on the proposed operator. Finally,a practical example is given to illustratethe developedapproaches, and further demonstrates the effectiveness of the proposedapproaches.

Key words: pythagorean fuzzy set, hamachert-norm and s-norm, multi-attribute group decision making, aggregation operator

摘要： 基于Pythagorean模糊环境下的信息集成算子很少见,本文探讨Pythagorean模糊Hamacher集结算子问题,具有一定的理论价值。首先,定义Hamacher算子在Pythagorean模糊环境下的运算规则;之后,给出几种Pythagorean模糊Hamacher信息集结算子,比如,Pythagorean模糊Hamacher算术平均算子,广义Pythagorean模糊Hamacher算术平均算子等,并研究其具有的性质,包括单调性、幂等性、有界性;之后,提出两种不同决策方法来解决Pythagorean模糊信息环境下的多属性群决策问题;最后,通过示例验证所提出方法的可行性和实用性。

关键词: Pythagorean模糊集, Hamacher算子, 多属性群决策, 集成算子