广义毕达哥拉斯正态模糊集成算子及其决策应用

Generalized Pythagorean Normal Fuzzy Aggregation Operators and Their Applications in Decision Making

将毕达哥拉斯模糊数与直觉正态模糊数相结合，提出了毕达哥拉斯正态模糊数，研究了其运算和运算性质，定义了毕达哥拉斯正态模糊数的得分函数和精确函数，实现其大小排序．然后，针对毕达哥拉斯正态模糊信息的集成问题，提出毕达哥拉斯正态模糊有序加权平均（PNFOWA）算子、广义有序加权平均（GPNFOWA）算子和毕达哥拉斯正态模糊有序加权几何平均（PNFOWGA）算子及广义有序加权几何平均（GPNFOWGA）算子，并研究了其性质．最后，提出基于广义毕达哥拉斯正态模糊集成算子的多属性决策方法，并通过实例说明该方法的有效性．

Combining the Pythagorean fuzzy numbers and the intuitionistic fuzzy numbers, the Pythagorean normal fuzzy numbers are proposed. The operation and the operational laws of the Pythagorean normal fuzzy numbers are given, and the score function and the accuracy function are also defined to compare and rank the Pythagorean normal fuzzy numbers. Several aggregation operators such as the Pythagorean normal fuzzy order weighted average （PNFOWA） operator, the generMized Pythagorean normal fuzzy ordered weighted average （GPNFOWA） operatorthe Pythagorean normal fuzzy order weighted geometric aver- age （PNFOWGA） operator and the generalized Pythagorean normal fuzzy ordered weighted geometric average （GPNFOWGA） operator are given to solve the information aggregate problem with the Pythagorean normal fuzzy numbers. The properties of these operators are also studied. Then the method for multi-criteria decision making by using the Pythagorean normal fuzzy aggregation operator are given to solve the problem with the Pythagorean normal fuzzy information and an example is given to illustrate the effectiveness of the proposed method.