图片模糊聚合算子及其在多属性决策中的应用

Picture fuzzy aggregation operators and their applicationto multi-attribute decision making

目的:研究图片模糊Frank聚合算子。方法:首先提出了图片模糊聚合算子的公理化定义。其次,基于图片模糊可表示三角范数和Frank三角范数,提出了一些运算。基于提出的运算,构造了图片模糊Frank加权平均聚合算子和图片模糊Frank加权几何聚合算子。结果:提出的聚合算子满足公理化定义,克服了现有的聚合算子的缺陷。结论:我们应用提出的聚合算子到多属性决策问题中,实例表明本文提出的聚合算子更灵活,更可靠。

Aims:This paper aims study the Frank aggregation operators for picture fuzzy sets.Methods:First,the axiomatic definition of the picture fuzzy aggregation operators was given.Some picture fuzzy operations were constructed based on picture fuzzy representable t-norm and Frank t-norm.By these operations,picture fuzzy Frank weighted averaging(PFFWA)aggregation operators and picture fuzzy Frank weighted geometric(PFFWG)aggregation operators were proposed.Results:The proposed aggregation operators satisfied the axiomatic definition and overcame the defects of existing aggregation operators.Conclusions:The proposed aggregation operators can be applied to solve the multi-attribute decision problem.The result of the example shows that the proposed aggregation operators are more reliable and flexible.