The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric ($PFWG$) aggregation operator, the picture fuzzy ordered weighted geometric ($PFOWG$) aggregation operator and the picture fuzzy hybrid geometric ($PFHG$) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

中文翻译：

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基于梯形模糊数的图像模糊几何聚合算子及其应用

图片模糊集是直觉模糊集的生成。聚合运算符是信息聚合过程中的重要工具。先前的论文中提出了一些图片模糊集的聚合算子，但其中一些对于图片模糊多属性决策是有缺陷的。本文介绍了一种图像模糊数和梯形模糊数的变换方法。基于此方法，提出了图像模糊乘法运算和图像模糊幂运算。此外，我们开发了图片模糊加权几何（$PF\mathrm{w\; ^}G$）聚合运算符，图片模糊有序加权几何（$PFØ\mathrm{w\; ^}G$集合算子与图片模糊混合几何（$PFHG$）集合运算符。还研究了相关特性。最后，我们将提出的聚合算子应用于多属性决策和模式识别。