【摘要】 LR模糊数是在模糊数中最常见的一类形式，因其可以通过左右扩张和左右形态函数分别表示不同的模糊组件而能够更真实和灵活地表示现实世界的模糊和不确定性.该文主要是通过两类在图像处理、模糊系统控制和决策等方面具有广泛应用的重叠和群组聚合算子对不同左右形态函数的作用提出了LR模糊数新的扩张算术运算，并重点研究了它们的一些基本运算性质.这极大地扩展和丰富了LR模糊数的构造方式，以适应在现实中各类不确定性场景的表达.更多还原

【Abstract】 LR fuzzy number is the most common form of fuzzy number, because it can represent different fuzzy components through left and right spread and left and right shape functions, so that it can more truly and flexibly represent the ambiguity and uncertainty of the real world.In this paper, some newly extended arithmetic operations of LR fuzzy numbers are proposed by using overlap and grouping aggregation operators, which are widely used in image processing, fuzzy system control and decision making, to act on the different left and right shape functions of LR fuzzy numbers.And some properties of the arithmetic operations are emphatically studied.These studies greatly expand and enrich the mode of construction of LR fuzzy numbers to adapt to the expression of various uncertain scenarios in reality.更多还原