Liu Xinwang
School of Economics and Management, Southeast University, Nanjing 210096, China.
IEEE Trans Syst Man Cybern B Cybern. 2006 Feb;36(1):118-27. doi: 10.1109/tsmca.2005.854496.
Based on the researches on ordered weighted average (OWA) operator, the weighted OWA operator (WOWA) and especially the quantifier guided aggregation method, with the generating function representation of regular increasing monotone (RIM) quantifier technique, we discuss the properties of WOWA operator with RIM quantifier in the respect of orness. With the continuous OWA and WOWA ideas recently proposed by Yager, an improvement on the continuous OWA and WOWA operator is proposed. The properties of WOWA are also extended from discrete to the continuous case. Based on these properties, two families of parameterized RIM quantifiers for WOWA operator are proposed, which have exponential generating function and piecewise linear generating function respectively. One interesting property of these two kinds of RIM quantifiers is that for any aggregated set (or variable) under any weighted (distribution) function, the aggregation values are always consistent with the orness (optimistic) levels, so they can be used to represent the decision maker's preference, and we can get the preference value of fuzzy sets or random variables with the orness level of RIM quantifier as their control parameter.
基于对有序加权平均（OWA）算子、加权OWA算子（WOWA）特别是量词引导聚合方法的研究，利用正则递增单调（RIM）量词技术的生成函数表示，我们从偏或度方面讨论了带RIM量词的WOWA算子的性质。基于Yager最近提出的连续OWA和WOWA思想，对连续OWA和WOWA算子提出了一种改进。WOWA的性质也从离散情形扩展到了连续情形。基于这些性质，提出了两类用于WOWA算子的参数化RIM量词，它们分别具有指数生成函数和分段线性生成函数。这两类RIM量词的一个有趣性质是，对于任何加权（分布）函数下的任何聚合集（或变量），聚合值总是与偏或度（乐观）水平一致，因此它们可用于表示决策者的偏好，并且我们可以以RIM量词的偏或度水平作为控制参数来得到模糊集或随机变量的偏好值。
