双极信息的聚合与分解∗

摘要

Information aggregation is one of the basic means for information processing. This paper mainly discusses about behavior of several aggregation operators. Firstly, from the perspective of generalized adjunction, the properties of generalized aggregation operators are discussed. Given one aggregation operatorA, two different methods are adopted to construct new aggregation operators greater (less) than or equal toA. Furthermore, several aggregation operators, such as bipolar t-norms and bipolar implications, are explored, and the condition is provided for bipolar aggregation operators to be decomposed into two unipolar aggregation operators. Under this condition, the aggregation processing for positive as well as negative information is also presented.%信息聚合是信息处理过程中的基本手段，主要讨论若干聚合算子的性态。首先，从广义伴随对的角度讨论了广义聚合算子的性质。从聚合算子 A 出发，给出两种不同的方法，构造了大于(小于)等于 A 的新的聚合算子；其次，对于处理双极信息用到的聚合算子、双极t-模和双极蕴涵做了讨论，得出了这两个双极聚合算子可分解为两个单级聚合算子的条件。在此条件下即清晰可见聚合双极信息时对正信息及负信息的聚合过程。这对提取特定信息具有极其重要的意义。