Characterization of bipolar information aggregation and decomposition

Bipolar information including positive information and negative information is an essential feature in information processing, positive information means that it is possible or preferential and negative information means that it is impossible or forbidden. This paper mainly discusses the mathematical characterization of bipolar information aggregation and decomposition. Firstly, some algebraic operators about bipolar information, such as bipolar algebra, bipolar t-norm, bipolar t-conorm, bipolar implication and bipolar co-implication, are introduced. Secondly, the conditions that a bipolar aggregation operator can be decomposed into two unipolar aggregation operators are provided. Under these conditions, the aggregation processing for positive as well as negative information is clearly presented. Finally, the algebraic structure for constraint bipolar information are established, and some methods of aggregation and decomposition for constraint bipolar information are also given.