Abstract
Fundamental operators of set theory, fuzzy sets and uncertain information processing explore a unipolar scale of the unit interval [0,1]. However, it is known that human beings also handle other types of scale including a bipolar one that can be expressed on the interval [-1,1]. This scale is of particular interest since it supports a representation of symmetric phenomena encountered in human behavior. in the paper, we investigate fundamental aspects of information aggregation operators from the standpoint of their symmetric behavior. Likewise, classical set operators are analyzed within the same setting. New type of aggregation operators - balanced operators - are defined and discussed.