A spectrum of compensation aggregation operators

In a decision process, when aggregating two values with conflict meaning, sometimes the result should be a tradeoff between the two values. Applicable to many real problems, compensation operators are aggregation operators with such a property. In order to offer more freedom in the selection of suitable compensation operators for various specific application, this paper explores new sorts of compensation operators. First, we introduce the concept of general compensation operators, which form a subclass of general aggregation operators. The two existing kinds of compensation operators, compensatory operators (a special case of uninorm operators) and averaging operators, are subclasses of our general compensation operators. Second, we identify seven new subclasses of the general compensation operators. Third, we construct a new kind of compensation operator, the gray averaging operator, which can include T-norms, T-conorm and averaging operators as its special cases.