A Spectrum of Weighted Compromise Aggregation Operators: A Generalization of Weighted Uninorm Operator

In Artificial Intelligence, 171(2–3):161–184, 2007. Luo and Jennings identify and analyze the complete spectrum of compromise aggregation operators that can be used to model the various attitudes that decision‐making agents can have toward risk in aggregation. In this paper, we extend these operators to deal with aggregation when the ratings have different degrees of importance. Specifically, we generalize the method of weighted uninorms to handle this issue. We choose this approach because uninorm compromise operators are a kind of common ones, and their weighted counterparts, which are widely accepted, can cover other common operators, such as weighted t‐norms and t‐conorms, as special cases. As per the analysis of weighted uninorms, we identify common properties that the weighting operators of the various compromise operators should satisfy, and in so doing, we introduce the concept of a general weighting operator for compromise operators and reveal the different properties that a specific type of weighting operator should obey. This, in turn, defines the concepts of the various weighting operators of the various compromise operators. We then go onto discuss the construction issue of weighting operators associated with the various compromise operators.