| Summary: | In many decision making problems, a number of independent attributes or criteria are often used to individually rate an alternative from an agent's local perspective and then these individual ratings are combined to produce an overall assessment. Now, in cases where these individual ratings are not in complete agreement, the overall rating should be somewhere in between the extremes that have been suggested. However, there are many possibilities for the aggregated value. Given this, this paper systematically explores the space of possible compromise operators for such multi-attribute decision making problems. Specifically, we axiomatically identify the complete spectrum of such operators in terms of the properties they should satisfy, and show the main ones that are widely used-namely averaging operators, uninorms and nullnorms-represent only three of the nine types we identify. For each type, we then go onto analyse their properties and discuss how specific instances can actually be developed. Finally, to illustrate the richness of our framework, we show how a wide range of operators are needed to model the various attitudes that a user may have for aggregation in a given scenario (bidding in multi-attribute auctions).
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