Lexicographic ordinal OWA aggregation of multiple criteria

We consider a special case of multi-criteria decision making. Here the information provided by the decision maker about an alternative’s satisfaction to the criteria by provided in terms of values that only have an ordinal nature. Linguistic terms such as high, medium and low are examples of this type of valuation. In addition we consider the situation in which there exists a lexicographic based priority ordering among the criteria. This type of lexicographic order can arise in situations in which we want to limit the ability of the low priority criteria to compensate for lack of satisfaction to higher priority criteria. For example in selecting an automobile where safety and cost are our criteria a lexicographic ordering arises when we do not want to allow the fact that a car is extremely inexpensive to compensate for the fact that it may not be safe. To help in the construction of multi-criteria aggregation functions we introduce the concept of criteria organization to indicate the body of knowledge that guides how we combine an alternative’s satisfactions to the individual criteria to obtain its overall satisfaction.