Multicriteria decision making using fuzzy quantifiers

Many financial decisions involve a need to satisfy multiple criteria (goals). This situation becomes particularly apparent in problems of investment allocation where we are faced with the problem of selecting from a collection of alternative investment packages one that meets our subjective goals such as growth, security and a reasonable return on investment. Another closely related problem, one that is becoming more important as the information highway paradigm is achieving reality, is that of information retrieval. Here we are faced with the problem of selecting from a large collection of documents those that satisfy a set of criteria describing the class of documents of interest to us. In cases of single criteria the problem is easily solved by just selecting the altemative(s) that best satisfies our criteria. In the multiple criteria environment we are faced with the prior problem of combining these multiple criteria to obtain an overall decision function before we can make any selection. A fundamental problem that arises in this task is to provide an ability to aggregate the multiple criteria in a way that corresponds to the decision makers presumed relationship that exists between the criteria. Do all criteria need be satisfied? Do some criteria have priority over others? Are some criteria more important than others? Essentially their is a need for tools to help in the construction of multiple criteria decision functions that enable us to model the various agendas a decision maker may have formulating these problems. Starting with the classic work of Bellman and Zadeh [l] fuzzy logic has been used as a tool to develop and model multicriteria decision problems. In this framework the criteria or goals of the decision maker are represented as fuzzy subsets over the space of decision alternatives (investment packages/documents) and fuzzy set operators are used to aggregate the individual criteria to form the overall decision function. As originally suggested by Bellman and Zadeh the criteria can be combined by the use of an intersection operation which implicitly implies a requirement that all the criteria be satisfied by a solution to the problem. As noted by Yager [2] this condition may not always be the appropriate relationship between the criteria. For example a decision maker may be satisfied if most of the criteria are satisfied. In this work we look at the issue of the formulation of these softer decision functions which we call quantifier guided aggregations. In [2] we suggested the use of the Ordered Weighted Averaging (OWA) operators as a tool to implement these kinds of aggregations. We here further develop this approach by considering environments in which the individual criteria have importances associated with them.