Abstract: Aggregation operations play an important role in decision-making
problems where a weighted combination of several criteria is used to select an
alternative with the strongest support. In fuzzy set theory, aggregation
operations are usually modeled as intersection, union, or as combination of
both. The particular form and algebraic properties of these operations vary
according to requirements for compensation among the criteria and other
characteristics of the given decision-making situation. Traditionally, only
algebraically well-behaved operations have been considered for this purpose. By
relaxing some algebraic constraints, more realistic operations can be obtained
that closely capture certain features of human decision-making, such as
preferences and a limited level of detail. This paper proposes a method to generate fuzzy aggregation
operations using genetic programming. It is shown that an evolutionary process,
facilitated by genetic programming, has the capacity to generate new valid
fuzzy aggregation operations and to reproduce existing ones. By varying process
conditions, encoded in a fitness function, it is possible to obtain operations
with different logical and algebraic properties. This approach, based solely on
the axioms which define the desired class of operations, explores the space of
possible functions and often leads to discovery of new operations. However, the
proposed system can also be used to generate aggregation operations that fit a
collected data set. This application is very important as it provides a
powerful new tool for modeling and processing empirical data.
