Genetic programming of fuzzy aggregation operations

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.