Automatic Discovery of Fuzzy Aggregation Operations

P. Musilek, G. Barreiro, and J. Pulido (Canada)


Fuzzy Sets, Aggregation Operations, Genetic Program ming


Aggregation operations play an important role in any type of decision–making problems where weighted combina tion of several criteria is used to select an alternative with the strongest support. In fuzzy set theory, aggregation op erations are usually modelled as intersection, union, or their combination. Particular form and algebraic proper ties of these operations vary with different requirements for compensation among the criteria and other character istics of given decision–making situation. Traditionally, only algebraically well-behaved operations have been con sidered for this purpose. However other aggregation oper ations can be devised with quite interesting semantic prop erties. Some of them are even more realistic in the sense of capturing more closely certain features of human decision– making process. This paper examines the possibility to discover fuzzy aggregation operations in an automated manner using ge netic programming. It is shown that evolutionary pro cess, facilitated by genetic programming, has the capacity to generate valid and useful fuzzy aggregation operations, both existing and new. By varying conditions of the pro cess, encoded in a fitness function, it is possible to obtain aggregation operations with different logical and algebraic properties. Some of these operations have very interesting semantic properties useful for modelling decision–making processes with priorities or with limited levels of granular ity.

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