This paper studies the fuzzification of the Pareto dominance relation and its application to the design of Evolutionary Many-Objective Optimization algorithms. A generic ranking scheme is presented that assigns dominance degrees to any set of vectors in a scale- independent, nonsymmetric and set-dependent manner. Different fuzzy-based definitions of optimality and dominated solution are introduced. The corresponding extension of the Standard Genetic Algorithm, so-called Fuzzy-Dominance GA (FDGA), will be presented as well. To verify the usefulness of such an approach, the approach is tested on analytical test cases in order to show its validity.
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Wang et al. (2007) studied this question.