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 Fazzy-Dominance-Driven GA (FDD-GA),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.