Fuzzy probability based randomness is utilized for polymorphic uncertain design and a priori parameters in design optimization tasks. Methods for the algorithmic interface between optimization and polymorphic uncertainty analysis are introduced. Uncertain design vectors are incorporated by affine transformation from deterministic design vectors. Multiple uncertainty reducing measures are discussed, which are required for the evaluation and comparability of fitness in optimization. Nested uncertainty reducing measures are mandatory for polymorphic uncertain objectives. The inherence of multiple nested objectives is pointed out, which leads to inherence of multi-objective optimization in single-objective optimization problems with polymorphic uncertain parameters. In this contribution, a framework is presented considering polymorphic uncertain a priori and design parameters in a multi-objective optimization. A parameter based geometric design optimization of a steel hook is investigated. Several uncertainty reducing measures are evaluated for optimization of performance and robustness. Fuzzy design parameters are considered with respect to geometry and, therefore, an automated geometry regeneration and remeshing method is propagated. Material characteristics are modeled with stochastic a priori parameters. The load conditions are assumed to be a priori polymorphic uncertain. PARETO optimality is evaluated depending on the surrogate formulation of uncertainty reducing measures.