Multiobjective fuzzy optimization with random variables in a mix of fuzzy and probabilistic environment

The fuzzy λ-formulation is used to solve multiobjective optimization problems in which the design variables are random, the constraints as a whole has a fuzzy probability or the constraints are mixed of deterministic, stochastic and fuzzy constraints. The fuzzy optimization strategy helps one to get the highest degree of satisfaction in reaching an optimum solution. The idea of expected value and the chance constrained programming technique allows one to convert a stochastic optimization problem into its equal deterministic form. The design of a three-bar truss illustrates the proposed design optimization in detail and the design of a machine-tool spindle express the comprehensive work of this technique. Results show that the proposed formulation and method can generate a natural, well-behaved, and reliable design