Mixed fuzzy-probabilistic programming approach for multiobjective engineering optimization with random variables

A mixed fuzzy-probabilistic fuzzy-probabilistic programming approach is presented to solve a multiobjective optimization problem with random variables, fuzzy probability in constraints, or a mix of deterministic, stochastic and fuzzy parameters. This paper also examines a problem that has a known or unknown probability density function (pdf). To construct the membership function with a known pdf, one can apply the possibility-probability consistency principle. To deal with the probabilistic constraints with fuzziness, one can use the fuzzy and stochastic formulation. The fuzzy optimization method helps one to get the highest degree of satisfaction in reaching an optimum solution. The characteristic of each constraint by optimizing a three-bar truss is investigated and compared with one another. The optimal design of a structural spindle is also used in order to illustrate this integrated strategy. Results show that the proposed approach provides a natural representation of a design problem and gives a reliable solution.