Expectation formulas for reduced fuzzy variables

In type-2 fuzzy optimization problems, the uncertain parameters are usually represented by type-2 fuzzy variables. To solve such fuzzy programming, we are required to reduce the type-2 fuzzy parameters. Based on the mean reduction results of type-2 fuzzy variables, this paper derives expectation formulas for reductions of two common type-2 fuzzy variables. Using the obtained results, we can build meaningful fuzzy optimization problems.