Evaluate fuzzy optimization problems based on biobjective programming problems

The embedding theorem shows that the set of fuzzy numbers can be embedded into a Banach space. Inspired by this embedding theorem, we propose a solution concept of the fuzzy optimization problem by solving a biobjective optimization problem, which is transformed from the original fuzzy optimization problem using the embedding theorem. We then also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed to be fuzzy numbers). Under a setting of core values of fuzzy numbers, we show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also an optimal solution of the original fuzzy optimization problem.