Solving linear Boolean programming problems with imprecise costs

The authors present a fuzzy linear Boolean programming problem with fuzzy costs and propose two different approaches for solving the problem. In the case considered, the objective has a fuzzy nature, and, associated to each feasible solution, there is a fuzzy number which is obtained by means of the fuzzy objective function. Hence, to solve the optimization problem, obtaining both the optimal solution and the corresponding fuzzy value of the objective, methods ranking the fuzzy numbers obtained from that function must be considered. The approaches are based on methods for ranking fuzzy numbers, and on the use of the decomposition theorem for fuzzy sets which provides a fuzzy solution to the problem