A novel approach for solving fully fuzzy linear programming problem with LR flat fuzzy numbers

摘要

The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh's decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, existed methods and results are limited if the fuzzy linear programming problem with generalized fuzzy numbers in its objective functions and constraints. In this paper, we discuss fully fuzzy linear programming (FFLP) problems of which all parameters are LR flat fuzzy numbers and a simple but practical method is developed to solve it. In this method, the approximate representation of fully fuzzy constraints is investigated by means of the arithmetic operations on LR flat fuzzy numbers space firstly. Meanwhile, we constructed a auxiliary multi-objective programming to solve the FFLP problems. After that, three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. Finally, the obtained results are compared with the existing works and numerical example is given to illustrate the effectiveness of the proposed method.