Fully Fuzzy Linear Programming Problem And Its Fuzzy Approximate Solution

The fuzzy linear programming problem with triangular fuzzy numbers in its objective function or constraint conditions 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 function and constraint conditions. This paper mainly analysis the fully fuzzy linear programming (FFLP) problem and its fuzzy approximate solution.First of all, the approximate representation and transformation theorem of fully fuzzy constraints are investigated by means of the definition of the extended LR fuzzy numbers. At the same time, the fully fuzzy linear programming problems are solved by transforming them into crisp linear programming problems under a new ordering of fuzzy numbers. Finally, the results obtained are compared with the existing works, and several numerical examples are given.Furthermore, the fully fuzzy linear programming problem with generalized fuzzy numbers in its objective functions and constraints is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers. After that, the results obtained are compared with the existing works, and numerical examples are given.At last, the approximate representation of fully fuzzy constraints is investi-gated by means of the arithmetic operations on LR flat fuzzy numbers space. We construct a multi-objective programming and propose three approaches to solve it, including optimistic approach, pessimistic approach and linear sum approach based on membership functions. Meanwhile, the fuzzy approximate solution of the fully fuzzy linear programming problems which all parameters are LR flat fuzzy num-bers is discussed. The obtained results are compared with the existing works, and numerical example is given to illustrate the effectiveness of the proposed method.