On Solving Fuzzy Linear Programming Using Linear Ranking Functions: Review with some Extensions

In this paper, the existing algorithms for solving fuzzy linear programming problems using linear ranking functions are reviewed. The solution approaches have been divided into three areas. The first area involves some approaches for solving reduced fuzzy numbers linear programming (RFNLP) in which only the cost coefficients are fuzzy numbers. The second area consists of some approaches for finding the fuzzy solution of fuzzy variables linear programming problems (FVLP) in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers. The third area considers the semi fully fuzzy linear programming problems (SFFLP) in which the cost coefficients, the right-hand-side vectors and decision variables are as symmetric trapezoidal fuzzy numbers. In this paper we show that whilst each problem is useful in a specialist area, no one methodology can be prescribed as the complete solution of fuzzy linear programming problems