An Unified Effect On Triangular Fuzzy Linear Fractional Programming Problem
Keywords:Linear Fractional Programming Problem, Triangular Fuzzy Number, Fuzzy Numbers.
The linear fractional programming (LFP) problem has attracted the attention of many researchers as it applies to many important fields such as production planning, finance and business planning, healthcare and hospital planning. Several methods have been proposed to solve this problem such as the variable transformation method  and the updated objective function method . The first method transforms the (LFP) problem into an equivalent linear programming problem, while the second method solves a sequence of linear programming problems in response to an update of the local gradient of the fractional objective function at consecutive points. Several topics on the concept of duality and the optimal conditions for (LFP) were also discussed by  and  respectively. Recent research on the theory and methods of fractional programming can be found in ,. Loganathan.T et al., proposed a solution approach to fully fuzzy linear fractional programming problems in . Jervin used two square determinant approaches for simplex method in .In addition, the fuzzy concepts are taken into account for this paper. The topic of fuzzy subsets was introduced in 1965. Researches across the world developed various concepts bridging fuzzy with most of the area in Mathematics and introduced Fuzzy Real line , fuzzy topology , fuzzy trigonometry , etc. Later, fuzzy numbers were defined and were found to have more application developments than fuzzy subsets. Fuzzy numbers have been used to obtain better results in problems where in decision making and analysis are involved. Fuzzy number, which is an extension of real numbers, has its own properties which can be related to theory of numbers.
The paper is organized as follows: section 2 deals with some preliminary definitions and the
Existing fuzzy sets and fuzzy numbers operations are given. An Algorithm is developed for solving Triangular fuzzy linear fractional programming problem and to strengthen our procedure, the Numerical example is given in section 3. Finally, concluding remarks are given in section 4.