An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function

Main Article Content

Rasha Jalal Mitlif

Abstract

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program.

Downloads

Download data is not yet available.

Article Details

How to Cite
1.
Mitlif RJ. An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function. Baghdad Sci.J [Internet]. [cited 2021Dec.4];19(1):0071. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4699
Section
article

References

Pramanik S, Maiti I, Mandal T. A Taylor Series based Fuzzy Mathematical Approach for Multi Objective Linear Fractional Programming Problem with Fuzzy Parameters. IJCA.2018; 180(45):22-29.

Chaners A, Cooper W W. Programming with linear fractional functionals. Naval Research logistics Quarterly.1962; 9: 181-186.

Effati S, Pakdaman M. Solving the Interval-Valued Linear Fractional Programming Problem.SCIRP.2012; 2(1):51-55.

Tantawy S. An Iterative Method for Solving Linear Fraction Programming (LFP) Problem with sensitivity Analysis. MCA.2008; 13(3): 147-151.

Borza1 M, Rambely A, Saraj Sh M. Solving Linear Fractional Programming Problems with Interval Coefficients in the Objective Function. A New Approach. Applied Mathematical Sciences. 2012; 6(69): 3443 – 3452.

Sharma S C, Bansal A. An Integer Solution of Fractional Programming Problem. Gen. Math. Notes. 2011; 4(2): 1-9.

Anzai Y. On Integer Fractional Programming.ORSJ.1974; 17(1): 49-66.

Verma V, Bakhshi H C, Puri M C. Ranking in Integer Linear Fractional Programming Problems. ZOR Methods and Models of Operation Research. 1990; 34(5): 325-334.

Mehdi M A, Chergui M E, Abbas M. An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem. Advances in Decision Sciences.2014:1-7.

Mohanaselvi S, Ganesan K. A new approach for solving linear fuzzy fractional transportation problem. IJCIET. 2017; 8(8):1123-1129.

Zhou C, Huang G, Chen J, Zhang X. Inexact fuzzy chance – constrained fractional programming for sustainable management of electric power systems. mathematical problems in engineering.2018: 1-13.

Kabiraj A, Nayak P K, Raha S. Solving Intuitionistic Fuzzy Linear Programming Problem. SCIRP.2019; 9(1): 44-58.

Malathi C, Umadevi P. A new procedure for solving linear programming problems in an intuitionistic fuzzy environment. ICACM. 2018; 1: 1-5.

Dinagar D S, Kamalanathan S. Solving Fuzzy Linear Programming Problem Using New Ranking Procedures of Fuzzy Numbers. IJAFSAI.2017; 7: 281-292.

Ingle S M, Ghadle K P. Solving FFLPP Problem with Hexagonal Fuzzy Numbers by New Ranking Method. IJAER .2019; 14(1):97-101.

Mitlif R J. Solving fuzzy fractional linear programming problems by ranking function methods. Journal of College Education .2016; 1:93-108.

Mitlif R J. A New Method for Solving Fully Fuzzy Multi-Objective Linear Programming Problems. IJS.2016; 57(3C):2307-2311.

Ammar E, Muamer M. On Solving Fuzzy Rough Linear Fractional Programming Problem. IRJET. 2016; 3(4):2099-2120.

Kalyani S, Maragatham L, Nagarani S. An Algorithm for Linear Fuzzy Fractional Transportation Problem. IJETMAS .2016; 4(10): 61-68.

Das S K, Edalatpanah S A. A General Form of Fuzzy Linear Fractional Programs with Trapezoidal Fuzzy Numbers. IJDEA.2016; 2(1): 16-19.

Das S K, Mandal T. A MOLFP Method for Solving Linear Fractional Programming under Fuzzy Environment. IJRIE .2017; 6(3): 202– 213.

Osman M S, Emam O E, Elsayed M A. Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters. BJBAS .2018; 7(1):139–149.

Muruganandam S, Ambika P. Harmonic Mean Technique to Solve Multi Objective Fuzzy Linear Fractional Programming Problems. GJPAM .2017; 13(10): 7321-7329.

Hussein I H, Mitlif R J. Ranking Function to Solve a Fuzzy Multiple Objective Function. Baghdad Sci J. 2021; 18(1): 144 – 148.

Purushothkumar M K, Ananathanarayanan M, Dhanasekar S. Fuzzy Diagonal Optimal Algorithm to Solve Fully Fuzzy Transportation Problems. ARPN J. Eng. Appl. Sci. 2019; 14(19): 3450 – 3454.

Hasan I, Hasan A. A new algorithm using ranking function to find solution for fuzzy transportation problem. IJMSS. 2015; 3(3):21-26.