An Approach to Compute the Multi-Objective Programming Problem Under Triangular Fuzzy Numbers
DOI:
https://doi.org/10.29304/jqcm.2022.14.3.1034Keywords:
Multi- objective function (MOF),, Triangular fuzzy number (TrFN),, Fractional programming problems (FrPP), Linear Programming Problem (LnPP), Simplex method (SM).Abstract
The most important one advantages of the operation research (OR) theory is displayed of this paper for tackling multi-objective function programming problems (MOFPP). In this study, we present an approach for multi-objective fractional programming problems (MOFrPP) using fuzzy numbers (FN) coefficients in the objective functions (OF). The objective functions' (OF) parameters are all considered to be fuzzy triangular fuzzy numbers (FTrFN). This problem's multi-objective function (MOF) case was resolved by transforming the MOF to a linear programming problem (LnPP) that could be resolved using the simplex method (SM). The problem is being solved using algorithms. Then the value is compared with a result, which obtained by simplex method (SM). These techniques are illustrated with numerical examples (NE). This study shows the reliability of our methods and their utility to this specific set of multi-objective functions (MOF).
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References
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[14] Rasha Jalal Mitlif , Solving fuzzy fractional linear programming problems by ranking function methods , JOURNAL OF COLLEGE OF EDUCATION, 2016, NO.1 , 93-108.
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[16] Purnima Pandit , Multi-objective Linear Programming Problems involving Fuzzy Parameters, International Journal of Soft Computing and Engineering (IJSCE), Volume-3, Issue-2, 2013 , 99-102.
[17] N. RAMESHAN and D. STEPHEN DINAGAR , A STUDY ON FUZZY CRITICAL PATH WITH QUADRILATERAL FUZZY NUMBERS , Advances and Applications in Mathematical Sciences 21(3), 2022, 1491-1508 .
[18] Vijay C. Makwana, Vijay P. Soni, Nayan I. Patel, Manoj Sahni, Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations , Mathematics and Statistics 10(1): 176-186, 2022.
[19] Nejmaddin A. Suleiman and Maher A. Nawkhass , A New Modified Simplex Method to Solve Quadratic Fractional Programming Problem and Compared it to a Traditional Simplex Method by Using Pseudoaffinity of Quadratic Fractional Functions, Applied Mathematical Sciences, Vol. 7, 2013, no. 76, 3749 – 3764.
[20] El- Saeed Ammar, Mohamed Muamer, Algorithm for Solving Multi Objective Linear Fractional Programming Problem with Fuzzy Rough Coefficients, Open Science Journal of Mathematics and Application , 2016; 4(1): 1-8.
[21] Chandra Sen , Duality in Solving Multi-Objective Optimization (MOO) Problems, American Journal of Operations Research, 2019, 9, 109-113.
[22] T. Ibaraki, Complementary programming, Oper. Res. 19 (1971), 1523–1529.
[23] Maher Nawkhass , Nejmaddin Sulaiman , Symmetric fuzzy approach to solve complementary multi-objective linear fractional programming problem , Int. J. Nonlinear Anal. Appl. In Press, 2022, 1–6.
[24] Rasha Jalal Mitlif , An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function , Baghdad Science Journal , 2022, 19(1): 71-76.
[2] Ronak M. Abdullah, Snoor O. Abdalla , Solution of Multi-Objective Linear Programming Problem by Advanced Transformation Technique, Samarra Journal of Pure and Applied Science, Samarra J. Pure Appl. Sci., 2022; 4 (2): 118-128.
[3] Samsun Nahar and Md. Abdul Alim , A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique , IOSR Journal of Mathematics (IOSR-JM) ,13(3), 2017,39-52.
[4] Farhana Akond Pramy, Md. Ainul Islam , Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application , Open Journal of Optimization, 2017, 6, 164-175.
[5] S. F. TANTAWY, SOLVING A SPECIAL CLASS OF MULTIPLE OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEMS, the ANZIAM journal, 56, 2014, 91–103.
[6] Moslem Ganji , Mansour Saraj , Solving Multi Objective Linear Fractional Programming Problem Under Uncertainty via Robust Optimization Approach , Journal of Informatics and Mathematical Sciences , Vol. 11 No. 2 , 2019, 115-125.
[7] R. Suganya and U. Afrin , SOLVING MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS BY STATISTICAL AVERAGING AND NEW STATISTICAL AVERAGING METHOD, International Journal of Mechanical Engineering , Vol. 7 No. 4 April, 2022 , 1038-1043.
[8] S. Muruganandam and P. Ambika , Harmonic Mean Technique to Solve Multi Objective Fuzzy Linear Fractional Programming Problems, Global Journal of Pure and Applied Mathematics , Volume 13, Number 10, (2017), pp. 7321-7329.
[9] Beena T Balan ,Solving Multi-Objective Fuzzy Linear Optimization Problem Using Fuzzy Programming Technique, IOSR Journal of Mathematics (IOSR-JM) , 2016, 18-21.
[10] P. A. Thakre, D. S. Shelar , S. P. Thakre , Solving fuzzy linear programming problem as multi objective linear programming problem, Journal of Engineering and Technology Research Vol. 2(5), pp. 82-85, 2009.
[11] Xiao-Peng Yang , Bing-Yuan Cao , Hai-Tao Lin , Multi-Objective Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers, 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2014, 165-171.
[12] Nejmaddin A. Sulaiman, Rebaz B. Mustafa , Using Harmonic Mean to Solve Multi-Objective Linear Programming Problems , American Journal of Operations Research, 2016, 6, 25-30.
[13] .Rasha Jalal Mitlif, A New Method for Solving Fully Fuzzy Multi-Objective Linear Programming Problems , Iraqi Journal of Science, 2016, Vol. 57, No.3C, pp:2307-2311.
[14] Rasha Jalal Mitlif , Solving fuzzy fractional linear programming problems by ranking function methods , JOURNAL OF COLLEGE OF EDUCATION, 2016, NO.1 , 93-108.
[15] I. H. Hussein and R. J. Mitlif, “Ranking Function to Solve a Fuzzy Multiple Objective Function”, Baghdad Science Journal, vol. 18, no. 1, pp. 144-148 , 2021.
[16] Purnima Pandit , Multi-objective Linear Programming Problems involving Fuzzy Parameters, International Journal of Soft Computing and Engineering (IJSCE), Volume-3, Issue-2, 2013 , 99-102.
[17] N. RAMESHAN and D. STEPHEN DINAGAR , A STUDY ON FUZZY CRITICAL PATH WITH QUADRILATERAL FUZZY NUMBERS , Advances and Applications in Mathematical Sciences 21(3), 2022, 1491-1508 .
[18] Vijay C. Makwana, Vijay P. Soni, Nayan I. Patel, Manoj Sahni, Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations , Mathematics and Statistics 10(1): 176-186, 2022.
[19] Nejmaddin A. Suleiman and Maher A. Nawkhass , A New Modified Simplex Method to Solve Quadratic Fractional Programming Problem and Compared it to a Traditional Simplex Method by Using Pseudoaffinity of Quadratic Fractional Functions, Applied Mathematical Sciences, Vol. 7, 2013, no. 76, 3749 – 3764.
[20] El- Saeed Ammar, Mohamed Muamer, Algorithm for Solving Multi Objective Linear Fractional Programming Problem with Fuzzy Rough Coefficients, Open Science Journal of Mathematics and Application , 2016; 4(1): 1-8.
[21] Chandra Sen , Duality in Solving Multi-Objective Optimization (MOO) Problems, American Journal of Operations Research, 2019, 9, 109-113.
[22] T. Ibaraki, Complementary programming, Oper. Res. 19 (1971), 1523–1529.
[23] Maher Nawkhass , Nejmaddin Sulaiman , Symmetric fuzzy approach to solve complementary multi-objective linear fractional programming problem , Int. J. Nonlinear Anal. Appl. In Press, 2022, 1–6.
[24] Rasha Jalal Mitlif , An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function , Baghdad Science Journal , 2022, 19(1): 71-76.
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Published
2022-09-24
How to Cite
Mitlif, R. J. (2022). An Approach to Compute the Multi-Objective Programming Problem Under Triangular Fuzzy Numbers. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(3), Math Page 101–110. https://doi.org/10.29304/jqcm.2022.14.3.1034
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Math Articles
