Solving Linear Programming Problems Involving Hexagonal and Octagonal Fuzzy Numbers via Two Ranking Functions
DOI:
https://doi.org/10.29304/jqcm.2022.14.4.1117Keywords:
Fuzzy set (FS),, Linear programming (LP), Simplex method (SM), Hexagonal fuzzy number (HFN), Octagonal fuzzy number (OFN)Abstract
Many types of ambiguous numbers have been studied in many mathematical fields. Two of these types, the obscure number hexagonal and octagonal are widely used, especially in mathematical programming. A linear fuzzy number (LFN), which generalizes these two types, is presented in this paper. Based on the definition of the order function by the total value, two ranking function for this linear fuzzy number is used. Arithmetic operations with their properties are entered on ambiguous numbers as a special case. It also turns out that the operations proposed on LFN are acceptable generalizations of conventional arithmetic operations on real numbers.
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References
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[11] S. H. Nasseri, E. Ardil, A. Yazdani, and R. Zaefarian , Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences , 1(10) , 2007 , 513-517.
[12] Rasha Jalal Mitlif. , An Application Model for Linear Programming with an Evolutionary Ranking Function, Ibn Al-Haitham Journal for Pure and Applied Sciences , 35(3) , 2022, 146-154.
[13] K. Slevakumari , R. Tamilarasi , Ranking of octagonal fuzzy numbers for solving fuzzy linear Programming problems, Int. Journal of Engineering Research and Application , 7( 10), 2017, 62-65.
[14] Rasha Jalal Mitlif. , A New Ranking Function of Triangular Fuzzy Numbers for SolvingFuzzy Linear Programming Problems with Big –M Method, Electronics Science Technology and Application , 6(1), 2019, 10-13.
[15] Rasha Jalal Mitlif ., An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function , Baghdad Science Journal , 19(1) , 2022 ,71-76.
[16] D. Stephen Dinagar and U. Hari Narayanan , On Inverse of Hexagonal Fuzzy Number Matrices , International Journal of Pure and Applied Mathematics, 115(9) , 2017, 147-158.
[17] Priyanka A. Pathade, Kirtiwant P. Ghadle , OPTIMAL SOLUTION OF BALANCED AND UNBALANCED FUZZY TRANSPORTATION PROBLEM BY USING OCTAGONAL FUZZY NUMBERS , International Journal of Pure and Applied Mathematics , 119 (4) , 2018, 617-625.
[18] S. H. Nasseri · E. Behmanesh , Linear Programming with Triangular Fuzzy Numbers —A Case Study in a Finance and Credit Institute, Fuzzy Inf. Eng. , 3 , 2013 , 295-315.
[19] V. JEYANTHI , S. RAMYA, R. SANDHIYA, A METHOD FOR SOLVING GENERALIZED OCTAGONAL FUZZY TRANSPORTATION PROBLEM-HARMONIC MEAN METHOD , INTERNATIONAL JOURNAL OF CREATIVE RESEARCH THOUGHTS (RJCRT) , 8 (12), 2020, 2662-2667.
[20] M. S. Annie Christi, Malini. D, Solving Transportation Problems with Hexagonal Fuzzy Numbers Using Best Candidates Method and Different Ranking Techniques , Int. Journal of Engineering Research and Applications , 6,(2) , 2016, 76-81.
[21] Rasha Jalal Mitlif , Computation the Optimal Solution of Octagonal Fuzzy Numbers, Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(4) , 2020 , 71–78.
[2] S.Sandhiya , K.Selvakumari , Decision Making Problem for Medical Diagnosis Using Hexagonal Fuzzy Number Matrix , International Journal of Engineering & Technology, 7 (34) , 2018 , 660-662.
[3] M.Prabhavathi, A.Elavarasi, M.Leelavathi,K.Ajitha , SOME OPERATION ON HEXAGONAL FUZZY NUMBER, International Journal of Research and Analytical Reviews (IJRAR), 2020, 7 (1) , 2020, 469-482.
[4] A. Thiruppathi , C. K. Kirubhashankar , Novel Fuzzy Assignment Problem Using Hexagonal Fuzzy Numbers, Journal of Physics: Conference Series, International Conference on Mathematical Sciences (ICMS ) , 2020, 1-8.
[5] P. Rajarajeswari, A.Sahaya Sudha , Ordering Generalized Hexagonal Fuzzy Numbers Using Rank, Mode, Divergence and Spread, IOSR Journal of Mathematics (IOSR-JM) , 10(3) , 2014, 15-22.
[6] S. JOHNSON SAVARIMUTHU, N. KARTHIKA , AN APPLICAION OF HEXAGONAL FUZZYNUMBER AND MATRICES TO SOLVE DECISION MAKING PROBLEM, Journal of Emerging Technologies and Innovative Research (JETIR) , 2018, Volume 5(9), 705-713.
[7] A. THIRUPPATHI , C. K. KIRUBHASHANKAR , NEW RANKING OF GENERALIZED HEXAGONAL FUZZY NUMBER USING CENTROIDS OF CENTROIDED METHOD, Advances in Mathematics: Scientific Journal , 9(8) , (2020), 6229–6240.
[8] M. S. Annie Christi, Malini. D, Solving Transportation Problems with Hexagonal Fuzzy Numbers Using Best Candidates Method and Different Ranking Techniques, Int. Journal of Engineering Research and Applications , 6(2),2016, 76-81.
[9] N.Rameshan , D.Stephen Dinagar , Solving Fuzzy Critical Path with Octagonal Intuitionistic Fuzzy Number , 1st International Conference on Mathematical Techniques and Applications, AIP Conference Proceedings 2277, 090002 (2020) , 090002-1 - 090002-8.
[10] M.Venkatachalapathy, A.Jayaraja , A.Edward Samuel , A Study on Solving Octagonal Fuzzy Numbers Using Modified Vogel’s Approximation Method , International Journal of Pure and Applied Mathematics , Applied Mathematics , 118 (6) , 2018, 201-207.
[11] S. H. Nasseri, E. Ardil, A. Yazdani, and R. Zaefarian , Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences , 1(10) , 2007 , 513-517.
[12] Rasha Jalal Mitlif. , An Application Model for Linear Programming with an Evolutionary Ranking Function, Ibn Al-Haitham Journal for Pure and Applied Sciences , 35(3) , 2022, 146-154.
[13] K. Slevakumari , R. Tamilarasi , Ranking of octagonal fuzzy numbers for solving fuzzy linear Programming problems, Int. Journal of Engineering Research and Application , 7( 10), 2017, 62-65.
[14] Rasha Jalal Mitlif. , A New Ranking Function of Triangular Fuzzy Numbers for SolvingFuzzy Linear Programming Problems with Big –M Method, Electronics Science Technology and Application , 6(1), 2019, 10-13.
[15] Rasha Jalal Mitlif ., An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function , Baghdad Science Journal , 19(1) , 2022 ,71-76.
[16] D. Stephen Dinagar and U. Hari Narayanan , On Inverse of Hexagonal Fuzzy Number Matrices , International Journal of Pure and Applied Mathematics, 115(9) , 2017, 147-158.
[17] Priyanka A. Pathade, Kirtiwant P. Ghadle , OPTIMAL SOLUTION OF BALANCED AND UNBALANCED FUZZY TRANSPORTATION PROBLEM BY USING OCTAGONAL FUZZY NUMBERS , International Journal of Pure and Applied Mathematics , 119 (4) , 2018, 617-625.
[18] S. H. Nasseri · E. Behmanesh , Linear Programming with Triangular Fuzzy Numbers —A Case Study in a Finance and Credit Institute, Fuzzy Inf. Eng. , 3 , 2013 , 295-315.
[19] V. JEYANTHI , S. RAMYA, R. SANDHIYA, A METHOD FOR SOLVING GENERALIZED OCTAGONAL FUZZY TRANSPORTATION PROBLEM-HARMONIC MEAN METHOD , INTERNATIONAL JOURNAL OF CREATIVE RESEARCH THOUGHTS (RJCRT) , 8 (12), 2020, 2662-2667.
[20] M. S. Annie Christi, Malini. D, Solving Transportation Problems with Hexagonal Fuzzy Numbers Using Best Candidates Method and Different Ranking Techniques , Int. Journal of Engineering Research and Applications , 6,(2) , 2016, 76-81.
[21] Rasha Jalal Mitlif , Computation the Optimal Solution of Octagonal Fuzzy Numbers, Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(4) , 2020 , 71–78.
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Published
2022-12-31
How to Cite
Mitlif, R. J., Hasen, S. S., & Ouda, E. H. (2022). Solving Linear Programming Problems Involving Hexagonal and Octagonal Fuzzy Numbers via Two Ranking Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(4), Math Page 66–73. https://doi.org/10.29304/jqcm.2022.14.4.1117
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Math Articles
