International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 10, Issue 4 (April 2023), Pages: 44-52

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 Original Research Paper

 Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

 Author(s): 

 Mohamed Solomon 1, *, Hegazy Mohamed Zaher 2, Naglaa Ragaa Saied 2

 Affiliation(s):

 1Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
 2Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0001-8555-865X

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2023.04.006

 Abstract:

An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development of the proposed algorithm is based on the principle of optimal decision set achieved by the intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Additionally, as the intuitionistic fuzzy optimization method utilizes the degree of belonging and degree of non-belonging, we used the linear membership function for belonging and non-belonging to see its impact on optimization and to get insight into such an optimization process. The proposed approaches have been illustrated with numerical examples.

 © 2023 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Parametric functions, Multi-objective linear programming, Intuitionistic fuzzy optimization, Intuitionistic fuzzy set, Multi-objective linear fractional programming

 Article History: Received 9 August 2022, Received in revised form 16 December 2022, Accepted 4 January 2023

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Solomon M, Zaher HM, and Saied NR (2023). Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems. International Journal of Advanced and Applied Sciences, 10(4): 44-52

 Permanent Link to this page

 Figures

 Fig. 1 

 Tables

 Table 1 Table 2

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 References (48)

  1. Almogy Y and Levin O (1971). A class of fractional programming problems. Operations Research, 19(1): 57-67. https://doi.org/10.1287/opre.19.1.57   [Google Scholar]
  2. Angelov PP (1997). Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems, 86(3): 299-306. https://doi.org/10.1016/S0165-0114(96)00009-7   [Google Scholar]
  3. Arévalo MT, Mármol AM, and Zapata A (1997). The tolerance approach in multiobjective linear fractional programming. Top, 5(2): 241-252. https://doi.org/10.1007/BF02568552   [Google Scholar]
  4. Atanassov KT (1999). Interval valued intuitionistic fuzzy sets. In: Atanassov KT (Ed.), Intuitionistic fuzzy sets: 139-177. Physica, Heidelberg, Germany. https://doi.org/10.1007/978-3-7908-1870-3   [Google Scholar]
  5. Atanassov KT (2016). Intuitionistic fuzzy sets. International Journal Bioautomation, 20: 1-6. https://doi.org/10.1016/S0165-0114(86)80034-3   [Google Scholar]
  6. Bellman RE and Zadeh LA (1970). Decision-making in a fuzzy environment. Management Science, 17(4): B-141-B-164. https://doi.org/10.1287/mnsc.17.4.B141   [Google Scholar]
  7. Borza M, Rambely AS, and Saraj M (2013). Parametric approach for linear fractional programming with interval coefficients in the objective function. In the AIP Conference Proceedings, American Institute of Physics, 1522(1): 643-647. https://doi.org/10.1063/1.4801185   [Google Scholar]
  8. Calvete HI and Galé C (1999). The bilevel linear/linear fractional programming problem. European Journal of Operational Research, 114(1): 188-197. https://doi.org/10.1016/S0377-2217(98)00078-2   [Google Scholar]
  9. Charnes A and Cooper WW (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3‐4): 181-186. https://doi.org/10.1002/nav.3800090303   [Google Scholar]
  10. Costa JP (2007). Computing non-dominated solutions in MOLFP. European Journal of Operational Research, 181(3): 1464-1475. https://doi.org/10.1016/j.ejor.2005.11.051   [Google Scholar]
  11. Dinkelbach W (1967). On nonlinear fractional programming. Management Science, 13(7): 492-498. https://doi.org/10.1287/mnsc.13.7.492   [Google Scholar]
  12. Dubey D and Mehra A (2011). Linear programming with triangular intuitionistic fuzzy number. In the 7th Conference of the European Society for Fuzzy Logic and Technology, Atlantis Press, Aix-les-Bains, France: 563-569. https://doi.org/10.2991/eusflat.2011.78   [Google Scholar]
  13. Dubey D, Chandra S, and Mehra A (2012). Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems, 188(1): 68-87. https://doi.org/10.1016/j.fss.2011.09.008   [Google Scholar]
  14. Ehrgott M (2005). Multicriteria optimization. Springer Science and Business Media, Auckland, New Zealand.   [Google Scholar]
  15. Gupta P and Bhatia D (2001). Sensitivity analysis in fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems, 122(2): 229-236. https://doi.org/10.1016/S0165-0114(99)00164-5   [Google Scholar]
  16. Güzel N (2013). A proposal to the solution of multiobjective linear fractional programming problem. Abstract and Applied Analysis, 2013: 435030. https://doi.org/10.1155/2013/435030   [Google Scholar]
  17. Jagannathan R (1966). On some properties of programming problems in parametric form pertaining to fractional programming. Management Science, 12(7): 609-615. https://doi.org/10.1287/mnsc.12.7.609   [Google Scholar]
  18. Jana B and Roy TK (2007). Multi-Objective intuitionistic fuzzy linear programming and its application in transportation model. Notes on Intuitionistic Fuzzy Sets, 13(1): 34-51.   [Google Scholar]
  19. Jo CL and Lee GM (1998). Optimality and duality for multiobjective fractional programming Involvingn-Set functions. Journal of Mathematical Analysis and Applications, 224(1): 1-13. https://doi.org/10.1006/jmaa.1998.5974   [Google Scholar]
  20. Lai YJ and Hwang CL (1994). Fuzzy multiple objective decision making. In: Lai YJ and Hwang CL (Eds.), Fuzzy multiple objective decision making: 139-262. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-642-57949-3   [Google Scholar]
  21. Leber M, Kaderali L, Schönhuth A, and Schrader R (2005). A fractional programming approach to efficient DNA melting temperature calculation. Bioinformatics, 21(10): 2375-2382. https://doi.org/10.1093/bioinformatics/bti379   [Google Scholar] PMid:15769839
  22. Liu JC and Yokoyama K (1999). ε-optimality and duality for multiobjective fractional programming. Computers and Mathematics with Applications, 37(8): 119-128. https://doi.org/10.1016/S0898-1221(99)00105-4   [Google Scholar]
  23. Luhandjula MK (1989). Fuzzy optimization: An appraisal. Fuzzy Sets and Systems, 30(3): 257-282. https://doi.org/10.1016/0165-0114(89)90019-5   [Google Scholar]
  24. Luo Y and Yu C (2008). A fuzzy optimization method for multi-criteria decision making problem based on the inclusion degrees of intuitionistic fuzzy sets. Journal of Information and Computing Science, 3(2): 146-152.   [Google Scholar]
  25. Mahapatra GS, Mitra M, and Roy TK (2010). Intuitionistic fuzzy multi-objective mathematical programming on reliability optimization model. International Journal of Fuzzy Systems, 12(3): 259-266.   [Google Scholar]
  26. Martos B (1964). Hyperbolic programming. Naval Research Logistics Quarterly, 11(2): 135-155. https://doi.org/10.21236/AD0622077   [Google Scholar]
  27. Miettinen K (2012). Nonlinear multiobjective optimization. Springer Science and Business Media, Stanford, USA.   [Google Scholar]
  28. Mohan C and Nguyen HT (2001). An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems. Fuzzy Sets and Systems, 117(1): 61-79. https://doi.org/10.1016/S0165-0114(98)00269-3   [Google Scholar]
  29. Nachammai AL and Thangaraj P (2012). Solving intuitionistic fuzzy linear programming problem by using similarity measures. European Journal of Scientific Research, 72(2): 204-210.   [Google Scholar]
  30. Nagoorgani A and Ponnalagu K (2012). A new approach on solving intuitionistic fuzzy linear programming problem. Applied Mathematical Sciences, 6(70): 3467-3474.   [Google Scholar]
  31. Nayak S and Ojha AK (2019). Solution approach to multi-objective linear fractional programming problem using parametric functions. Opsearch, 56: 174-190. https://doi.org/10.1007/s12597-018-00351-2   [Google Scholar]
  32. Patel R (2005). Mixed-type duality for multiobjective fractional variational control problems. International Journal of Mathematics and Mathematical Sciences, 2005: 849539. https://doi.org/10.1155/IJMMS.2005.109   [Google Scholar]
  33. Saad OM (2005). An iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems. Applied Mathematics and Computation, 170(1): 216-225. https://doi.org/10.1016/j.amc.2004.11.026   [Google Scholar]
  34. Sahinidis NV (2004). Optimization under uncertainty: State-of-the-art and opportunities. Computers and Chemical Engineering, 28(6-7): 971-983. https://doi.org/10.1016/j.compchemeng.2003.09.017   [Google Scholar]
  35. Sakawa M and Nishizaki I (2001). Interactive fuzzy programming for two-level linear fractional programming problems. Fuzzy Sets and Systems, 119(1): 31-40. https://doi.org/10.1016/S0165-0114(99)00066-4   [Google Scholar]
  36. Sakawa M and Yano H (1989). An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, 30(3): 221-238. https://doi.org/10.1016/0165-0114(89)90017-1   [Google Scholar]
  37. Sakawa M, Nishizaki I, and Uemura Y (2000). Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Fuzzy Sets and Systems, 115(1): 93-103. https://doi.org/10.1016/S0165-0114(99)00027-5   [Google Scholar]
  38. Sharma MK, Dhiman N, Mishra VN, Mishra LN, Dhaka A, and Koundal D (2022). Post-symptomatic detection of COVID-2019 grade based mediative fuzzy projection. Computers and Electrical Engineering, 101: 108028. https://doi.org/10.1016/j.compeleceng.2022.108028   [Google Scholar] PMid:35498557 PMCid:PMC9042789
  39. Stancu-Minasian IM and Pop B (2003). On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy Sets and Systems, 134(3): 397-405. https://doi.org/10.1016/S0165-0114(02)00142-2   [Google Scholar]
  40. Tanaka H and Asai K (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets and Systems, 13(1): 1-10. https://doi.org/10.1016/0165-0114(84)90022-8   [Google Scholar]
  41. Tigan S and Stancu-Minasian IM (2000). On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program. Mathematica Bohemica, 125(2): 227-234. https://doi.org/10.21136/MB.2000.125953   [Google Scholar]
  42. Valipour E, Yaghoobi MA, and Mashinchi M (2014). An iterative approach to solve multiobjective linear fractional programming problems. Applied Mathematical Modelling, 38(1): 38-49. https://doi.org/10.1016/j.apm.2013.05.046   [Google Scholar]
  43. Wolf H (1986). Solving special nonlinear fractional programming problems via parametric linear programming. European Journal of Operational Research, 23(3): 396-400. https://doi.org/10.1016/0377-2217(86)90305-X   [Google Scholar]
  44. Yadav SR and Mukherjee RN (1990). Duality for fractional minimax programming problems. The ANZIAM Journal, 31(4): 484-492. https://doi.org/10.1017/S0334270000006809   [Google Scholar]
  45. Zadeh LA (1965). Fuzzy sets. Information and Control, 8(3): 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X   [Google Scholar]
  46. Zhong Z and You F (2014). Parametric solution algorithms for large-scale mixed-integer fractional programming problems and applications in process systems engineering. Computer Aided Chemical Engineering, 33: 259-264. https://doi.org/10.1016/B978-0-444-63456-6.50044-2   [Google Scholar]
  47. Zimmermann HJ (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1): 45-55. https://doi.org/10.1016/0165-0114(78)90031-3   [Google Scholar]
  48. Zimmermann HJ (1983). Fuzzy mathematical programming. Computers and Operations Research, 10(4): 291-298. https://doi.org/10.1016/0305-0548(83)90004-7   [Google Scholar]