نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده علوم ریاضی، دانشگاه مازندران، بابلسر، ایران.

2 دانشکده علوم ریاضی، دانشگاه صنعتی شاهرود، ایران، شاهرود.

10.22105/dmor.2021.255385.1247

چکیده

دراین مقاله با یک مساله برنامه‌ریزی خطی با اعداد فازی شهودی ذوزنقه‌ای نامتقارن سرو کار داریم. در سال‌های اخیر، نویسندگانزیادی به مطالعه بر روی اعداد فازی شهودی ذوزنقه‌ای متقارن پرداختند. آن‌ها بعد از تعریفیک تابع رتبه‌بندی و عملیات حساب بر روی این اعداد، به حل مساله برنامه‌ریزی خطی فازی شهودی پرداختند. اما مشکل اصلی روش آنها این بود که تنها برای اعداد فازی شهودی ذوزنقه‌ای متقارن برقرار بود. حال به منظور رفع این مشکل، ما در این مقاله به ارائه یک حساب جدید و همچنینیک ترتیب جدید برای اعداد فازی شهودی ذوزنقه‌ای نامتقارن می‌پردازیم. در ادامه ما مدل کلی مسائل برنامه‌ریزی خطی با اعداد فازی شهودی ذوزنقه‌ای نامتقارن را ارائه کرده و به اثبات تعدادی از قضایای مهم برای حل آن می‌پردازیم. سپس به ارائه الگوریتم سیمپلکس فازی شهودی پرداخته و در انتها با ارائه دو مثال، کاربرد این رویکرد جدید را نشان داده و برتری آن را نسبت به حالت فازی نشان خواهیم داد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Proposing a new approach for solving intuitionistic fuzzy linear programming problem with non-symmetric parameters

نویسندگان [English]

  • Morteza Goli 1
  • Hadi Nasseri 1
  • Mehrdad Ghaznavi 2

1 Faculty of Mathematical Sciences, Mazandaran University, Babolsar, Iran.

2 Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood. Iran.

چکیده [English]

In this paper, we deal with a linear programming problem with non-symmetric trapezoidal intuitionistic fuzzy numbers. In recent years, many authors have studied the symmetric trapezoidal intuitionistic fuzzy numbers. After defining a ranking function and arithmetic operations on these numbers, they solved the intuitionistic fuzzy linear programming problem.But the main problem with their method was that only available for symmetric trapezoidal intuitionistic fuzzy numbers. Now in order to overcome this limitation, in this paper, we present a new arithmetic and a new ordering for non-symmetric trapezoidal intuitionistic fuzzy numbers. Then, we present the general model of an intuitionistic fuzzy linear programming problems and prove a number of important theorems for solving it. Then we present the intuitionistic fuzzy simplex algorithm and finally, by presenting two examples, we will show the application of this new approach and show its superiority over the fuzzy mode.

کلیدواژه‌ها [English]

  • Fuzzy linear programming
  • Intuitionistic fuzzy arithmetic
  • Trapezoidal intuitionistic fuzzy number
  • Intuitionistic fuzzy linear programming
Angelov, P. P. (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
 Atalik, G., & Senturk, S. (2019). A new lexicographic ranking method for triangular intuitionistic fuzzy number based on Gergonne point. Journal of quantitative sciences, 1, 59-73.
Atanassov, K. A. (1999).  Intuitionistic fuzzy sets: theory and applications. Physica-Verlag.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141. https://doi.org/10.1287/mnsc.17.4.B141
Bharati, S. K., & Singh, S. R. (2015). A note on solving a fully intuitionistic fuzzy linear programming problem based on sign distance. International journal of computer applications, 119(23), 30-35.
Suresh, M., Vengataasalam, S., & Arun Prakash, K. (2014). Solving intuitionistic fuzzy linear programming problems by ranking function. Journal of intelligent & fuzzy systems, 27(6), 3081-3087.
Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied intelligence, 46(3), 509-519. https://doi.org/10.1007/s10489-016-0779-x
Dubey, D., & Mehra, A. (2011). Linear programming with triangular intuitionistic fuzzy number. Proceedings of the 7th conference of the european society for fuzzy logic and technology (pp. 563-569). Atlantis Press. https://doi.org/10.2991/eusflat.2011.78
Ejegwa, P. A., Akowe, S. O., Otene, P. M., & Ikyule, J. M. (2014). An overview on intuitionistic fuzzy sets. International journal of scientific and technology research, 3(3), 142-145.
Ganesan, K., & Veeramani, P. (2006). Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of operations research, 143(1), 305-315. https://doi.org/10.1007/s10479-006-7390-1
Ghaznavi, M., Soleimani, F., & Hoseinpoor, N. (2016). Parametric analysis in fuzzy number linear programming problems. International journal of fuzzy systems, 18(3), 463-477. https://doi.org/10.1007/s40815-015-0123-3
Hepzibah, R. I., & Vidhya, R. (2015). Modified new operations for symmetric trapezoidal intuitionistic fuzzy numbers: an application of diet problem. Int j fuzzy math arch, 9(1), 35-43.
Hosseinzadeh, A., & Edalatpanah, S. A. (2016). A new approach for solving fully fuzzy linear programming by using the lexicography method. Advances in fuzzy systems, 16, 42-61. https://doi.org/10.1155/2016/1538496
Jayalakshmi, M., Anuradha, D., Sujatha, V., & Deepa, G. (2019, December). A simple mathematical approach to solve intuitionistic fuzzy linear programming problems. AIP conference proceedings (Vol. 2177, No. 1, p. 020025). AIP Publishing LLC. https://doi.org/10.1063/1.5135200
Kabiraj, A., Nayak, P. K., & Raha, S. (2019). Solving intuitionistic fuzzy linear programming problem. International journal of intelligence science, 9(1), 44-58. DOI: 10.4236/ijis.2019.91003 
Kar, R., & Shaw, A. K. (2019). Some arithmetic operations on triangular intuitionistic fuzzy number and its application in solving linear programming problem by simplex algorithm. International journal of bioinformatics and biological sciences, 7(1/2), 21-28. DOI: 10.30954/2319-5169.01.2019.4
Mahdavi-Amiri, N., & Nasseri, S. H. (2007). Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy sets and systems, 158(17), 1961-1978. https://doi.org/10.1016/j.fss.2007.05.005
Mahdavi, A. N., Naseri, S., & Yazdani, A. (2009). Fuzzy primal simplex algorithms for solving fuzzy linear programming problems. Iranian journal of operational research, 1(2), 68–84.
Nagoorgani, A., & Ponnalagu, K. (2012). A new approach on solving intuitionistic fuzzy linear programming problem. Applied mathematical sciences, 6(70), 3467-3474.
Najafi, H. S., & Edalatpanah, S. A. (2013). A note on “a new method for solving fully fuzzy linear programming problems”. Applied mathematical modelling, 37(14-15), 7865-7867. https://doi.org/10.1016/j.apm.2013.02.039
Najafi, H. S., Edalatpanah, S. A., & Dutta, H. (2016). A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alexandria engineering journal, 55(3), 2589-2595. https://doi.org/10.1016/j.aej.2016.04.039
Nasseri, S. H., & Bavandi, S. (2018). Amelioration of Verdegay̕s approach for fuzzy linear programs with stochastic parameters. Iranian journal of management studies, 11(1), 71-89.
Nasseri, S. H., & Ebrahimnejad, A. (2010). A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems. European journal of industrial engineering, 4(3), 372-389. https://doi.org/10.1504/EJIE.2010.033336
Nasseri, S. H., Ebrahimnejad, A., & Cao, B. Y. (2019). Fuzzy linear programming. In fuzzy linear programming: solution techniques and applications (pp. 39-61). Cham: Springer. https://doi.org/10.1007/978-3-030-17421-7_2
Nasseri, S. H., Goli, M., & Bavandi, S. (2018). An approach for solving linear programming problem with intuitionistic fuzzy objective coefficient. Fuzzy systems and applications. (In Persian). http://jfsa.fuzzy.ir/article_86076.html
Noori Skandari, M. N., & Ghaznavi, M. (2018). An efficient algorithm for solving fuzzy linear programming problems. Neural process lett, 1563-1582. https://doi.org/10.1007/s11063-018-9785-9
Parvathi, R., & Malathi, C. (2012). Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers. International journal of soft computing and engineering, 2(2), 268-273.
Parvathi, R., & Malathi, C. (2012). Intuitionistic fuzzy simplex method. International journal of computer applications, 48(6), 39-48.
Prabakaran, K., & Ganesan, K. (2017). Duality theory for intuitionistic fuzzy linear programming problems. International journal of civil engineering and technology (IJCIET), 8(11), 546-560.
Ramík, J., & Vlach, M. (2016). Intuitionistic fuzzy linear programming and duality: a level sets approach. Fuzzy optimization and decision making, 15(4), 457-489. https://doi.org/10.1007/s10700-016-9233-0
Shamooshaki, M. M., Hosseinzadeh, A., & Edalatpanah, S. A. (2015). A new method for solving fully fuzzy linear programming problems by using the lexicography method. Applied and computational mathematics, 1, 53-55.
Sidhu. S. K. (2015). A new approach to solve intuitionistic fuzzy linear programming problem with symmetric trapezoidal intuitionistic fuzzy numbers. Mathematical theory and modeling, 5(5), 66-74.
Sidhu, S. K., & Kumar, A. (2019). Mehar methods to solve intuitionistic fuzzy linear programming problems with trapezoidal intuitionistic fuzzy numbers. In Performance prediction and analytics of fuzzy, reliability and queuing models (pp. 265-282). Singapore: Springer. https://doi.org/10.1007/978-981-13-0857-4_20
Singh, V., & Yadav, S. P. (2017). Development and optimization of unrestricted LR-type intuitionistic fuzzy mathematical programming problems. Expert systems with applications, 80, 147-161. https://doi.org/10.1016/j.eswa.2017.03.015
Tanaka, H., & 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
Zadeh, L. A. (1965). Fuzzy sets. Information and control8, 338-353.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1, 45-55. https://doi.org/10.1016/0165-0114(78)90031-3