Interval type-2 fuzzy linear programming problem with vagueness parameters
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Interval type-2 fuzzy linear programming models, which are extensions of type-2 fuzzy linear programming models, have been extensively considered and used in recent years, and numerous studies have been conducted to solve this type of problem. However, so far, not many studies have been conducted on the fuzzy linear programming problem with vagueness in the parameters with interval type-2 membership functions, and this is a necessity for conducting this research. In these types of problems, the input data are modeled using fuzzy preference-based membership functions. This study investigates interval type-2 fuzzy linear programming problems with vagueness parameters. In addition, we present the membership functions associated with each model and propose new modeling techniques. Depending on the position of vagueness in the problem, such as vagueness in the objective function vector, technological coefficients, resources vector, and any possible combination of them, various problems arise. Therefore, we introduce these types of problems, provide membership functions, and propose different solution methods. We evaluate the efficiency and performance of each of the proposed methods using an example.
Abstract
Interval type-2 fuzzy linear programming models, which are extensions of type-2 fuzzy linear programming models, have been extensively considered and used in recent years, and numerous studies have been conducted to solve this type of problem. However, so far, not many studies have been conducted on the fuzzy linear programming problem with vagueness in the parameters with interval type-2 membership functions, and this is a necessity for conducting this research. In these types of problems, the input data are modeled using fuzzy preference-based membership functions. This study investigates interval type-2 fuzzy linear programming problems with vagueness parameters. In addition, we present the membership functions associated with each model and propose new modeling techniques. Depending on the position of vagueness in the problem, such as vagueness in the objective function vector, technological coefficients, resources vector, and any possible combination of them, various problems arise. Therefore, we introduce these types of problems, provide membership functions, and propose different solution methods. We evaluate the efficiency and performance of each of the proposed methods using an example.
참고문헌 (33)
- L. A. Zadeh, "Fuzzy sets", Information and control, 8(3), pp.338~353 (1965)
- L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8(3), pp.199~249 (1975)
- L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-II", Inform. Sci, 8(4), pp.301~357 (1975)
- L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-III", Inform. Sci, 9(1), pp.43~80 (1975)
- H. Tanaka, "A value of information in FLP problems via sensitivity analysis", Fuzzy Sets and Systems, 18(2), pp.119~129 (1986)
- R. E. Bellman, "Decision-making in a fuzzy environment", Management science, 17(4), pp.141~146 (1970)
- S. Karmakar, "Type-2 intuitionistic fuzzy matrix games based on a new distance measure: Application to biogas-plant implementation problem", Applied Soft Computing, 106 (2021)[DOI]
- M. R. Seikh, "A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem", Iranian Journal of Fuzzy Systems, 18(5), pp.155~172 (2021)[DOI]
- M. El Alaoui, "Type 2 fully Fuzzy linear programming", International Journal of Fuzzy System Applications (IJFSA), 10(4), pp.37~56 (2021)
- M. Javanmard, "A solving method for fuzzy linear programming problem with interval type-2 fuzzy numbers", International Journal of Fuzzy Systems, 21, pp.882~891 (2019)
- Y. J. Lai, "Fuzzy Mathematical Programming", pp.74~186 (1992), Springer Berlin Heidelberg
- H. J. Zimmerman, "Fuzzy programming and linear programming with several objective functions", Fuzzy Sets and Systems, 1(1), pp.45~55 (1978)
- J. C. Figueroa-Garcia, "A method for solving linear programming models with interval type-2 fuzzy constraints", Pesquisa Operacional, 34, pp.73~89 (2014)
- S. Sargolzaei, "Interval type-2 fuzzy linear programming problem with vagueness in the resources vector", Journal of Mahani Mathematical Research, 13(2), pp.233~261 (2024)[DOI]
- S. Sargolzaei, "Multi-objective interval type-2 fuzzy linear programming problem with vagueness in coefficient", CAAI Trans. Intell. Technol, pp.1~20 (2024)[DOI]
- H. Mishmast Nehi, "An algorithm for multi-objective fuzzy linear programming problem with interval type-2 fuzzy numbers and ambiguity in parameters", Journal of Mathematical Modeling, 12(1), pp.177~197 (2024)
- Z. Golpayegani, "Interval type-2 fuzzy linear programming: general uncertainty model", 44th Annual Iranian Mathematics Conference, pp.85~88 (2013)
- R. R. Gasimov, "Solving fuzzy linear programming problems with linear membership function", Turkish Journal of mathematics, 26(4), pp.375~396 (2002)
- S. Chandra, "On solving fuzzy linear programming problems: A revisit to Zimmermann’s approach", Journal of Intelligent and Fuzzy Systems, 27(5), pp.2603~2610 (2014)
- B. Farhadinia, "Solving fuzzy linear programming problems with linear membership functorrevisited", Caspian Journal of Mathematical Sciences (CJMS), 3(2), pp.317~328 (2014)
- J. M. Mendel, "Fuzzy sets for words: A new beginning", The 12th IEEE International Conference on Fuzzy Systems, 2003 FUZZ’03, 1, pp.37~42 (2003), IEEE
- J. M. Mendel, "Interval type-2 fuzzy logic systems made simple", IEEE transactions on fuzzy systems, 14(6), pp.808~821 (2006)
- G. Klir, "Fuzzy sets and fuzzy logic", pp.1~12 (1995), Prentice Hall
- M. Allahdadi, "Improving the modified interval linear programming method by new techniques", Inform. Sci, 339, pp.224~236 (2016)
- H. A. Ashayerinasab, "Solving the interval linear programming problem: A new algorithm for a general case", Expert Systems with Applications, 93, pp.39~49 (2018)
- Y. R. Fan, "A robust two-step method for solving interval linear programming problems within an environmental management context", Journal of Environmental Informatics, 19(1), pp.1~9 (2012)
- X. Wang, "Violation analysis on two-step method for interval linear programming", Information Sciences, 281, pp.85~96 (2014)
- F. Zhou, "Enhanced-interval linear programming", European journal of operational research, 199(2), pp.323~333 (2009)
- T. Shaocheng, "Interval number and fuzzy number linear programmings", Fuzzy Sets and Systems, 66(3), pp.301~306 (1994)
- H. Mishmast Nehi, "Interval type-2 fuzzy linear programming", 7th International Conference on Iranian Operations Research (2014)
- M. R. Seikh, "Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem", International Journal of Intelligent Systems, 36(10), pp.6066~6100 (2021)
- M. R. Seikh, "Solution of interval-valued matrix games using intuitionistic fuzzy optimisation technique: an effective approach", International Journal of Mathematics in Operational Research, 20(3), pp.297~322 (2021)
- M. R. Seikh, "Solution of matrix games with pay-offs of single-valued trapezoidal neutrosophic numbers", Soft Computing, 26(3), pp.921~936 (2022)