The multiple attribute group decision-making problems with interval-valued intuitionistic fuzzy numbers: A linear programming approach
محورهای موضوعی : Fuzzy sets theory
Maryam Arshi
1
,
Abdollah Hadi-Vencheh
2
,
Adel Aazami
3
,
Tara Hamlehvar
4
1 - Department of mathematics, Islamic Azad University,Najafabad Branch,
2 - Department of Mathematics,Islamic Azad University, Khorasgan Branch, Isfahan, Iran
3 - Department of Global Business and Trade, Institute for Transport and Logistics Management, Vienna University of Economics and Business, Vienna, Austria
4 - Department of Industrial & System Engineering, Auburn University, Alabama State, United States
کلید واژه: Interval-valued intuitionistic fuzzy sets, Multiple attribute group decision-making, Linear programming, Aggregation operator, Variable transformation,
چکیده مقاله :
The objective of this manuscript is to introduce an innovative methodology for addressing multiple attribute group decision-making (MAGDM) problems utilizing interval-valued intuitionistic fuzzy sets (IVIFS). The proposed approach solves the problem using a mathematical programming methodology. In the present investigation, a group decision-making problem characterized by IVIF multiple attributes is conceptualized as a linear programming model and resolved expeditiously. The models that are being proposed have been reformulated into two analogous linear programming (LP) models through the application of a variable transformation and the concept of aggregation operators. The obtained LP models are solvable by common approaches. The principal benefit of the suggested methodology is its facilitation of decision-makers (DM) in identifying an alternative that exhibits optimal performance, and the decision-making process does not rely on DM knowledge. Application of the proposed method is represented in a decision-making problem, and the results are compared with similar methods, proving the compatibility of the proposed method with previous ones. The solid and understandable logic with computational easiness are the main advantages of the proposed method.
The objective of this manuscript is to introduce an innovative methodology for addressing multiple attribute group decision-making (MAGDM) problems utilizing interval-valued intuitionistic fuzzy sets (IVIFS). The proposed approach solves the problem using a mathematical programming methodology. In the present investigation, a group decision-making problem characterized by IVIF multiple attributes is conceptualized as a linear programming model and resolved expeditiously. The models that are being proposed have been reformulated into two analogous linear programming (LP) models through the application of a variable transformation and the concept of aggregation operators. The obtained LP models are solvable by common approaches. The principal benefit of the suggested methodology is its facilitation of decision-makers (DM) in identifying an alternative that exhibits optimal performance, and the decision-making process does not rely on DM knowledge. Application of the proposed method is represented in a decision-making problem, and the results are compared with similar methods, proving the compatibility of the proposed method with previous ones. The solid and understandable logic with computational easiness are the main advantages of the proposed method.
Abdollahi, A., & Pour-Moallem, N. (2020). Dynamic negawatt demand response resource modeling and prioritizing in power markets. Scientia Iranica, 27(3), 1361–1372.
Abootalebi, S., Hadi-Vencheh, A., & Jamshidi, A. (2018). An improvement to determining expert weights in group multiple attribute decision making problem. Group Decision and Negotiation, 27, 215–221.
Ali Khan, M. S., Abdullah, S., & Ali, A. (2019). Multiattribute group decision making based on Pythagorean fuzzy Einstein prioritized aggregation operators. International Journal of Intelligent Systems, 34(5), 1001–1033.
Arshi, M., Hadi-Vencheh, A., Aazami, A., & Jamshidi, A. (2024). A Nonlinear Model to Solve Multiple Attribute Decision-Making Problems with Interval-Valued Neutrosophic Numbers. International Journal of Industrial Engineering, 35(4), 1–15.
Arshi, M., Hadi-Vencheh, A., Nazari, M., & Jamshidi, A. (2023). A NON-LINEAR PROGRAMMING MODEL TO SOLVE MADM PROBLEMS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY NUMBERS. International Journal of Industrial Engineering, 30(3).
Atanassov, K. (2016). Intuitionistic fuzzy sets. International Journal Bioautomation, 20, 1.
Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349. https://doi.org/https://doi.org/10.1016/0165-0114(89)90205-4
Azam, M., Ali Khan, M. S., & Yang, S. (2022). A Decision Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment. Journal of Mathematics, 2022(1), 9704466.
Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73–79.
Chen, S.-M., Lee, L.-W., Liu, H.-C., & Yang, S.-W. (2012). Multiattribute decision making based on interval-valued intuitionistic fuzzy values. Expert Systems with Applications, 39(12), 10343–10351.
Chen, Z., Chen, Q., Chen, W., & Wang, Y. (2004). Grey linear programming. Kybernetes, 33(2), 238–246.
Climaco, J. (2012). Multicriteria Analysis: Proceedings of the XIth International Conference on MCDM, 1-6 August 1994, Coimbra, Portugal. Springer Science & Business Media.
Dang, S. L. Y., & Forrest, J. (2009). On positioned solution of linear programming with grey parameters. 2009 IEEE International Conference on Systems, Man and Cybernetics, 751–756.
Elsayed, A. (2024). Multi-Criteria Decision-Making Framework for Evaluating Green Fuels Alternatives: A Hybrid MEREC-TODIM Approach. Neutrosophic Optimization and Intelligent Systems, 3, 41–56. https://doi.org/10.61356/j.nois.2024.3323
Garg, H., & Arora, R. (2018). A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information. Applied Intelligence, 48, 2031–2046.
Garg, H., & Kumar, K. (2020). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artificial Intelligence Review, 53, 595–624.
Gau, W.-L., & Buehrer, D. J. (1993). Vague sets. IEEE Transactions on Systems, Man, and Cybernetics, 23(2), 610–614.
Grattan Guinness, I. (1976). Fuzzy membership mapped onto intervals and many valued quantities. Mathematical Logic Quarterly, 22(1), 149–160.
Hajek, P., & Froelich, W. (2019). Integrating TOPSIS with interval-valued intuitionistic fuzzy cognitive maps for effective group decision making. Information Sciences, 485, 394–412.
Hajiagha, S. H. R., Mahdiraji, H. A., Hashemi, S. S., & Zavadskas, E. K. (2015). Evolving a linear programming technique for MAGDM problems with interval valued intuitionistic fuzzy information. Expert Systems with Applications, 42(23), 9318–9325.
Isen, E., & Boran, S. (2018). A novel approach based on combining ANFIS, genetic algorithm and fuzzy c-means methods for multiple criteria inventory classification. Arabian Journal for Science and Engineering, 43, 3229–3239.
Ishibuchi, H., & Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48(2), 219–225.
Ishizaka, A., & Siraj, S. (2018). Are multi-criteria decision-making tools useful? An experimental comparative study of three methods. European Journal of Operational Research, 264(2), 462–471.
Jimenez, M., Arenas, M., Bilbao, A., & Rodr, M. V. (2007). Linear programming with fuzzy parameters: an interactive method resolution. European Journal of Operational Research, 177(3), 1599–1609.
Jin, F., Pei, L., Chen, H., & Zhou, L. (2014). Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making. Knowledge-Based Systems, 59, 132–141.
Kaur, J., & Kumar, A. (2013). A new method to find the unique fuzzy optimal value of fuzzy linear programming problems. Journal of Optimization Theory and Applications, 156, 529–534.
Khan, M. S. A., Khan, A. S., Khan, I. A., Mashwani, W. K., & Hussain, F. (2021). Linguistic interval-valued q-rung orthopair fuzzy TOPSIS method for decision making problem with incomplete weight. Journal of Intelligent & Fuzzy Systems, 40(3), 4223–4235.
Khan, M. S. A., Khan, F., Lemley, J., Abdullah, S., & Hussain, F. (2020). Extended topsis method based on Pythagorean cubic fuzzy multi-criteria decision making with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 38(2), 2285–2296.
Li, D.-F. (2011). Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Applied Soft Computing, 11(4), 3402–3418.
Madansky, A. (1960). Inequalities for stochastic linear programming problems. Management Science, 6(2), 197–204.
Meng, F. Y., & Tan, C. Q. (2017). Distance measures for intuitionistic hesitant fuzzy linguistic sets. Econ Comput Econ Cyber Stud Res, 51(4), 207–224.
Mohammadghasemi, A., Hadi-Vencheh, A., Hosseinzadeh Lotfi, F., & Khalilzadeh, M. (2019). Group multiple criteria ABC inventory classification using the TOPSIS approach extended by Gaussian interval type-2 fuzzy sets and optimization programs. Scientia Iranica, 26(5), 2988–3006.
Pamu ar, D., Stevi, Z., & Zavadskas, E. K. (2018). Integration of interval rough AHP and interval rough MABAC methods for evaluating university web pages. Applied Soft Computing, 67, 141–163.
Park, J. H., Cho, H. J., & Kwun, Y. C. (2011). Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optimization and Decision Making, 10, 233–253.
Park, J. H., Park, I. Y., Kwun, Y. C., & Tan, X. (2011). Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Applied Mathematical Modelling, 35(5), 2544–2556.
Perez-Canedo, B., & Verdegay, J. L. (2023). On the application of a lexicographic method to fuzzy linear programming problems. Journal of Computational and Cognitive Engineering, 2(1), 47–56.
Ponstein, J. P. (2004). Approaches to the Theory of Optimization (Issue 77). Cambridge University Press.
Ramanathan, R. (2006). ABC inventory classification with multiple-criteria using weighted linear optimization. Computers & Operations Research, 33(3), 695–700.
Sadabadi, S. A., Hadi-Vencheh, A., Jamshidi, A., & Jalali, M. (2021). A linear programming technique to solve fuzzy multiple criteria decision making problems with an application. RAIRO-Operations Research, 55(1), 83–97.
Saffarzadeh, S., Hadi-Vencheh, A., & Jamshidi, A. (2020). Weight determination and ranking priority in interval group MCDM. Scientia Iranica, 27(6), 3242–3252.
Simon, H. A. (1977). The logic of heuristic decision making. In Models of discovery: And other topics in the methods of science (pp. 154–175). Springer.
Tan, C. (2011). A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Systems with Applications, 38(4), 3023–3033.
Tang, J., & Meng, F. (2018). An approach to interval-valued intuitionistic fuzzy decision making based on induced generalized symmetrical Choquet Shapley operator. Scientia Iranica, 25(3), 1456–1470.
Vincke, P. (1992). Multicriteria decision-aid. John Wiley & Sons.
Wan, S., & Dong, J. (2020). Decision making theories and methods based on interval-valued intuitionistic fuzzy sets. Springer Nature.
Wan, S., Dong, J., Wan, S., & Dong, J. (2020). A new method for Atanassov’s interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information. Decision Making Theories and Methods Based on Interval-Valued Intuitionistic Fuzzy Sets, 37–69.
Wang, Z.-J., & Li, K. W. (2012). An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives. Expert Systems with Applications, 39(18), 13509–13516.
Xu, Z. (2007). Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision, 22(2), 215–219.
Ye, F. (2010). An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Systems with Applications, 37(10), 7050–7055.
Yovits, M. C. (1988). Advances in computers. Academic Press.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control.
Zhao, H., Xu, Z., Ni, M., & Liu, S. (2010). Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 25(1), 1–30.
Zimmermann, H.-J. (1987). Fuzzy sets, decision making, and expert systems (Vol. 10). Springer Science & Business Media.
