Document Type : Research Paper


1 Department of Industrial Engineering, Payame Noor University, Tehran, Iran.

2 Department of Statistics, Payame Noor University, Tehran, Iran.


Recently, fuzzy linguistic variables have gained a great deal of attention from researchers in many decision-making problems. In this problems, type-2 fuzzy sets have been used to better cover linguistic data uncertainty. However, many of research works in this regard have been performed in type-2 fuzzy domain and in static mode. Since the decision-making problems in the real world usually fluctuate over time, so it need to use decision-making models in multi-period of time. In the present research, a Multi-Period (Dynamic) Multi-Attribute Group Decision-Making (MPMADM) method is presented based on type-2 fuzzy sets where decision-making attributes are first expressed in linguistic terms and then incorporated, as interval type-2 fuzzy numbers, into problem-solving where a new integrating operator called Multi-Period Trapezoidal Interval Type-2 Fuzzy Number Weighted Arithmetic averaging (MPTIT2FNWA) is defined on type-2 interval fuzzy numbers to integrate decision-making information in multiple periods of time. Once finished with explaining the proposed method, a numerical example is given to evaluate the proposed method in terms of effectiveness and applicability, with the results compared to those of other methods.


Main Subjects

  • Xu, Z. S. (2008). On multi-period, multi-attribute decision making. Knowledge based systems, 21(2), 164–171.
  • Lin, Y. H., Lee, P. C., & Ting, H. I. (2008). Dynamic multi-attribute decision making model with grey number evaluations. Expert systems with applications, 35(4), 1638–1644.
  • Xu, Z. S., & Yager, R. R. (2008). Dynamic intuitionistic fuzzy multi-attribute decision making. International journal of approximate reasoning, 48, 246–262.
  • Yong, H. L., Pin, C. L., & Hsin, I. T. (2008). Dynamic multi-attribute decision making model with grey number evaluations. Expert systems with applications, 35, 1638–1644.
  • Chen, Y., & Li, B. (2011). Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers. Scientica Iranica, 18, 268-274.
  • Zhu, J., & Hipel, K. W. (2012). Multiple stages grey target decision making method with incomplete. Information science, 212, 15–32.
  • Hu, J., & Yang, L. (2011). Dynamic stochastic multi-criteria decision-making method based on cumulative prospect theory and set pair analysis. Systems engineering procedia, 1, 432–439.
  • Sadeghian, R., & Forootan, S. (2012). Application of multiple attribute, multiple period models using regressions models, International journal of industrial engineering and production management, 2(23), 140-148.
  • Park, J. H., Cho, J. H., & Kwun, Y. C. (2013). Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making. Computers and mathematics with applications, 14, 71-744.
  • Liu, L., Qing, W., Zhilan, Z., & Zuolei, W. (2013). The multi-attribute decision making dynamic model with extensible interval number. International journal of nonlinear science, 15(2), 134-138.
  • Li, G., Kou, G., & Peng, Y. (2015). Dynamic fuzzy multiple criteria decision making for performance evaluation. Technological and economic development of economy21(5), 705-719.
  • Bai, R., Li, F., & Yang, J. (2014, May). A dynamic fuzzy multi-attribute group decision making method for supplier evaluation and selection. The 26th Chinese control and decision conference (2014 CCDC)(pp. 3249-3256). IEEE.
  • Bera, A. K., Jana, D. K., Banerjee, D., & Nandy, T. (2021). A two-phase multi-criteria fuzzy group decision making approach for supplier evaluation and order allocation considering multi-objective, multi-product and multi-period. Annals of data science, 8, 577-601.
  • Li, G., Kou, G., Li, Y., & Peng, Y. (2020). A group decision making approach for supplier selection with multi-period fuzzy information and opinion interaction among decision makers. Journal of the operational research society, 1-14.
  • Fei, L., & Feng, Y. (2021). A dynamic framework of multi-attribute decision making under Pythagorean fuzzy environment by using Dempster–Shafer theory. Engineering applications of artificial intelligence, 101, 104213.
  • Xu, Z. S. (2010). An integrated model-based interactive approach to FMAGDM with incomplete preference information. Fuzzy optimization and decision making, 9(3), 333–357.
  • Qin, J., & Liu, X. (2015). Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment. Information sciences297, 293-315.
  • Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences8(3), 199-249.
  • Turksen, I. B. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy sets and systems20(2), 191-210.
  • Mendel, J. M. (2007). Computing with words and its relationships with fuzzistics. Information sciences177(4), 988-1006.
  • Mendel, J. M., & Wu, H. (2006). Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: part 1, forward problems. IEEE transactions on fuzzy systems14(6), 781-792.
  • Mendel, J. M., John, R. I., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE transactions on fuzzy systems14(6), 808-821.
  • Lazar Farokhi, A. (2019). Application of fuzzy AHP and TOPSIS methods for risk evaluation of gas transmission facility. International journal of research in industrial engineering, 8(4), 339-365.
  • Ghasempoor Anaraki, M., Dmitriy, S. V., Karbasian, M., Osintsev, N., & Nozick, V. (2021). Evaluation and selection of supplier in supply chain with fuzzy analytical network process approach. Journal of fuzzy extension & applications, 2(1), 69-87.
  • Hassanzadeh, R., & Asghari, H. (2020). Identification and ranking of affecting factors on sales and operations planning (S&OP) process implementation by using fuzzy AHP and fuzzy TOPSIS approach (case study: dairy industry). Journal of applied research on industrial engineering, 7(1), 57-78.
  • Liu, H., & Rodriguez, R. M. (2014). A fuzzy envelope for hesitant fuzzy linguistic term set, its application to multi criteria decision-making. Information sciences, 258, 220–238.
  • Rodríguez, R. M., Martínez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic terms sets for decision making. IEEE transactions on fuzzy systems, 20(1), 109–119.
  • Wang, J. Q., Wu, J. T., Wang, J., Zhang, H., & Chen, X. (2014). Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Information sciences, 288, 55-72.
  • Lee, L. W., & Chen, S. M. (2008, July). A new method for fuzzy multiple attributes group decision-making based on the arithmetic operations of interval type-2 fuzzy sets. 2008 International conference on machine learning and cybernetics(pp. 3084-3089). IEEE.
  • Chen, S. M., & Lee, L. W. (2010). Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert system with applications, 37(1) 824–833.
  • Celik, E., Bilisik, O. N., Erdogan, M., Gumus, A. T., & Baracli, H. (2013). An integrated novel interval type-2 fuzzy MCDM method to improve customer satisfaction in public transportation for Istanbul. Transportation research: part E, 58, 28–51.
  • Chen, T. Y. (2013). A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets. Applied soft computing13(5), 2735-2748.
  • Zhong, L., & Yao, L. L. (2017). An ELECTRE I-based multi-criteria group decision making method with interval type-2 fuzzy numbers and its application to supplier selection. Applied soft computing, 57, 556–576.
  • Wu, T., & Liu, X. W. (2016). An interval type-2 fuzzy clustering solution for large-scale multiple-criteria group decision-making problems. Knowledge-based systems, 114, 118-127.
  • Chen, S. M., Yang, M. W., Lee, L. W., & Yang, S. W. (2012). Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets. Expert systems with applications, 39(5), 5295–5308.
  • Abdullah, L., & Najib, L. (2014). A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process. Expert systems with applications, 41, 3297–3305.
  • Edalatpanah, S. A. (2020). Neutrosophic structured element. Expert systems, 37(5), 1- 17.
  • Mendel, J. M. (2002). An architecture for making judgments using computing with words. International journal of applied mathematics and computer science, 12(3), 325–335.
  • Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338–353.
  • Lin, W., Yan, G., & Shi, Y. (2014). Dynamic multi-attribute group decision making model based on generalized interval-valued trapezoidal fuzzy numbers. Cybernetics and information technologies, 14(4), 11-28.
  • Chiao, K. P. (2021). Multi-criteria decision making with interval type 2 fuzzy Bonferroni mean. Expert systems with applications, 176, 114789.
  • Li, H., Wu, P., Zhou, L., & Chen, H. (2021). A new approach for multicriteria group decision making under interval type-2 fuzzy environment. Measurement172, 108818.
  • Reda Boukezzoula, R., & Coquin, D. (2020). A decision-making computational methodology for a class of type-2 fuzzy intervals: an interval-based approach. Information sciences, 510, 256-282.