A note on "An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts"

Document Type : Original Manuscript

Author

Department of Management, Zabol Branch, Islamic Azad University, Zabol, Iran

10.22094/joie.2020.1869275.1657

Abstract

The technique for order of preference by similarity to ideal solution (TOPSIS) is a method based on the ideal solutions in which the most desirable alternative should have the shortest distance from positive ideal solution and the longest distance from negative ideal solution. Depending on type of evaluations or method of ranking, different approaches have been proposing to calculate distances in the TOPSIS method. In a recent paper, Dymova et al. (2015) extended the TOPSIS approach using interval type 2 fuzzy sets (IT2FSs) in which distances were calculated using alpha cuts. When investigating their paper, we found out that the extended method has some drawbacks such that it leads to the incorrect calculations and results when solving an IT2FSs-based multi-criteria decision making (MCDM) problem. In this note, the corrected version of extended TOPSIS method is being presented to eliminate its limitations. In order to show effectiveness and possibility of the proposed approach, it is also implemented in two illustrative examples and one case study. The results have showed that the optimal alternative obtained by the corrected TOPSIS approach has the similar rank to the others, whereas it is different from the results of existing TOPSIS approach.

Keywords


Abbasimehr, H., & Tarokh, M.J. (2016). A novel intervaltype-2 fuzzy AHP-TOPSIS approach for ranking reviewers in online communities. Scientia Iranica, 23, 2355-2373.
Ashtiani, B., Haghighirad, F., Makui, A., & Montazer, G.A. (2009). Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets.  Applied Soft Computing, 9, 457–461.
Baykasoğlu, A., & Gölcük, I. (2018). Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS. Expert Systems with Applications, 70, 37-51.
Çebi, F., & Otay, İ. (2015). Multi-Criteria and Multi-Stage Facility Location Selection under Interval Type-2 Fuzzy Environment: A Case Study for a cement Factory. International Journal of Computational Intelligence Systems, 8, 330-344.
Chen, S.M., & Lee, L.W. (2010). Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method. Expert Systems with Applications, 37, 2790–2798.
Chen, T.Y. (2015). An interval type-2 fuzzy technique for order preference by similarity to ideal solutions using a likelihood-based comparison approach for multiple criteria decision analysis. Computers & Industrial Engineering, 85, 57–72.
Deveci, M., Canıtez, F., & Gokasar. (2018). WASPAS and TOPSIS based interval type-2 fuzzy MCDM method for a selection of a car sharing station. Sustainable Cities and Society, 41, 777-791.
Dymova, L., Sevastjanov, P., &  Tikhonenko, A.  (2015). An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts. Knowledge-Based Systems, 83, 116-127.
Erdoğan, M., & Kaya, İ. (2014). A Type-2 Fuzzy MCDM Method for Ranking Private Universities in İstanbul. Proceedings of the World Congress on Engineering 2014 Vol I, WCE 2014, London, UK.
Ghaemi Nasab, F., & Rostamy-Malkhalifeh, M. (2010). Extension of TOPSIS for Group Decision Making Based on the Type-2 Fuzzy Positive and Negative Ideal Solutions. International Journal of Industrial Mathematics, 199-213.
Ghorabaee, M.K. (2016). Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robotics and Computer-Integrated Manufacturing, 37, 221-232.
Gündoğdu, F.K., & Kahraman, C. (2019). A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets. Engineering Applications of Artificial Intelligence, 85, 307-323.
Hwang, C.L., & Yoon, K. (1981). Multiple attributes decision making method and application, Springer, Berlin.
Liu, K., Liu, Y., & Qin, J. (2018). An integrated ANP-VIKOR methodology for sustainable supplier selection with interval type-2 fuzzy sets. Granular Computing, 3, 193–208.
Mohamadghasemi, A., Hadi-Vencheh, A. Hosseinzadeh Lotfi, F., & Khalilzadeh M. (2018). Group multiple criteria ABC inventory classification using TOPSIS approach extended by Gaussian interval type-2 fuzzy sets and optimization programs. Scientia Iranica, Doi: 10.24200/SCI.2018.5539.1332.
Mokhtariana, M.N., Sadi-nezhada, S., & Makui, A. (2014). “A new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process. Applied Soft Computing, 23, 509–520.
Rashid, T., Beg, I., & Husnine, S. M. (2014). Robot selection by using generalized interval-valued fuzzy numbers with TOPSS. Applied Soft Computing, 21, 462–468.
Saremi, H.Q., & Montazer, G.A. (2008). An application of Type-2 Fuzzy Notions in Website Structures Selection: Utilizing Extended TOPSIS Method. WSEAS Transactions on Computers, 7, 8-15.
Temur, G.T., Kaya, T., & Kahraman, C. (2014). Facility location selection in reverse logistics using a type-2 fuzzy decision ad method, In: C. KahramanB. Öztayşi, Supply Chain Management Under Fuzziness, 591-606, Springer, Berlin.
Wang, H., Yao, J. and Zhang, X. (2018). A new multi-attribute decision making method based on interval normal type-2 fuzzy numbers. International Conference on Fuzzy Theory and Its Applications iFUZZY.
Yong, Q., Zhenyu, Z., Xinwang, L., Man, L. and Linlin, K. (2015). Dynamic risk assessment of metro station with interval type-2 fuzzy set and TOPSIS method.  Journal of Intelligent & Fuzzy Systems, 29, 93-106.
Zadeh, L. (1975). The concept of a linguistic variable and its application to approximate reasoning, Part 1. Information Sciences, 8, 199–249.