Nimet YAPICI PEHLİVAN, Aynur ŞAHİN

A Novel Multi-Criteria Decision Making Method based on The Ranking Values of Interval Type-2 Fuzzy Sets: An Application of a Manager Selection for a Telecommunication Company

Type-2 fuzzy sets (T2FSs), characterized by a fuzzy membership function, are much useful tool for representing the decision knowledge in the decision making process. Interval Type-2 fuzzy sets (IT2FSs) are the most commonly used T2FSs. In this study, a method based upon ranking values of IT2FSs is used to tackle multi-criteria decision making (MCDM) problems. First, some basic concepts and arithmetic operations for IT2FSs are presented. Then, three kinds of fuzzy ranking methods, proposed by [1], based on arithmetic average (AA), geometric average (GA) and harmonic average (HA) operators to compute the ranking values of IT2FSs are applied. Finally, the outcomes of MCDM methods based on the ranking values of IT2FSs are obtained and also compared with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method based on Type-1 fuzzy sets (T1FSs) for a numerical example.

Anahtar Kelimeler:

Multi-criteria decision making, Interval Type-2 fuzzy sets; Fuzzy ranking methods

PDF

___

[1] Quin, J., Liu, X. 2015. Multi-attribute group decision making using combined ranking vaue under interval type-2 fuzzy environment. Information Sciences 297, 293-315.
[2] Chen, S. M. 1988. A new approach to handling fuzzy decision making problems. IEEE Transactions on Systems, Man, and Cybernetics, 18(6), 1012–1016.
[3] Chen, C. T. 2000. Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 114(1), 1–9.
[4] Wang, W., Liu X., Quin, Y. 2012. Multi-attribute group decision making models under interval type-2 fuzzy environment. Knowledge-Based System 30 (2012),121-128.
[5] Liginlal, D., Ow, T. T. 2006. Modeling attitude to risk in human decision processes: An application of fuzzy measures. Fuzzy Sets and Systems, 157(23), 3040–3054.
[6] Wang T. C., Chang, T. H. 2007. Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment. Expert Systems with Applications, 33(4), 870–880.
[7] Fu, G. 2008. A fuzzy optimization method for multicriteria decision making: An application to reservoir flood control operation. Expert Systems with Applications, 34(1), 145–149.
[8] Hua, Z., Gong, B., Xu, X. 2008. A DS–AHP approach for multi-attribute decision making problem with incomplete information. Expert Systems with Applications, 34(3), 2221–2227.
[9] 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.
[10] Zadeh, L. A. 1965. Fuzzy sets. Information and Control, 8, 338–353.
[11] Zadeh, L. A. 1975. The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3), 199-249.
[12] Lee, L. W. , Chen, S. M. 2008. A new method for fuzzy multiple attributes group decision-making based on the arithmetic operations of interval type-2 fuzzy sets. International Conference on Machine Learning and Cybernetic, Kunming, China. 3084–3089.
[13] Chen, S. M., Lee, L. W. 2010a. Fuzzy multiple attributes group decision-making based on ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Systems with Applications, 37(1), 824–833.
[14] Chen, S. M., Lee, L. W. 2010b. Fuzzy multiple attributes group decision-making based on interval type-2 TOPSIS method. Expert Systems with Applications, 37(4), 2790–2798.
[15] Chen, S. M., Yang, M. Y., 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, 5295–5308.
[16] Sahin, A. , Yapıcı Pehlivan, N., 2017. Evaluation of life quality by integrated method of AHP and TOPSIS based on interval type-2 fuzzy sets. Hacettepe Journal of Mathematics and Statistics, 46 (3) , 511- 523.
[17] Mendel, J. M., John, R. I., & Liu, F. L. 2006. Interval type-2 fuzzy logical systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808–821.
[18] Ashtiani, B., Haghighirad, F., Makui, A., Montazer, G. 2009. Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Applied Soft Computing, 9, 457–461.
[19] 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.
[20] Hu, J., Zhang, Y., Chen, X., Liu, Y, 2013. Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number, Knowledge-Based System 43,21–29.