Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment
Keywords:
TODIM method, trapezoidal intuitionistic fuzzy number, multiple attribute decision making, ranking methodAbstract
In actual decision making process, the final decision result is often affected by decision maker’s psychological behavior, however, for the multiple attribute decision making (MADM) problem in which attributes values are expressed with trapezoidal intuitionistic fuzzy numbers (TIFNs), there is few literature considering the decision maker's behavior factors in decision making process. For this case, this paper first proposes a new distance measure of TIFNs and a new ranking method which considers decision maker’s attitude behavior, and then develops an extended TODIM decision making method. Finally an example is given to illustrate the validity and practicability of the proposed method.References
Atanassov, K.T. (1986). Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, 87-96,1986. https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K. T.; Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(3), 343-349, 1989. https://doi.org/10.1016/0165-0114(89)90205-4
Bozic, M.; Ducic, N.; Djordjevic, G.; Slavkovic, R. (2017). Optimization of Wheg Robot Running with Simulation of Neuro-Fuzzy Control, International Journal of Simulation Modelling, 16(1), 19-30, 2017. https://doi.org/10.2507/IJSIMM16(1)2.363
Dalman, H.; Gazel, N.; Sivri M.(2016). A Fuzzy set-based approach to multi-objective multiitem solid transportation problem under uncertainty, InternationalJournal of Fuzzy Systems, 18(4), 716-729, 2016. https://doi.org/10.1007/s40815-015-0081-9
Fan, Z.P.; Zhang, X.; Chen, F.D., Liu, Y. (2013). Extended TODIM method for hybrid multiple attribute decision making problems, Knowlege-Based Systems, 42, 40-48, 2013. https://doi.org/10.1016/j.knosys.2012.12.014
Gomes, L. F. A. M.; Lima, M. M. P. P.(1992). From modeling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model, Foundations of Computing and Decision Sciences, 17, 171-184, 1992.
Gomes, L. F. A. M.; Rangel, L. A. D. (2009). An application of the TODIM method to the multicriteria rental evaluation of residential properties, European Journal of Operational Research, l193, 204-211, 2009. https://doi.org/10.1016/j.ejor.2007.10.046
Govindan, K.; Jepsen, M. B.(2016). Supplier risk assessment based on trapezoidal intuitionistic fuzzy numbers and ELECTRE TRI-C: a case illustration involving service suppliers, Journal of the Operational Research Society, 67(2), 339-376, 2016. https://doi.org/10.1057/jors.2015.51
Grzegorzewski, P. (1998). Metrics and orders in space of fuzzy numbers, Fuzzy sets and Systems, 97(1), 83-94, 1998. https://doi.org/10.1016/S0165-0114(96)00322-3
Grzegrorzewski, P. (2003). In ISTANBULL,The Hamming distance between intuitionistic fuzzy sets, Springer, Proc. of the IFSA 2003 World Congress, 35-38, 2003.
Gu,Y. K.;Zhu, F. L.; Tang, S. Y.(2012). Reliability analysis method based on fuzzy probability importance degree, Journal of Jiangxi University of Science and Technology, 33(5), 51-55, 2012.
Herrera, F.; Viedma, E. H. (2000). Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy Sets and Systems, 115(1), 67-82, 2000. https://doi.org/10.1016/S0165-0114(99)00024-X
Kahneman D.; Tversky, A. (1979). Prospect theory: an analysis of decision under risk, Econometrica, 47, 263-292, 1979. https://doi.org/10.2307/1914185
Lakshmana, G. N. V.; Jeevaraj, S.; Dhanasekaran, P. (2016.; A linear ordering on the class of trapezoidal intuitionistic fuzzy numbers, Expert Systems with Applications, 60, 269-279, 2016. https://doi.org/10.1016/j.eswa.2016.05.003
Li, D.-F. (2003). Fuzzy Multiobjective Many-Person Decision Making and Games. National Defense Industry Press, 2003.
Li, X. H.; Chen, X. H. (2015). Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information, Applied Soft Computing, 30, 454-461, 2015. https://doi.org/10.1016/j.asoc.2015.01.054
Liou, T. S.; Wang, M. J. (1992). Fuzzy weighted average:an improved algorithm, Fuzzy Sets and Systems, 49(3), 307-315, 1992. https://doi.org/10.1016/0165-0114(92)90282-9
Llopis-Albert, C.; Palacios-Marqus, D.; Merigo, J. M. (2016). Decision making under uncertainty in environmental projects using mathematical simulation modeling, Environmental Earth Sciences, 75(19), 1320-1330, 2016. https://doi.org/10.1007/s12665-016-6135-y
Lourenzutti, R.; Krohling, R. A. (2014). The Hellinger distance in multicriteria decision making: an illustration to the TOPSIS and TODIM methods, Expert Systems with Applications, 41(9), 4414-4421, 2014. https://doi.org/10.1016/j.eswa.2014.01.015
Mousavi, M.; Yap, H. J.; Musa, S. N.; Dawal, S. Z. M. (2017). A Fuzzy Hybrid GA-PSO Algorithm for Multi-Objective AGV Scheduling in FMS, International Journal of Simulation Modelling, 16(1), 58-71, 2017. https://doi.org/10.2507/IJSIMM16(1)5.368
Nehi, H. M.; Maleki, H. R. (2005). In Athens, Intuitionistic fuzzy numbers and it's applications in fuzzy optimization problem, Proceedings of the 9th WSEAS International Conference On Systems, 2005,1-5, 2005.
Pham, V. N.; Long, T. N.; Pedrycz W. (2016). Interval-valued fuzzy set approach to fuzzy co-clustering for data classification, Knowledge-Based Systems, 107, 1-13, 2016. https://doi.org/10.1016/j.knosys.2016.05.049
Qin, Q.; Liang, F.; Li, L.; Wu, G. F. (2017). A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers, Applied Soft Computing, 55, 93-10, 2017. https://doi.org/10.1016/j.asoc.2017.01.041
Ren, H. P.; Liu, M. F. (2014). VIKOR method for MADM problem with triangular fuzzy number considering behavior of decision maker, ICIC Express Letters, Part B: Applications, 5(3), 879-884, 2014.
Ren, P.; Xu, Z.; Gou, X.(2016). Pythagorean fuzzy TODIM approach to multi-criteria decision making, Applied Soft Computing, 42, 246-259, 2016 https://doi.org/10.1016/j.asoc.2015.12.020
Sang, X.; Liu, X. (2016). An interval type-2 fuzzy sets-based TODIM method and its application to green supplier selection, Journal of the Operational Research Society, 67(5), 722-734, 2016. https://doi.org/10.1057/jors.2015.86
Shu, M. H.; Cheng, C. H.; Chang, J. R.(2006). Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelect ronics Reliability, 46(12), 2139-2148, 2006. https://doi.org/10.1016/j.microrel.2006.01.007
Wan, S. P. (2009); Method of attitude index for interval multi-attribute decision-making, Control and Decision, 24(1), 35-38, 2009.
Wan, S. P.; Dong, J. Y. (2015). Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making, Applied Soft Computing, 29, 153-168, 2015. https://doi.org/10.1016/j.asoc.2014.12.031
Wang, J.; Wang, J. Q.; Zhang, H. Y. (2016). A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing, Computers & Industrial Engineering, 99, 287-299, 2016. https://doi.org/10.1016/j.cie.2016.07.023
Wang, J. Q.; Zhang, Z. (2008). Programming method of multi-criteria decision-making based on intuitionistic fuzzy number with incomplete certain information, Control and Decision, 23(10), 1145-1148, 2008.
Ye, J. (2012). Multicriteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy number, Group Decision Negotiation, 21, 519-530, 2012. https://doi.org/10.1007/s10726-010-9224-4
Zhang, M.; Liu, P.; Shi L. (2016). An extended multiple attribute group decision-making TODIM method based on the neutrosophic numbers, Journal of Intelligent & Fuzzy Systems, 30(3), 1773-1781, 2016. https://doi.org/10.3233/IFS-151889
Zindani, D.; Maity, S. R. Bhowmik, S.; Chakraborty, S. (2017). A material selection approach using the TODIM (TOmada de Decisao Interativa Multicriterio) method and its analysis, International Journal of Materials Research, 108(5), 345-354, 2017. https://doi.org/10.3139/146.111489
Zhu, B.; Xu, Z.S. (2014). A fuzzy linear programming method for group decision making with additive reciprocal fuzzy preference relations, Fuzzy Sets and Systems, 246, 19-33, 2014. https://doi.org/10.1016/j.fss.2014.01.001
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.