Extended Intuitionistic Fuzzy VIKOR Method in Group Decision Making: The Case of Vendor Selection Decision
Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.
[1] Saen, R. F., An algorithm for ranking technology suppliers in the presence of nondiscretionary factors. Applied Mathematics and Computation, 2006. 181(2): p. 1616-1623.
[2] Wu, T., et al., AIDEA: a methodology for supplier evaluation and selection in a supplier-based manufacturing environment. International Journal of Manufacturing Technology and Management 2007. 11(2): p. 2 174 - 192.
[3] Talluri, S., A buyer-seller game model for selection and negotiation of purchasing bids. European Journal of Operational Research, 2002. 143(1): p. 171-180.
[4] Hong, G. H., et al., An effective supplier selection method for constructing a competitive supply-relationship. Expert Systems with Applications, 2005. 28(4): p. 629-639.
[5] Muralidharan, C., N. Anantharaman, and S. G. Deshmukh, A Multi-Criteria Group Decisionmaking Model for Supplier Rating. Journal of Supply Chain Management, 2002. 38(4): p. 22-33.
[6] Hou, J. and D. Su, EJB-MVC oriented supplier selection system for mass customization. Journal of Manufacturing Technology Management, 2007. 18(1): p. 54 - 71.
[7] Sarkis, J. and S. Talluri, A Model for Strategic Supplier Selection. Journal of Supply Chain Management, 2002. 38(1): p. 18-28.
[8] Chen, C.-T., C.-T. Lin, and S.-F. Huang, A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 2006. 102(2): p. 289-301.
[9] Bottani, E. and A. Rizzi, An adapted multi-criteria approach to suppliers and products selection-An application oriented to lead-time reduction. International Journal of Production Economics, 2008. 111(2): p. 763-781.
[10] Choy, K. L. and W. B. Lee, A generic tool for the selection and management of supplier relationships in an outsourced manufacturing environment: the application of case based reasoning. Logistics Information Management, 2002. 15(4): p. 235 - 253.
[11] Choy, K. L., et al., A knowledge-based supplier intelligence retrieval system for outsource manufacturing. Knowledge-Based Systems, 2005. 18(1): p. 1-17.
[12] Ramanathan, R., Supplier selection problem: integrating DEA with the approaches of total cost of ownership and AHP. Supply Chain Management: An International Journal, 2007. 12(4): p. 258 - 261.
[13] Jain, V., M. K. Tiwari, and F. T. S. Chan, Evaluation of the supplier performance using an evolutionary fuzzy-based approach. Journal of Manufacturing Technology Management, 2004. 15(8): p. 735-744.
[14] Sanayei, A., S. F. Mousavi, and A. Yazdankhah, Group decision making process for supplier selection with VIKOR under fuzzy environment Expert Systems with Applications, 2010. 37(1): p. 24-30.
[15] Wu, D. D., et al., Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach. European Journal of Operational Research, 2010. 200(3): p. 774-787.
[16] Awasthi, A., S. S. Chauhan, and S. K. Goyal, A fuzzy multicriteria approach for evaluating environmental performance of suppliers. International Journal of Production Economics, 2010. 126(2): p. 370-378.
[17] Boran, F. E., et al., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method Expert Systems with Applications, 2009. 36(8): p. 11363-11368.
[18] Zadeh, L. A., Fuzzy sets Information and Control, 1965. 8(3): p. 338-353.
[19] Atanassov, K.T., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986. 20(1): p. 87-96.
[20] Atanassov, K. T., More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989. 33(1): p. 37-45.
[21] Atanassov, K. T., New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1994. 61(2): p. 137-142.
[22] De, S. K., R. Biswas, and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis Fuzzy Sets and Systems, 2001. 117(2): p. 209-213.
[23] Khatibi, V. and G. A. Montazer, Intuitionistic fuzzy set vs. fuzzy set application in medical. Artificial Intelligence in Medicine, 2009. 47(1): p. 43-52.
[24] Chaira, T., A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Applied Soft Computing, 2011. 11(2): p. 1711-1717.
[25] Xu, Z., J. Chen, and J. Wu, Clustering algorithm for intuitionistic fuzzy set. Information Sciences, 2008. 178(19): p. 3775-3790.
[26] Boran, F. E., Erratum to “Distance measure between intuitionistic fuzzy sets” [Pattern Recognition Lett. 26 (2005) 2063-2069] Pattern Recognition Letters, 2009. 30(4): p. Page 468.
[27] Hung, W.-L. and M.-S. Yang, On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition Information Sciences, 2008. 178(6): p. 1641-1650.
[28] Vlachos, I. K. and G. D. Sergiadis, Intuitionistic fuzzy information - Applications to pattern recognition. Pattern Recognition Letters, 2007. 28(2): p. 197-206.
[29] Zhang, C. and H. Fu, Similarity measures on three kinds of fuzzy sets. Pattern Recognition Letters, 2006. 27(12): p. 1307-1317.
[30] Liang, Z. and P. Shi, Similarity measures on intuitionistic fuzzy sets Pattern Recognition Letters, 2003. 24(15): p. 2687-2693.
[31] Mondal, T. K. and S. K. Samanta, On intuitionistic gradation of openness. Fuzzy Sets and Systems, 2002. 131(3): p. 323-336.
[32] Mursaleen, M. and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. Journal of Computational and Applied Mathematics, 2009. 233(2): p. 142-149.
[33] Mursaleen, M., S. A. Mohiuddine, and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces Computers & Mathematics with Applications, 2010. 59(2): p. 603-611.
[34] Yılmaz, Y., On some basic properties of differentiation in intuitionistic fuzzy normed spaces. Mathematical and Computer Modelling, 2010. 52(3-4): p. 448-458.
[35] W. L. Gau and D. J. Buehrer, Vague sets. IEEE Transactions on Systems, Man and Cybernetics, 1993. 23(2): p. 610-614.
[36] Bustince, H. and P. Burillo, Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1996. 79(3): p. 403-405.
[37] Grzegorzewski, P., Distance between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 2004. 148(2): p. 319-328.
[38] Szmidt, E. and J. Kacprzyk, Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 2000. 114(3): p. 505-518.
[39] Wang, W. and X. Xin, Distance measure between intuitionistic fuzzy sets Pattern Recognition Letters, 2005. 26(13): p. 2063-2069.
[40] Hung, W.-L. and M.-S. Yang, Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance Pattern Recognition Letters, 2004. 25(14): p. 1603-1611.
[41] Li, D.-F., Some measures of dissimilarity in intuitionistic fuzzy structures. Journal of Computer and System Sciences, 2004. 68(1): p. 115-122.
[42] Li, D.-F., F. Shan, and C.-T. Cheng, On properties of four IFS operators Fuzzy Sets and Systems, 2005. 154(1): p. 151-155.
[43] Li, Y., D.L. Olson, and Z. Qin, Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis. Pattern Recognition Letters, 2007. 28(2): p. 278-285.
[44] Burillo, P. and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 1996. 78(3): p. 305-316.
[45] Ye, J., Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. European Journal of Operational Research, 2010. 205(1): p. 202-204.
[46] Zhang, H., W. Zhang, and C. Mei, Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowledge-Based Systems, 2009. 22(6): p. 449-454.
[47] Xu, Z. and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets International Journal of General Systems, 2006. 35(4): p. 417 - 433.
[48] Xu, Z., Intuitionistic Fuzzy Aggregation Operators. Fuzzy Systems, IEEE Transactions on 2007. 15(6): p. 1179 - 1187
[49] Atanassov, K., G. Pasib, and R. Yagerc, Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making International Journal of Systems Science, 2005. 36(14): p. 859 - 868
[50] Li, D.-F., et al., Fractional programming methodology for multi-attribute group decision-making using IFS. Applied Soft Computing, 2009. 9(1): p. 219-225.
[51] Wei, G., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied Soft Computing, 2010. 10(2): p. 423-431.
[52] Liu, H.-W. and G.-J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research, 2007. 179(1): p. 220-233.
[53] Xu, Z. and R. R. Yager, Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 2008. 48(1): p. 246-262.
[54] Wei, G.-W., GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowledge-Based Systems, 2010. 23(3): p. 243-247.
[55] Xu, Z., A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Information Sciences, 2010. 180(1): p. 181-190.
[56] Wu, J.-Z. and Q. Zhang, Multicriteria decision making method based on intuitionistic fuzzy weighted entropy. Expert Systems with Applications, 2011. 38(1): p. 916-922.
[57] Opricovic, S. and G.-H. Tzeng, Multicriteria Planning of Post-Earthquake Sustainable Reconstruction. Computer-Aided Civil and Infrastructure Engineering, 2002. 17(3): p. 211-220.
[58] Cristóbal, J. R. S., Multi-criteria decision-making in the selection of a renewable energy project in spain: The Vikor method. Renewable Energy, 2011. 36(2): p. 498-502.
[59] Kuo, M.-S. and G.-S. Liang, Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment Expert Systems with Application, 2011. 38(3): p. 1304-1312.
[60] Bazzazi, A. A., M. Osanloo, and B. Karimi, Deriving preference order of open pit mines equipment through MADM methods: Application of modified VIKOR method. Expert Systems with Applications, 2011. 38(3): p. 2550-2556.
[61] Chang, C.-L. and C.-H. Hsu, Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed. Journal of Environmental Management, 2009. 90(11): p. 3226-3230.
[62] Chen, L. Y. and T.-C. Wang, Optimizing partners' choice in IS/IT outsourcing projects: The strategic decision of fuzzy VIKOR. International Journal of Production Economics, 2009. 120(1): p. 233-242.
[63] Sayadi, M. K., M. Heydari, and K. Shahanaghi, Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 2009. 33(5): p. 2257-2262.
[64] Opricovic, S. and G.-H. Tzeng, Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research, 2007. 178(2): p. 514-529.
[65] Kaya, T. and C. Kahraman, Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: The case of Istanbul. Energy, 2010. 35(6): p. 2517-2527.
[66] Devi, K., Extension of VIKOR method in intuitionistic fuzzy environment for robot selection. Expert Systems with Applications, 2011. 38 (11): p. 14163–14168.
[67] Ho, W., X. Xu, and P. K. Dey, Multi-Criteria Decision Making Approaches for Supplier Evaluation and Selection: A Literature Review. European Journal of Operational Research, 2010. 202(1): p. 16-24.
[1] Saen, R. F., An algorithm for ranking technology suppliers in the presence of nondiscretionary factors. Applied Mathematics and Computation, 2006. 181(2): p. 1616-1623.
[2] Wu, T., et al., AIDEA: a methodology for supplier evaluation and selection in a supplier-based manufacturing environment. International Journal of Manufacturing Technology and Management 2007. 11(2): p. 2 174 - 192.
[3] Talluri, S., A buyer-seller game model for selection and negotiation of purchasing bids. European Journal of Operational Research, 2002. 143(1): p. 171-180.
[4] Hong, G. H., et al., An effective supplier selection method for constructing a competitive supply-relationship. Expert Systems with Applications, 2005. 28(4): p. 629-639.
[5] Muralidharan, C., N. Anantharaman, and S. G. Deshmukh, A Multi-Criteria Group Decisionmaking Model for Supplier Rating. Journal of Supply Chain Management, 2002. 38(4): p. 22-33.
[6] Hou, J. and D. Su, EJB-MVC oriented supplier selection system for mass customization. Journal of Manufacturing Technology Management, 2007. 18(1): p. 54 - 71.
[7] Sarkis, J. and S. Talluri, A Model for Strategic Supplier Selection. Journal of Supply Chain Management, 2002. 38(1): p. 18-28.
[8] Chen, C.-T., C.-T. Lin, and S.-F. Huang, A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 2006. 102(2): p. 289-301.
[9] Bottani, E. and A. Rizzi, An adapted multi-criteria approach to suppliers and products selection-An application oriented to lead-time reduction. International Journal of Production Economics, 2008. 111(2): p. 763-781.
[10] Choy, K. L. and W. B. Lee, A generic tool for the selection and management of supplier relationships in an outsourced manufacturing environment: the application of case based reasoning. Logistics Information Management, 2002. 15(4): p. 235 - 253.
[11] Choy, K. L., et al., A knowledge-based supplier intelligence retrieval system for outsource manufacturing. Knowledge-Based Systems, 2005. 18(1): p. 1-17.
[12] Ramanathan, R., Supplier selection problem: integrating DEA with the approaches of total cost of ownership and AHP. Supply Chain Management: An International Journal, 2007. 12(4): p. 258 - 261.
[13] Jain, V., M. K. Tiwari, and F. T. S. Chan, Evaluation of the supplier performance using an evolutionary fuzzy-based approach. Journal of Manufacturing Technology Management, 2004. 15(8): p. 735-744.
[14] Sanayei, A., S. F. Mousavi, and A. Yazdankhah, Group decision making process for supplier selection with VIKOR under fuzzy environment Expert Systems with Applications, 2010. 37(1): p. 24-30.
[15] Wu, D. D., et al., Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach. European Journal of Operational Research, 2010. 200(3): p. 774-787.
[16] Awasthi, A., S. S. Chauhan, and S. K. Goyal, A fuzzy multicriteria approach for evaluating environmental performance of suppliers. International Journal of Production Economics, 2010. 126(2): p. 370-378.
[17] Boran, F. E., et al., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method Expert Systems with Applications, 2009. 36(8): p. 11363-11368.
[18] Zadeh, L. A., Fuzzy sets Information and Control, 1965. 8(3): p. 338-353.
[19] Atanassov, K.T., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986. 20(1): p. 87-96.
[20] Atanassov, K. T., More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989. 33(1): p. 37-45.
[21] Atanassov, K. T., New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1994. 61(2): p. 137-142.
[22] De, S. K., R. Biswas, and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis Fuzzy Sets and Systems, 2001. 117(2): p. 209-213.
[23] Khatibi, V. and G. A. Montazer, Intuitionistic fuzzy set vs. fuzzy set application in medical. Artificial Intelligence in Medicine, 2009. 47(1): p. 43-52.
[24] Chaira, T., A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Applied Soft Computing, 2011. 11(2): p. 1711-1717.
[25] Xu, Z., J. Chen, and J. Wu, Clustering algorithm for intuitionistic fuzzy set. Information Sciences, 2008. 178(19): p. 3775-3790.
[26] Boran, F. E., Erratum to “Distance measure between intuitionistic fuzzy sets” [Pattern Recognition Lett. 26 (2005) 2063-2069] Pattern Recognition Letters, 2009. 30(4): p. Page 468.
[27] Hung, W.-L. and M.-S. Yang, On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition Information Sciences, 2008. 178(6): p. 1641-1650.
[28] Vlachos, I. K. and G. D. Sergiadis, Intuitionistic fuzzy information - Applications to pattern recognition. Pattern Recognition Letters, 2007. 28(2): p. 197-206.
[29] Zhang, C. and H. Fu, Similarity measures on three kinds of fuzzy sets. Pattern Recognition Letters, 2006. 27(12): p. 1307-1317.
[30] Liang, Z. and P. Shi, Similarity measures on intuitionistic fuzzy sets Pattern Recognition Letters, 2003. 24(15): p. 2687-2693.
[31] Mondal, T. K. and S. K. Samanta, On intuitionistic gradation of openness. Fuzzy Sets and Systems, 2002. 131(3): p. 323-336.
[32] Mursaleen, M. and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. Journal of Computational and Applied Mathematics, 2009. 233(2): p. 142-149.
[33] Mursaleen, M., S. A. Mohiuddine, and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces Computers & Mathematics with Applications, 2010. 59(2): p. 603-611.
[34] Yılmaz, Y., On some basic properties of differentiation in intuitionistic fuzzy normed spaces. Mathematical and Computer Modelling, 2010. 52(3-4): p. 448-458.
[35] W. L. Gau and D. J. Buehrer, Vague sets. IEEE Transactions on Systems, Man and Cybernetics, 1993. 23(2): p. 610-614.
[36] Bustince, H. and P. Burillo, Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1996. 79(3): p. 403-405.
[37] Grzegorzewski, P., Distance between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 2004. 148(2): p. 319-328.
[38] Szmidt, E. and J. Kacprzyk, Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 2000. 114(3): p. 505-518.
[39] Wang, W. and X. Xin, Distance measure between intuitionistic fuzzy sets Pattern Recognition Letters, 2005. 26(13): p. 2063-2069.
[40] Hung, W.-L. and M.-S. Yang, Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance Pattern Recognition Letters, 2004. 25(14): p. 1603-1611.
[41] Li, D.-F., Some measures of dissimilarity in intuitionistic fuzzy structures. Journal of Computer and System Sciences, 2004. 68(1): p. 115-122.
[42] Li, D.-F., F. Shan, and C.-T. Cheng, On properties of four IFS operators Fuzzy Sets and Systems, 2005. 154(1): p. 151-155.
[43] Li, Y., D.L. Olson, and Z. Qin, Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis. Pattern Recognition Letters, 2007. 28(2): p. 278-285.
[44] Burillo, P. and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 1996. 78(3): p. 305-316.
[45] Ye, J., Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. European Journal of Operational Research, 2010. 205(1): p. 202-204.
[46] Zhang, H., W. Zhang, and C. Mei, Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowledge-Based Systems, 2009. 22(6): p. 449-454.
[47] Xu, Z. and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets International Journal of General Systems, 2006. 35(4): p. 417 - 433.
[48] Xu, Z., Intuitionistic Fuzzy Aggregation Operators. Fuzzy Systems, IEEE Transactions on 2007. 15(6): p. 1179 - 1187
[49] Atanassov, K., G. Pasib, and R. Yagerc, Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making International Journal of Systems Science, 2005. 36(14): p. 859 - 868
[50] Li, D.-F., et al., Fractional programming methodology for multi-attribute group decision-making using IFS. Applied Soft Computing, 2009. 9(1): p. 219-225.
[51] Wei, G., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied Soft Computing, 2010. 10(2): p. 423-431.
[52] Liu, H.-W. and G.-J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research, 2007. 179(1): p. 220-233.
[53] Xu, Z. and R. R. Yager, Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 2008. 48(1): p. 246-262.
[54] Wei, G.-W., GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowledge-Based Systems, 2010. 23(3): p. 243-247.
[55] Xu, Z., A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Information Sciences, 2010. 180(1): p. 181-190.
[56] Wu, J.-Z. and Q. Zhang, Multicriteria decision making method based on intuitionistic fuzzy weighted entropy. Expert Systems with Applications, 2011. 38(1): p. 916-922.
[57] Opricovic, S. and G.-H. Tzeng, Multicriteria Planning of Post-Earthquake Sustainable Reconstruction. Computer-Aided Civil and Infrastructure Engineering, 2002. 17(3): p. 211-220.
[58] Cristóbal, J. R. S., Multi-criteria decision-making in the selection of a renewable energy project in spain: The Vikor method. Renewable Energy, 2011. 36(2): p. 498-502.
[59] Kuo, M.-S. and G.-S. Liang, Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment Expert Systems with Application, 2011. 38(3): p. 1304-1312.
[60] Bazzazi, A. A., M. Osanloo, and B. Karimi, Deriving preference order of open pit mines equipment through MADM methods: Application of modified VIKOR method. Expert Systems with Applications, 2011. 38(3): p. 2550-2556.
[61] Chang, C.-L. and C.-H. Hsu, Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed. Journal of Environmental Management, 2009. 90(11): p. 3226-3230.
[62] Chen, L. Y. and T.-C. Wang, Optimizing partners' choice in IS/IT outsourcing projects: The strategic decision of fuzzy VIKOR. International Journal of Production Economics, 2009. 120(1): p. 233-242.
[63] Sayadi, M. K., M. Heydari, and K. Shahanaghi, Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 2009. 33(5): p. 2257-2262.
[64] Opricovic, S. and G.-H. Tzeng, Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research, 2007. 178(2): p. 514-529.
[65] Kaya, T. and C. Kahraman, Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: The case of Istanbul. Energy, 2010. 35(6): p. 2517-2527.
[66] Devi, K., Extension of VIKOR method in intuitionistic fuzzy environment for robot selection. Expert Systems with Applications, 2011. 38 (11): p. 14163–14168.
[67] Ho, W., X. Xu, and P. K. Dey, Multi-Criteria Decision Making Approaches for Supplier Evaluation and Selection: A Literature Review. European Journal of Operational Research, 2010. 202(1): p. 16-24.
@article{"International Journal of Business, Human and Social Sciences:79598", author = "Nastaran Hajiheydari and Mohammad Soltani Delgosha", title = "Extended Intuitionistic Fuzzy VIKOR Method in Group Decision Making: The Case of Vendor Selection Decision", abstract = "Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.
", keywords = "Group decision making, intuitionistic fuzzy entropy measure, intuitionistic fuzzy set, vendor selection VIKOR.", volume = "14", number = "5", pages = "378-8", }
