Abstract
The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.
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References
Atanassov K. (1994) Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 64: 159–174
Atanassov K., Gargov G. (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31: 343–349
Burillo P., Bustince H. (1996) Entropy on intuitionistic fuzzy sets and interval-valued fuzzy sets. Fuzzy Sets and Systems 78: 305–316
Büyüközkan G., Ruan D. (2008) Evaluation of software development projects using a fuzzy multi-criteria decision approach. Mathematics and Computers in Simulation 77: 464–475
Chang C. L., Hsu C. H. (2009) Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed. Journal of Environmental Management 90: 3226–3230
Chen T.Y., Tsao C.Y. (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets and Systems 159: 1410–1428
Grzegorzewski P. (2004) Distance between intuitionistic fuzzy sets and/or interval-valued fuzzy sets on the Hausdorff metric. Fuzzy Sets and Systems 148: 319–328
Horn R. A., Johnson C. R. (1990) Matrix analysis. Cambridge University Press, Cambridge
Hwang C. L., Yoon K. (1992) Fuzzy multiple attribute decision making: Theory and applications. Springer, Berlin
Jahanshaloo G.R., Hosseinzadeh Lotfi F., Izadikhah M. (2006a) An algorithmic method to extend TOPSIS method for decision-making problems with interval data. Applied Mathematics and Computation 175: 1375–1384
Jahanshaloo G.R., Hosseinzadeh Lotfi F., Izadikhah M. (2006b) Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation 181: 1544–1551
Kim S. H., Ahn B. S. (1999) Interactive group decision making procedure under incomplete information. European Journal of Operational Research 116: 498–507
Kim S. H., Choi S. H., Kim H. (1999) An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach. European Journal of Operational Research 118: 139–152
Klir G. J. (2006) Uncertainty and information: Foundations of generalized information theory. Wiley, Hoboken, NJ
Opricovic S. (1998) Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade
Opricovic S., Tzeng G. H. (2003) Fuzzy multicriteria model for post-earthquake land-use planning. Natural Hazards Review 4: 59–64
Opricovic S., Tzeng G. H. (2004) The compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research 156: 445–455
Opricovic S., Tzeng G. H. (2007) Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research 178: 514–529
Park J. H., Lim K. M., Park J. S., Kwun Y. C. (2008) Distances between interval-valued intuitionistic fuzzy sets. Journal of Physics: Conference Series 96: 012089
Park, J. H., Park, I. Y., Kwun, Y. C., & Tan, X. G. (2010). Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Applied Mathematical Modelling. doi:10.1016/j.apm.2010.11.025. (in press).
Sayadi M. K., Heydaria M., Shahanaghia K. (2009) Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling 33: 2257–2262
Szmidt E., Kacprzky J. (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lecture Notes in Artificial Intelligence 3070: 388–393
Tzeng G. H., Lin C. W., Opricovic S. (2005) Multi-criteria analysis of alternative-fuel buses for public transportation. Energy Policy 33: 1373–1383
Wei, G. W., & Wang, X. R. (2007). Some geometric aggregation operators on interval-valued intuitionistic fuzzy sets and their application to group decision making. In Proceedings of. 2007 ICCIS (pp. 495–499).
Xu Z. S. (2005) An overview of methods for determining OWA weights. International Journal of Intelligent Systems 20: 843–865
Xu Z. S. (2007a) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision 22: 215–219
Xu Z. S. (2007b) Multi-person multi-criteria decision making models under intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making 6: 221–236
Xu Z. S. (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Informing Science 180: 190–1181
Xu Z. S., Cai X. Q. (2009) Incomplete interval-valued intuitionistic fuzzy preference relations. International Journal of General Systems 38: 871–886
Xu, Z. S., & Chen, J. (2007a). On geometric aggregation over interval-valued intuitionistic fuzzy information. In Proceedings of fourth international conference on fuzzy systems and knowledge discovery (FSKD’07) (Vol. 2, pp. 466–471).
Xu Z. S., Chen J. (2007b) An approach to group decision making based on interval-valued intuitionistic judgement matrices. System Engineer-Theory & Practice 27: 126–133
Xu Z. S., Yager R. R. (2008) Dynamic intuitionistic fuzzy multi-alltribute decision making. International Journal of Approximate Reasoning 48: 246–262
Xu Z. S., Yager R. R. (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making 8: 123–139
Yang T., Hung C.C. (2007) Multi-attribute decision making methods for plant layout design problem. Robotics and Computer-Integrated Manufacturing 23: 126–137
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Park, J.H., Cho, H.J. & Kwun, Y.C. Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optim Decis Making 10, 233–253 (2011). https://doi.org/10.1007/s10700-011-9102-9
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DOI: https://doi.org/10.1007/s10700-011-9102-9