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Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information

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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

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov K., Gargov G. (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31: 343–349

    Article  MATH  MathSciNet  Google Scholar 

  • Burillo P., Bustince H. (1996) Entropy on intuitionistic fuzzy sets and interval-valued fuzzy sets. Fuzzy Sets and Systems 78: 305–316

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Chen T.Y., Tsao C.Y. (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets and Systems 159: 1410–1428

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Horn R. A., Johnson C. R. (1990) Matrix analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Hwang C. L., Yoon K. (1992) Fuzzy multiple attribute decision making: Theory and applications. Springer, Berlin

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Kim S. H., Ahn B. S. (1999) Interactive group decision making procedure under incomplete information. European Journal of Operational Research 116: 498–507

    Article  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Klir G. J. (2006) Uncertainty and information: Foundations of generalized information theory. Wiley, Hoboken, NJ

    Google Scholar 

  • Opricovic S. (1998) Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade

    Google Scholar 

  • Opricovic S., Tzeng G. H. (2003) Fuzzy multicriteria model for post-earthquake land-use planning. Natural Hazards Review 4: 59–64

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Opricovic S., Tzeng G. H. (2007) Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research 178: 514–529

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Google Scholar 

  • Tzeng G. H., Lin C. W., Opricovic S. (2005) Multi-criteria analysis of alternative-fuel buses for public transportation. Energy Policy 33: 1373–1383

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Xu Z. S. (2007a) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision 22: 215–219

    Google Scholar 

  • Xu Z. S. (2007b) Multi-person multi-criteria decision making models under intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making 6: 221–236

    Article  MATH  MathSciNet  Google Scholar 

  • Xu Z. S. (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Informing Science 180: 190–1181

    Google Scholar 

  • Xu Z. S., Cai X. Q. (2009) Incomplete interval-valued intuitionistic fuzzy preference relations. International Journal of General Systems 38: 871–886

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Xu Z. S., Yager R. R. (2008) Dynamic intuitionistic fuzzy multi-alltribute decision making. International Journal of Approximate Reasoning 48: 246–262

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Yang T., Hung C.C. (2007) Multi-attribute decision making methods for plant layout design problem. Robotics and Computer-Integrated Manufacturing 23: 126–137

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Division of Mathematical Sciences, Pukyong National University, Pusan, 608-737, Republic of Korea

    Jin Han Park & Hyun Ju Cho

  2. Department of Mathematics, Dong-A University, Pusan, 604-714, Republic of Korea

    Young Chel Kwun

Authors
  1. Jin Han Park
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  2. Hyun Ju Cho
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  3. Young Chel Kwun
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Correspondence to Young Chel Kwun.

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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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