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Multi-attribute decision making based on a novel IF point operator

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Abstract

Intuitionistic fuzzy (IF) point operators transform an intuitionistic fuzzy set to a fuzzy set, or an intuitionistic fuzzy set with a smaller degree of hesitance. The purpose of which is to empower the operations of intuitionistic fuzzy sets with traditional fuzzy set methodologies. In the present paper, a new IF point operator is proposed. Different from the existing IF point operators, the new approach includes two parametric functions with respect to the number of iterations. It is proved that the newly proposed method could be degenerated to the traditional IF point operators. Meanwhile, the new IF point operator can extend our horizons in the exploration of the relationship between fuzzy sets and intuitionistic fuzzy sets. Specifically, a special case of the new IF point operator would be entitled as the memoryless multi-stage voting method, with which the decision makers are assumed to be affected only by the outcomes of the latest round of voting. It is proved that the memoryless multi-stage voting method converges to the limit produced by the infinite number of iterations much faster than the traditional voting method. Furthermore, a numerical example is employed to demonstrate the validity and performance of the memoryless multi-stage voting approach.

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References

  • Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.

    Article  MATH  MathSciNet  Google Scholar 

  • Burillo, P., & Bustince, H. (1996). Construction theorems for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 84, 271–281.

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, S., & Hwang, C. (1992). Fuzzy multiple attributes decision making: Methods and applications. Berlin: Springer.

    Book  Google Scholar 

  • Chen, T. Y. (2015). IVIF-PROMETHEE outranking methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Fuzzy Optimization and Decision Making, 14, 173–198.

    Article  MathSciNet  Google Scholar 

  • Dubois, D., & Prade, H. (1980). Fuzzy sets and systems: Theory and applications. New York: Academic Press.

    MATH  Google Scholar 

  • Gou, X., & Xu, Z. (2016). Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optimization and Decision Making. doi:10.1007/s10700-016-9243-y.

  • Li, D. F. (2005). Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences, 70, 73–85.

    Article  MATH  MathSciNet  Google Scholar 

  • Li, D. F. (2011). Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations. Fuzzy Optimization and Decision Making, 10, 45–58.

    Article  MATH  MathSciNet  Google Scholar 

  • Li, P. K., & Fang, S. C. (2009). A survey on fuzzy relational equations, part I: Classification and solvability. Fuzzy Optimization and Decision Making, 8, 179–229.

    Article  MATH  MathSciNet  Google Scholar 

  • Lin, L., Yuan, X. H., & Xia, Z. Q. (2007). Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. Journal of Computer and System Sciences, 73(1), 84–88.

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, H., & Wang, G. (2007). Multicriteria decision-making methods based on intuitionistic fuzy sets. European Journal of Operational Research, 179, 220–233.

    Article  Google Scholar 

  • Meng, F., & Chen, X. (2016). Entropy and similarity measure for Atannasovs interval-valued intuitionistic fuzzy sets and their application. Fuzzy Optimization and Decision Making, 15, 75–101.

    Article  MathSciNet  Google Scholar 

  • Park, J. H., Cho, H. J., & Kwun, Y. C. (2011). Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optimization and Decision Making, 10, 233–253.

    Article  MATH  MathSciNet  Google Scholar 

  • Pei, Z. (2013). Rational decision making models with incomplete weight information for production line assessment. Information Sciences, 222, 696–716.

    Article  MATH  MathSciNet  Google Scholar 

  • Pei, Z., & Zheng, L. (2012). A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets. Expert Systems with Applications, 39(3), 2560–2566.

    Article  Google Scholar 

  • Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505–518.

    Article  MATH  MathSciNet  Google Scholar 

  • Tan, C., Jiang, Z. Z., Chen, X., et al. (2015). Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making. Fuzzy Optimization and Decision Making, 14, 139–172.

    Article  MathSciNet  Google Scholar 

  • Wan, S.P., Wang, F., & Xu, G., et al. (2016). An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations. Fuzzy Optimization and Decision Making. doi:10.1007/s10700-016-9250-z.

  • Wang, J. C., & Chen, T. Y. (2015). Likelihood-based assignment methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Fuzzy Optimization and Decision Making, 14(4), 425–457.

    Article  MathSciNet  Google Scholar 

  • Wang, X., & Kerre, E. E. (2001a). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 118(3), 375–385.

  • Wang, X., & Kerre, E. E. (2001b). Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems, 118(3), 387–405.

  • Wang, Z., Li, K., & Wang, W. (2009). An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Information Sciemces, 179, 3026–3040.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, Z. J. (2015). Geometric consistency based interval weight elicitation from intuitionistic preference relations using logarithmic least square optimization. Fuzzy Optimization and Decision Making, 14, 289–310.

    Article  MathSciNet  Google Scholar 

  • Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15, 1179–1187.

    Article  Google Scholar 

  • Xu, Z. S., & Cai, X. (2010). Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optimization and Decision Making, 9, 359–381.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy environment. International Journal of General Systems, 35, 417–433.

    Article  MATH  MathSciNet  Google Scholar 

  • Ye, J. (2009). Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Systems with Applications, 36(3), 6899–6902.

    Article  MathSciNet  Google Scholar 

  • Ye, J. (2010). Using an improved measure function of vague sets for multicriteria fuzzy decision-making. Expert Systems with Applications, 37(6), 4706–4709.

    Article  Google Scholar 

  • Zhang, X., & Xu, Z. (2012). A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making, 11, 135–146.

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

The author is grateful for the financial support partly from the NSF Project (No. 51305400) of China, and from the NSF Project (No. LQ12G01008) of Zhejiang Province.

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Authors and Affiliations

  1. Department of Industrial Engineering, Zhejiang University of Technology, Hangzhou, China

    Zhi Pei

  2. Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA

    Zhi Pei

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  1. Zhi Pei
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Correspondence to Zhi Pei.

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Pei, Z. Multi-attribute decision making based on a novel IF point operator. Fuzzy Optim Decis Making 16, 505–524 (2017). https://doi.org/10.1007/s10700-016-9255-7

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