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Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making

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Abstract

Intuitionistic fuzzy numbers (IFNs) have already been applied to many fields, especially in multi-attribute decision making (MADM). Based on the basic operational laws and information aggregation methods of IFNs, MADM with intuitionistic fuzzy information has become more and more popular. In this paper, we investigate the MADM problems where the attribute values take the form of interval numbers and the weight information on the attributes are expressed as IFNs. We first propose a novel exponential operational law based on IFNs and interval numbers, and then study some of its desirable properties. Based on the exponential operational law, we put forward an intuitionistic fuzzy weighted exponential aggregation operator, and utilize it to develop a MADM method. Finally, we apply our method to solve the decision making problem under uncertainty.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov, K. (1999). Intuitionistic fuzzy sets: Theory and applications. Heidelberg: Physica.

    Book  MATH  Google Scholar 

  • Bustince, H., Herrera, F., & Montero, J. (2008). Fuzzy sets and their extensions: Representation aggregation and models. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Chen, S. M., & Tan, J. M. (1994). Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets and Systems, 67, 163–172.

    Article  MathSciNet  MATH  Google Scholar 

  • Da, Q. L., & Liu, X. W. (1999). Interval number linear programming and the satisfactory solution. Systems Engineering-Theory & Practice, 19, 3–7.

    Google Scholar 

  • Da, Q. L., & Xu, Z. S. (2002). Single-objective optimization model in uncertain multi-attribute decision making. Journal of Systems Engineering, 17, 50–55.

    Google Scholar 

  • Hong, D. H., & Choi, C. H. (2000). Multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114, 103–113.

    Article  MATH  Google Scholar 

  • Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making and applications. New York: Springer.

    Book  MATH  Google Scholar 

  • Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. Upper Saddle River, NJ: Prentice Hall.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Li, D. F., Chen, G. H., & Huang, Z. G. (2010). Linear programming method for multi-attribute group decision making using IF sets. Information Sciences, 180, 1591–1609.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, B. S., Shen, Y. H., Chen, Y., Chen, X. H., & Wang, Y. M. (2015). A two-layer weight determination method for complex multi-attribute large-group decision making experts in a linguistic environment. Information fusion, 23, 156–165.

    Article  Google Scholar 

  • Meng, F. Y., Tan, C. Q., & Zhang, Q. (2014). An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators. Journal of Intelligent & Fuzzy System: Applications in Engineering and Technology, 26, 769–780.

    MathSciNet  MATH  Google Scholar 

  • Singh, N. P., & Singh, B. (2014). Vertical handoff decision in 4G wireless networks using multi-attribute decision making approach. Wireless Networks, 20, 1203–1211.

    Article  Google Scholar 

  • Sun, B. Z., & Ma, W. M. (2015). An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application. Omega, 51, 83–92.

    Article  Google Scholar 

  • Xu, Z. S. (2001). An algorithm of the ranking of fuzzy complementary judgment matrix. Journal of Systems Engineering, 16, 311–314.

    Google Scholar 

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

    Article  Google Scholar 

  • Xu, Z. S. (2015). Uncertain multi-attribute decision making: Methods and applications. Berlin: Springer.

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  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  MathSciNet  MATH  Google Scholar 

  • Xu, R. N., & Zhai, X. Y. (1992). Extensions of the analytic hierarchy process in fuzzy environment. Fuzzy Sets and Systems, 52, 251–257.

    Article  MathSciNet  Google Scholar 

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–356.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank the editors and the anonymous referees for their insightful and constructive comments and suggestions that have led to this improved version of the paper. The work was supported in part by the National Natural Science Foundation of China (Nos. 61273209 and 71571123), and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, China

    Xunjie Gou & Zeshui Xu

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  1. Xunjie Gou
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  2. Zeshui Xu
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Correspondence to Zeshui Xu.

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Gou, X., Xu, Z. Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optim Decis Making 16, 183–204 (2017). https://doi.org/10.1007/s10700-016-9243-y

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