Skip to main content
Log in

A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Brunelli, M. (2011). A note on the article “Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean” Fuzzy Sets and Systems161 (2010) 1604–1613. Fuzzy Sets and Systems, 176, 76–78.

    Article  MathSciNet  MATH  Google Scholar 

  • Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17, 233–247.

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, D. Y. (1996). Application of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95, 649–655.

    Article  MATH  Google Scholar 

  • Dong, Y. C., & Herrera-Viedma, E. (2015). Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relations. IEEE Transactions on Cybernetics, 45, 780–792.

    Article  Google Scholar 

  • Kwiesielewicz, M. (1998). A note on the fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 95, 161–172.

    Article  MathSciNet  MATH  Google Scholar 

  • Leung, L. C., & Cao, D. (2000). On consistency and ranking of alternatives in fuzzy AHP. European Journal of Operational Research, 124, 102–113.

    Article  MATH  Google Scholar 

  • Liu, F., Zhang, W. G., & Zhang, L. H. (2014). Consistency analysis of triangular fuzzy reciprocal preference relations. European Journal of Operational Research, 235, 718–726.

    Article  MathSciNet  MATH  Google Scholar 

  • Meng, F. Y., & Chen, X. H. (2016). A new method for triangular fuzzy compare wise judgment matrix process based on consistency analysis. International Journal of Fuzzy Systems,. doi:10.1007/s40815-016-0150-8.

    Google Scholar 

  • Meng, F. Y., Tan, C. Q., & Chen, X. H. (2016). Multiplicative consistency analysis for interval reciprocal preference relations: A comparative study. Omega,. doi:10.1016/j.omega.2016.05.006.

    Google Scholar 

  • Ramik, J., & Korviny, P. (2010). Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets and Systems, 161, 1604–1613.

    Article  MathSciNet  MATH  Google Scholar 

  • Saaty, T. L., & Vargas, L. G. (1987). Uncertainty and rank order in the analytic hierarchy process. European Journal of Operational Research, 32, 107–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Ureña, R., Chiclana, F., Morente, J. A., & Herrera-Viedma, E. (2015). Managing incomplete preference relations in decision making: A review and future trends. Information Sciences, 302, 14–32.

    Article  MathSciNet  MATH  Google Scholar 

  • van Laarhoven, P. J. M., & Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11, 229–241.

    Article  MathSciNet  MATH  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 

  • Wang, T. C., & Chen, Y. H. (2008). Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Information Sciences, 178, 3755–3765.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, Y. M., & Chin, K. S. (2008). A linear goal programming priority method for fuzzy analytic hierarchy process and its applications in new product screening. International Journal of Approximate Reasoning, 49, 451–465.

    Article  MATH  Google Scholar 

  • Wang, Y. M., Elhag, T. M. S., & Hua, Z. S. (2006). A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and Systems, 157, 3055–3071.

    Article  MathSciNet  MATH  Google Scholar 

  • Wu, J., & Chiclana, F. (2014a). Visual information feedback mechanism and attitudinal prioritisation method for group decision making with triangular fuzzy complementary preference relations. Information Sciences, 279, 716–734.

    Article  MathSciNet  MATH  Google Scholar 

  • Wu, J., & Chiclana, F. (2014b). Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Systems, 71, 187–200.

    Article  Google Scholar 

  • Xia, M. M., & Xu, Z. S. (2011). Methods for fuzzy complementary preference relations based on multiplicative consistency. Computers and Industrial Engineering, 61, 930–935.

    Article  Google Scholar 

  • Xu, R. (2000). Fuzzy least-squares priority method in the analytic hierarchy process. Fuzzy Sets and Systems, 112, 359–404.

    Article  MathSciNet  Google Scholar 

  • Xu, Z. S. (2001). A practical method for priority of interval number complementary judgment matrix. Operational Research and Management Sciences, 10, 16–19.

    Google Scholar 

  • Xu, Z. S. (2002). A method for priorities of triangular fuzzy number complementary judgement matrices. Fuzzy Systems and Mathematics, 16, 47–50.

    MathSciNet  MATH  Google Scholar 

  • Xu, Z. S. (2004). On compatibility of interval fuzzy preference relations. Fuzzy Optimization and Decision Making, 3, 217–225.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, Z. S. (2005). A procedure for decision making based on incomplete fuzzy preference relation. Fuzzy Optimization and Decision Making, 4, 175–189.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, Z. S. (2010). An integrated model-based interactive approach to FMAGDM with incomplete preference information. Fuzzy Optimization and Decision Making, 9, 333–357.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, Z. S., & Da, Q. L. (2003). An approach to improving consistency of fuzzy preference matrix. Fuzzy Optimization and Decision Making, 2, 3–12.

    Article  MathSciNet  Google Scholar 

  • Xu, Y. J., Li, K. W., & Wang, H. M. (2014). Incomplete interval fuzzy preference relations and their applications. Computers and Industrial Engineering, 67, 93–103.

    Article  Google Scholar 

  • Yager, R. R. (1980). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24, 143–161.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, G. Q., Dong, Y. C., & Xu, Y. F. (2012). Linear optimization modeling of consistency issues in fuzzy group decision making. Expert Systems with Applications, 39, 2415–2420.

    Article  Google Scholar 

Download references

Acknowledgements

The authors first gratefully thank the Associate Editor and the anonymous referees for their valuable and constructive comments which have much improved the paper. This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71571192, 71501189, 71201089, 71271217, and 51204100), the Hunan Province Foundation for Distinguished Young Scholars of China (2016JJ1024), and the Postdoctoral Science Special Foundation of China (2015T80901), the Innovation-Driven Planning Foundation of Central South University (No. 2016CXS027).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fanyong Meng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, F., Chen, X. A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations. Fuzzy Optim Decis Making 17, 49–73 (2018). https://doi.org/10.1007/s10700-016-9262-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-016-9262-8

Keywords

Navigation