Research review on Saaty's comments on fuzzy logic is not applicable to analytic hierarchy process

ZHU Ke-yu, YANG Shan-lin

Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (1) : 197-206.

PDF(977 KB)
PDF(977 KB)
Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (1) : 197-206. DOI: 10.12011/1000-6788(2014)1-197

Research review on Saaty's comments on fuzzy logic is not applicable to analytic hierarchy process

  • ZHU Ke-yu, YANG Shan-lin
Author information +
History +

Abstract

Fuzzy analytic hierarchy process has been widely used in many fields, but Thomas L. Saaty, the architect of AHP, questioned the validity of fuzzy AHP and had published three articles which show the invalidity of using fuzziness with the AHP. In this paper, we review Saaty's comments on fuzzy AHP from three aspects: fuzzy AHP is lack of mathematical validity; the judgments in AHP are themselves already fuzzy and fuzzy them again has no meaning; improving inconsistency need not improve the validity of the outcome. Through this paper, we do further analysis on both AHP and fuzzy. We hope it will make some help for decision-makers when using AHP.

Key words

AHP / fuzzy AHP / fuzzy logic / fuzzy number

Cite this article

Download Citations
ZHU Ke-yu , YANG Shan-lin. Research review on Saaty's comments on fuzzy logic is not applicable to analytic hierarchy process. Systems Engineering - Theory & Practice, 2014, 34(1): 197-206 https://doi.org/10.12011/1000-6788(2014)1-197

References

[1] Van Laarhoven P J M, Pedrycz W. A fuzzy extension of Saaty's priority theory[J]. Fuzzy Sets and Systems, 1983(1): 229-241.
[2] Saaty T L. There is no mathematical validity for using fuzzy number crunching in the analytic hierarchy process[J]. Journal of Systems Science and Systems Engineering, 2006, 15(4): 457-464.
[3] Saaty T L, Tran L T. On the invalidity of fuzzifying numerical judgments in the analytic hierarchy process[J]. Mathematical and Computer Modelling, 2007, 46(7-8): 962-975.
[4] Saaty T L, Tran L T. Fuzzy judgments and fuzzy sets[J]. International Journal of Strategic Decision Sciences, 2010, 1(1): 23-40.
[5] 高会生,冉静学,孙逸群.基于改进的FAHP 电力通信网风险评估[J]. 系统工程理论与实践, 2008, 28(3): 133-138.Gao H S, Ran J X, Sun Y Q. Risk evaluation of communication network of electric power based on improved FAHP[J]. Systems Engineering——Theory & Practice, 2008, 28(3): 133-138.
[6] Saaty T L. Principia mathematica decernendi: Mathematical principles of decision making[M]. RWS Publications, Pittsburgh, 2010.
[7] 姚敏,张森.模糊一致矩阵及其在软科学中的应用[J].系统工程, 1997, 15(2): 54-57.Yao M, Zhang S. Fuzzy consistent matrix and its applications in soft science[J]. Systems Engineering, 1997, 15(2): 54-57.
[8] Nurmi H. Approaches to collective decision making with fuzzy preference relations[J]. Fuzzy Sets and Systems, 1981, 6(3): 249-259.
[9] Bezdek J C, Spillman B, Spillman R. A fuzzy relation space for group decision theory[J]. Fuzzy Sets and Systems, 1978, 1(4): 255-268.
[10] Dubois D, Prade H. Operations on fuzzy numbers[J]. International Journal of Systems Science, 1978, 9(6): 613-626.
[11] Chang D Y. Applications of the extent analysis method on fuzzy AHP[J]. European Journal of Operational Research, 1996(3): 649-655.
[12] Buckley J J. Fuzzy hierarchical analysis[J]. Fuzzy Set and Systems, 1985, 17: 233-247.
[13] Buckley J J, Feuring T, Hayashi Y. Fuzzy hierarchical analysis revisited[J]. European Journal of Operational Research, 2001, 129: 48-64.
[14] 朱建军,王梦光,刘士新. AHP 判断矩阵一致性改进的若干问题研究[J].系统工程理论与实践, 2007, 27(1): 18-22.Zhu J J, Wang M G, Liu S X. Research on consistency modification problem of comparison matrix in the analytical hierarchy process[J]. Systems Engineering——Theory & Practice, 2007, 27(1): 18-22.
[15] 姚敏,张森.模糊一致矩阵及其在决策分析中的应用[J].系统工程理论与实践, 1998, 18(5): 78-81.Yao M, Zhang S. Fuzzy consistent matrix and its application in decision making[J]. Systems Engineering——Theory & Practice, 1998, 18(5): 78-81.
[16] 张吉军.模糊层次分析法(FAHP)[J].模糊系统与数学, 2004, 14(2): 80-88.Zhang J J. Fuzzy analytical hierarchy process[J]. Fuzzy Systems and Mathematics, 2004, 14(2): 80-88.
[17] 罗震波.基于模糊层次分析法的变电站选址理论与应用技术[D].大庆:大庆石油学院, 2009.Luo Z B. Theory and application technology about selection of substation location based on the fuzzy analytic hierarchy process[D]. Daqing: Daqing Shiyou University, 2009.
[18] 彭祖赠, 孙韫玉.模糊数学及其应用[M]. 2版.武汉: 武汉大学出版社, 2007.Peng Z Z, Sun W Y. Fuzzy mathematics and its application[M]. 2nd ed. Wuhan: Wuhan University Press, 2007.
[19] Wang Y M, Chin K S. Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology[J]. International Journal of Approximate Reasoning, 2011, 52(4): 541-553.
PDF(977 KB)

529

Accesses

0

Citation

Detail

Sections
Recommended

/