Document Type : Research Paper
Authors
Abstract
The Analytic Hierarchical Process (AHP) determines the relative
importance of a set of alternatives in a multi-criteria decision problem.
AHP has a hierarchial structure and based on pairwise comparisons of
the project alternatives as well as pairwise comparisons of the multi
criteria. Two separate algorithms have been presented for measuring
the inconsistency ratioes of pairwise comparisons matrix and
hierarchical structure. In this paper these algorithms and one of the
approximation methods, have been extended for measuring the
inconsistency ratioes and alternatives’ weights in fuzzy AHP. A
numerical example is used to illustrate these methods.
Keywords
منابع
0. آذر، عادل و حجت فرجی،”علم مدیریت فازی“، مرکز مطالعات مدیریت و بهره وری
. ایران، 0.00
2. اصغرپور، محمد جواد،”تصمیم گیری های چند معیاره“، انتشارات دانشگاه تهران،
.0.00
.. قدسی پور، حسن، " فرایند تحلیل سلسله مراتبی"، انتشارات دانشگاه صنعتی امیر
. کبیر، . 0.0
.. وانگ، لی،”سیستم های فازی و کنترل فازی“، ترجمة محمد تشنه لب و دیگران،
. انتشارات دانشگاه صنعتی خواجه نصیرالدین طوسی، 0.00
5. Buckley, J.J., "Fuzzy hierarchical analysis", Fuzzy Sets and Systems,
Vol. 17, 1985, pp. 233-247.
6. Cebeci, U., "Customer satisfaction of catering service companies in
turkey", Proceedings of the 6th International Conference on ISO 9000 and
TQM (6th ICIT), Glasgow, April 2001, pp. 519-524.
7. Cebeci, U. and C. Kahraman, "Measuring customer satisfaction of
catering service companies using fuzzy AHP: the case of turkey",
Proceedings of International Conference on Fuzzy Systems and Soft
Computational Intelligence in Management and Industrial Engineering,
Istanbul, May 2002, pp. 315-325.
8. Chan, F.T.S., Chan, M.H. and N.K.H. Tang, "Evaluation methodologies
for technology selection", Journal Materials Processing Technology, Vol.
107, 2000, pp. 330-337.
9. Chan, F.T.S., Jiang, B. and N.K.H. Tang, "The development of
intelligent decision support tools to aid the design of flexible
manufacturing systems", International Journal of Production Economics,
Vol. 65, No. 1, 2000, pp. 73-84.
10. Chang, D. Y., "Applications of the extent analysis method on fuzzy
AHP", European Journal of Operational Research, Vol. 95, 1996, pp. 649-
655
11. Chang, C.W., Wu, C.R. and H.L. Lin, "Applying fuzzy hierarchy
multiple attributes to construct an expert decision making process",
Expert Systems with Applications, Volume 36, Issue 4, 2009, Pages 7363-
7368.
12. Cheng, C.H., Yang, K.L. and C.L. Hwang, "Evaluating attack
helicopters by AHP based on linguistic variable weight", European
Journal of Operational Research, Vol. 116, No. 2, 1999, pp. 423-443.
13. Ching-Hsue, C., "Evaluating naval tactical missile systems by fuzzy
AHP based on the grade value of membership function", European
Journal of Operational Research, Vol. 96, No. 2, 1997, pp. 343-350.
14. Dağdeviren, M. and İ. Yüksel, "Developing a fuzzy analytic hierarchy
process (AHP) model for behavior-based safety management",
Information Sciences, Volume 178, Issue 6, 2008, Pages 1717-1733.
محاسبة میزان ناسازگاری ساختار سلسله مراتبی... 999
15. Deng, H., "Multicriteria analysis with fuzzy pairwise comparison",
International Journal of Approximate Reasoning, Vol. 21, No. 3, 1999, pp.
215-231.
16. Kahraman, Ulukan, Z., and E. Tolga, "A fuzzy weighted evaluation
method using objective and subjective measures", Proceedings of
International ICSC symposium on Engeneering of Intelligent systems
(EIS,98), Vol. 1, University of La Laguna, Tenerife, 1998, pp. 57-63.
17. Kahraman, C., Cebeci, U. and D. Ruan, "Multi-attribute comparision of
catering service companies using fuzzy AHP: the case of turkey",
Production Economics, 2004, No.87, pp. 171-184.
18. Kuo, R.J., Chi, S.C. and S.S. Kao, "A decision support system for
selecting convenience store location through integration of fuzzy AHP
and artificial neural network", Computers in Industry, 2002, No. 47, pp.
199-214.
19. Laarhoven, V. and W. Pedrycz, "A fuzzy extension of Saaty,s priority
theory", Fuzzy Sets and Systems, vol. 11,1983, pp. 229-241.
20. Lee, M., Pham, H. AND X. Zhang, "A methodology for priority setting
with application to software development process", European Journal of
Operational Research, Vol. 118, 1999, pp. 375-389.
21. Leung, L.C. and D. Cao, "On consistency and ranking of alternatives in
fuzzy AHP", European Journal of Operational Research, Vol. 124, 2000,
pp. 102-113.
22. Liu, F., "Acceptable consistency analysis of interval reciprocal
comparison matrices", Fuzzy Sets and Systems, Volume 160, Issue 18,
2009, Pages 2686-2700.
23. Mamat N.J.Z. and J.K. Daniel, "Statistical analyses on time complexity
and rank consistency between singular value decomposition and the
duality approach in AHP: A case study of faculty member selection",
Mathematical and Computer Modelling, Volume 46, Issues 7-8, 2007,
Pages 1099-1106.
24. Stam, A., Minghe, S. and M. Haines, "Artificial neural network
representations for hierarchical preference structures", Computers &
Operations Research, Vol. 23, No. 12, 1996, pp. 1191-1201.
25. Wang, Y.M., Elhag, T.M.S. and Z. Hua, "A modified fuzzy logarithmic
least squares method for fuzzy analytic hierarchy process", Fuzzy Sets
and Systems, Volume 157, Issue 23, 2006, Pages 3055-3071.
26. Weck, M., Klocke, F., Schell, H. and E. Roenauver, "Evaluating
alternative production cycles using the extended fuzzy AHP method",
European Journal of Operational Research, Vol. 100, No. 2, 1997, pp. 351-
366
27. Zhu, K.J., Jing, Y. and D.Y. Chang, "A discussion on extent analysis
method and applications of fuzzy AHP", European Journal of
Operational Research, Vol. 116, 1999, pp. 450-456
0. آذر، عادل و حجت فرجی،”علم مدیریت فازی“، مرکز مطالعات مدیریت و بهره وری
. ایران، 0.00
2. اصغرپور، محمد جواد،”تصمیم گیری های چند معیاره“، انتشارات دانشگاه تهران،
.0.00
.. قدسی پور، حسن، " فرایند تحلیل سلسله مراتبی"، انتشارات دانشگاه صنعتی امیر
. کبیر، . 0.0
.. وانگ، لی،”سیستم های فازی و کنترل فازی“، ترجمة محمد تشنه لب و دیگران،
. انتشارات دانشگاه صنعتی خواجه نصیرالدین طوسی، 0.00
5. Buckley, J.J., "Fuzzy hierarchical analysis", Fuzzy Sets and Systems,
Vol. 17, 1985, pp. 233-247.
6. Cebeci, U., "Customer satisfaction of catering service companies in
turkey", Proceedings of the 6th International Conference on ISO 9000 and
TQM (6th ICIT), Glasgow, April 2001, pp. 519-524.
7. Cebeci, U. and C. Kahraman, "Measuring customer satisfaction of
catering service companies using fuzzy AHP: the case of turkey",
Proceedings of International Conference on Fuzzy Systems and Soft
Computational Intelligence in Management and Industrial Engineering,
Istanbul, May 2002, pp. 315-325.
8. Chan, F.T.S., Chan, M.H. and N.K.H. Tang, "Evaluation methodologies
for technology selection", Journal Materials Processing Technology, Vol.
107, 2000, pp. 330-337.
9. Chan, F.T.S., Jiang, B. and N.K.H. Tang, "The development of
intelligent decision support tools to aid the design of flexible
manufacturing systems", International Journal of Production Economics,
Vol. 65, No. 1, 2000, pp. 73-84.
10. Chang, D. Y., "Applications of the extent analysis method on fuzzy
AHP", European Journal of Operational Research, Vol. 95, 1996, pp. 649-
655
11. Chang, C.W., Wu, C.R. and H.L. Lin, "Applying fuzzy hierarchy
multiple attributes to construct an expert decision making process",
Expert Systems with Applications, Volume 36, Issue 4, 2009, Pages 7363-
7368.
12. Cheng, C.H., Yang, K.L. and C.L. Hwang, "Evaluating attack
helicopters by AHP based on linguistic variable weight", European
Journal of Operational Research, Vol. 116, No. 2, 1999, pp. 423-443.
13. Ching-Hsue, C., "Evaluating naval tactical missile systems by fuzzy
AHP based on the grade value of membership function", European
Journal of Operational Research, Vol. 96, No. 2, 1997, pp. 343-350.
14. Dağdeviren, M. and İ. Yüksel, "Developing a fuzzy analytic hierarchy
process (AHP) model for behavior-based safety management",
Information Sciences, Volume 178, Issue 6, 2008, Pages 1717-1733.
محاسبة میزان ناسازگاری ساختار سلسله مراتبی... 999
15. Deng, H., "Multicriteria analysis with fuzzy pairwise comparison",
International Journal of Approximate Reasoning, Vol. 21, No. 3, 1999, pp.
215-231.
16. Kahraman, Ulukan, Z., and E. Tolga, "A fuzzy weighted evaluation
method using objective and subjective measures", Proceedings of
International ICSC symposium on Engeneering of Intelligent systems
(EIS,98), Vol. 1, University of La Laguna, Tenerife, 1998, pp. 57-63.
17. Kahraman, C., Cebeci, U. and D. Ruan, "Multi-attribute comparision of
catering service companies using fuzzy AHP: the case of turkey",
Production Economics, 2004, No.87, pp. 171-184.
18. Kuo, R.J., Chi, S.C. and S.S. Kao, "A decision support system for
selecting convenience store location through integration of fuzzy AHP
and artificial neural network", Computers in Industry, 2002, No. 47, pp.
199-214.
19. Laarhoven, V. and W. Pedrycz, "A fuzzy extension of Saaty,s priority
theory", Fuzzy Sets and Systems, vol. 11,1983, pp. 229-241.
20. Lee, M., Pham, H. AND X. Zhang, "A methodology for priority setting
with application to software development process", European Journal of
Operational Research, Vol. 118, 1999, pp. 375-389.
21. Leung, L.C. and D. Cao, "On consistency and ranking of alternatives in
fuzzy AHP", European Journal of Operational Research, Vol. 124, 2000,
pp. 102-113.
22. Liu, F., "Acceptable consistency analysis of interval reciprocal
comparison matrices", Fuzzy Sets and Systems, Volume 160, Issue 18,
2009, Pages 2686-2700.
23. Mamat N.J.Z. and J.K. Daniel, "Statistical analyses on time complexity
and rank consistency between singular value decomposition and the
duality approach in AHP: A case study of faculty member selection",
Mathematical and Computer Modelling, Volume 46, Issues 7-8, 2007,
Pages 1099-1106.
24. Stam, A., Minghe, S. and M. Haines, "Artificial neural network
representations for hierarchical preference structures", Computers &
Operations Research, Vol. 23, No. 12, 1996, pp. 1191-1201.
25. Wang, Y.M., Elhag, T.M.S. and Z. Hua, "A modified fuzzy logarithmic
least squares method for fuzzy analytic hierarchy process", Fuzzy Sets
and Systems, Volume 157, Issue 23, 2006, Pages 3055-3071.
26. Weck, M., Klocke, F., Schell, H. and E. Roenauver, "Evaluating
alternative production cycles using the extended fuzzy AHP method",
European Journal of Operational Research, Vol. 100, No. 2, 1997, pp. 351-
366
27. Zhu, K.J., Jing, Y. and D.Y. Chang, "A discussion on extent analysis
method and applications of fuzzy AHP", European Journal of
Operational Research, Vol. 116, 1999, pp. 450-456
)