An additive scale model for the analytic hierarchy process

International Journal of Information and Management Sciences

Volumn 20, Issue 1, 2009, Pages 71-88

  Guh, Yuh Yuan ^a   Lou, Kuo Ren ^b   Po, Rung Wei ^c  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b TAMKANG UNIVERSITY   (Taiwan)

^c NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Additive scale; Analytic hierarchy process; Multicriteria; Pairwise comparison scale; Ratio scale; Scale transitivity

Indexed keywords

CURVE FITTING; HIERARCHICAL SYSTEMS; LEAST SQUARES APPROXIMATIONS;

CONSISTENCY INDICES; CORRELATION ANALYSIS; DECISION PROBLEMS; FUZZY MODELS; LEAST SQUARES METHODS; MATHEMATICAL DENOTATIONS; MULTICRITERIA; PAIRWISE COMPARISON SCALE; RATIO SCALE; SCALE MODELS; SCALE MULTIPLIERS; SCALE TRANSITIVITY;

ANALYTIC HIERARCHY PROCESS;

EID: 63549089763     PISSN: 10171819     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (43)

1. Alkahtani, A. M. S., Woodward, M. E. and Al-Begain, K., Prioritised best effort routing with four quality of service metrics applying the concept of the analytic hierarchy process, Comput and Opl Res., Vol. 33, pp.559-580, 2006.
2. Badri, M. A., Abdulla, M. and Al-Madani, A., Information technology center service quality: Assessment and application of SERVQUAL, J. Qual. Reliab Management, Vol. 22, pp.819-848, 2005.
3. Belton, V. and Gear, A. E., On a shortcoming of Saaty' method of analytical hierarchies, Omega, Vol. 11, pp.227-230, 1983.
4. Belton, V. and Gear, A. E. The legitimacy of rank reversal- a comment, Omega, Vol. 13, pp.143-144, 1985.
5. Chow, C.C. and Luk, P., A strategic service quality approach using analytic hierarchy process, Manag Serv Qual, Vol. 15, pp.278-289, 2005.
6. Dodd, F. J., Donegan, H. A and McMaster, T. B. M., Scale horizons in analytic hierarchies, J. Multi-criteria Decis Anal, Vol. 4, pp.177-188, 1995.
7. Donegan, H. A., Dodd, F. J. and McMaster, T. B. M., A new approach to AHP decision-making, Statistician, Vol. 41, pp.295-302, 1992.
8. Fichtner, J., On deriving priority vectors from matrices of pairwise comparisons, Socio-Economic Planning Sci., Vol. 20, pp.341-345, 1986.
9. Forgionne, G. A., Kohli, R. and Jennings, D., An AHP analysis of quality in AI and DSS journals, Omega, Vol. 30, pp.171-183, 2002.
10. Forman, E. H. and Gass, S. L., The analytic hierarchy process-an exposition, Opns Res., Vol. 49, pp.469-486, 2001.
11. Foster, B. and Al-Dubaibi, A., An axiomatic approach to pairwise comparisons. Working paper. Department of Mathematics and Statistics Brunel University, 1995.
12. Harker, P. T. and Vargas, L. G., The theory of ratio scale estimation: Satty analytic hierarchy process, Mngt Sci., Vol. 33, pp.1383-1403, 1987.
13. Ji, P. and Jiang, R., Scale transitivity in the AHP, J. Opl. Res. Soc., Vol. 54, pp.896-905, 2003.
14. Kahraman, C., Cebeci, U. and Ruan, D., Multi-attribute comparison of catering service companies using fuzzy AHP: The case of Turkey, J. Prod. Econs., Vol. 87, pp.171-184, 2004.
15. Kahraman, C., Ertay, T. and Buyukozkan, G., A fuzzy optimization model for QFD planning process using analytic network approach, Eur. J. Opl. Res. Vol. 171, pp.390-411, 2006.
16. Kandal, A., Fuzzy Mathematical Techniques with Application, Addison- Wesley. Mass., 1986.
17. Kaufmann, A., Introduction to the theory of fuzzy subsets, Academic Press, New York, 1975.
18. Kickert, W. J. M., Fuzzy Theories on Decision Making, Martines Nijhoff, Boston, 1987.
19. Klir, G. J. and Folger, T. A., Fuzzy Sets, Uncertainty and Information, Prentice- Hall, London, 1988.
20. Lootsma, F. A., Scale sensitivity in the multiplicative AHP and SMART, J. Multi-criteria Decis Anal., Vol. 2, pp.87-110, 1993.
21. Lootsma, F. A., Multi-criteria Decision Analysis via Ratio and Difference Judgment, Kluwer Academic Publishers: Dordrecht, 1999.
22. Ma, D. and Zheng, X., 9/9-9/1 Scale Method of AHP. Proceedings of the second International Symposium on the AHP, Vol. 1. University of Pittsburgh, Pittsburgh, PA, pp.197-202, 1991.
23. Saaty, T. L. A scaling method for priorities in hierarchical structures, J. Math. Psychol, Vol. 15, pp.234-281, 1977.
24. Saaty, T. L., The Analytic Hierarchy Process. McGraw-Hill, New York, 1980.
25. Saaty, T. L., Axiomatic foundation of the analytic hierarchy process, Management Sci., Vol. 32, pp.841-855, 1986.
26. Saaty, T. L., Highlights and critical points in the theory and application of the analytic hierarchy process, Eur. J. Opl. Res., Vol. 74, pp.426-447, 1994.
27. Salo, A. A. and Hamalainen, R. P., On the measurement of preferences in the analytic hierarchy process, J. Multi-criteria Decis Anal., Vol. 6, pp.309-319, 1997.
28. Sampson, S. E. and Showalter, M. J., The performance-importance response function: Observations and implications, J. Service Industries 1, Vol. 19, pp. 1-25, 1999.
29. Tsaur, S. H. and Lin, Y. C. Promoting service quality in tourist hotels: The role of HRM practices and service behavior, Tourism Management, Vol. 25, pp.471-481, 2004.
30. Torgerson, W. S., Distances and Ratios in Psych-Physical Scaling, Acta Psychological, Vol. XIX, pp.201-205, 1961.
31. Vargas, L. G., An overview of the analytic hierarchy process and its applications, Eur. J. Opl. Res., Vol. 48, pp.2-8, 1990.
32. Zimmermann, H. J., Fuzzy set theory - and its applications, Kluwer-Nijhoff, Boston, 1985.
33. Crawford, G. and Williams, C., A note on the analysis of subjective judgment matrices, J. of Mathematical Psychology, Vol. 29, pp.387-405, 1985.
34. Golany, B., Kress, M.(1993). A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices, Eur. J. Opl Res, 69: 210-220
35. Jensen, R. E., Comparison of Eigenvector, Least squares, Chi square and Logarithmic least square methods of scaling a reciprocal matrix, Working Paper 153, 1983. http://www.trinity.edu/rjensen/127wp/127wp.htm
36. Saaty, T. L. and Vargas, L. G., Comparison of eigenvalues, logarithmic least squares and least squares methods in estimating ratios, Mathematical Modeling, Vol. 5, pp.309-324, 1984.
37. Takeda, E., Cogger, K. O. and Yu, P. L., Estimating criterion weights using eigenvectors: A comparative study, Eur. J. Opl Res., Vol. 29, pp.360-369, 1987.
38. Ali, I., Cook, W. D. and Kress, M., Ordinal ranking and intensity of preference: a linear programming approach, Management Science, Vol. 32, pp. 1642-1647, 1986.
39. Hochbaum, D.S., Walter, A. and A. Levin (2006). Methodologies and algorithms for group rankings decision, http://pluto.mscc.huji.ac.il/~levinas/ nsf.pdf.
40. Chang, P. T. and Lee, E. S., The estimation of normalized fuzzy weights, Computers & Mathematics with Applications, Vol. 29, pp.21-42, 1995.
41. Zhu, K. J., Jing, Y. and Chang, D. Y., A discussion on Extent Analysis Method and applications of fuzzy AHP, European Journal of Operational Research, Vol. 116, pp.450-456, 1999.
42. Mikhailov, L., Group prioritization in the AHP by fuzzy preference programming method, Computers & Operations Research, Vol. 3, pp.293-301, 2004.
43. Wang, Y. M. and Elhag, T. M. S., On the normalization of interval and fuzzy weights, Fuzzy Sets and Systems, Vol. 157, pp.2456-2471, 2006.