Comparison of Fuzzy Extent Analysis Technique and its Extensions with Original Eigen Vector Approach

Faran Ahmed, Kemal Kilic

Abstract

Fuzzy set theory has been extensively incorporated in the original Analytical Hierarchical Process (AHP) with an aim to better represent human judgments in comparison matrices. One of the most popular technique in the domain of Fuzzy AHP is Fuzzy Extent Analysis method which utilizes the concept of extent analysis combined with degree of possibility to calculate weights from fuzzy comparison matrices. In original AHP, where the comparison matrices are composed of crisp numbers, Satty proposed that Eigen Vector of these comparison matrices estimate the required weights. In this research we perform a comparison analysis of these two approaches based on a data set of matrices with varying level of inconsistency. Furthermore, for the case of FEA, in addition to degree of possibility, we use centroid defuzzification and defuzzification by using the mid number of triangular fuzzy number to rank the final weights calculated from fuzzy comparison matrices.

References

  1. Ataei, M., Mikaeil, R., Hoseinie, S. H., and Hosseini, S. M. (2012). Fuzzy analytical hierarchy process approach for ranking the sawability of carbonate rock. International Journal of Rock Mechanics and Mining Sciences, 50:83-93.
  2. Boender, C., De Graan, J., and Lootsma, F. (1989). Multicriteria decision analysis with fuzzy pairwise comparisons. Fuzzy sets and Systems, 29(2):133-143.
  3. Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy sets and systems, 17(3):233-247.
  4. Büyüközkan, G., Kahraman, C., and Ruan, D. (2004). A fuzzy multi-criteria decision approach for software development strategy selection. International Journal of General Systems, 33(2-3):259-280.
  5. Chang, D.-Y. (1996). Applications of the extent analysis method on fuzzy ahp. European journal of operational research, 95(3):649-655.
  6. Deng, H. (1999). Multicriteria analysis with fuzzy pairwise comparison. International Journal of Approximate Reasoning, 21(3):215-231.
  7. Ding, Y., Yuan, Z., and Li, Y. (2008). Performance evaluation model for transportation corridor based on fuzzyahp approach. In Fuzzy Systems and Knowledge Discovery, 2008. FSKD'08. Fifth International Conference on, volume 3, pages 608-612. IEEE.
  8. Forman, E. H. and Gass, S. I. (2001). The analytic hierarchy process-an exposition. Operations research, 49(4):469-486.
  9. Golany, B. and Kress, M. (1993). A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices. European Journal of Operational Research, 69(2):210-220.
  10. Kahraman, C., Cebeci, U., and Ulukan, Z. (2003). Multicriteria supplier selection using fuzzy ahp. Logistics information management, 16(6):382-394.
  11. Kilic, K., Sproule, B. A., T ürksen, I. B., and Naranjo, C. A. (2004). Pharmacokinetic application of fuzzy structure identification and reasoning. Information Sciences, 162(2):121-137.
  12. Ross, T. J. (1995). Fuzzy Logic With Engineering Applications. Mcgraw-Hill College, first edition edition.
  13. Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation (Decision Making Series). Mcgraw-Hill (Tx).
  14. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. Systems, Man and Cybernetics, IEEE Transactions on, (1):116-132.
  15. Tang, Y.-C., Beynon, M. J., et al. (2005). Application and development of a fuzzy analytic hierarchy process within a capital investment study. Journal of Economics and Management, 1(2):207-230.
  16. Tsaur, S.-H., Chang, T.-Y., and Yen, C.-H. (2002). The evaluation of airline service quality by fuzzy mcdm. Tourism management, 23(2):107-115.
  17. Uncu, O., Kilic, K., and Turksen, I. (2004). A new fuzzy inference approach based on mamdani inference using discrete type 2 fuzzy sets. In Systems, Man and Cybernetics, 2004 IEEE International Conference on, volume 3, pages 2272-2277. IEEE.
  18. Uncu, O., Turksen, I., and Kilic, K. (2003). Localm-fsm: A new fuzzy system modeling approach using a two-step fuzzy inference mechanism based on local fuzziness level. In Proceedings of international fuzzy systems association world congress, pages 191-194.
  19. Van Laarhoven, P. and Pedrycz, W. (1983). A fuzzy extension of saaty's priority theory. Fuzzy sets and Systems, 11(1):199-227.
  20. Wang, Y.-M., Elhag, T., and Hua, Z. (2006). A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and Systems, 157(23):3055-3071.
  21. Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3):338 - 353.
  22. Zhü, K. (2014). Fuzzy analytic hierarchy process: Fallacy of the popular methods. European Journal of Operational Research, 236(1):209-217.
Download


Paper Citation


in Harvard Style

Ahmed F. and Kilic K. (2016). Comparison of Fuzzy Extent Analysis Technique and its Extensions with Original Eigen Vector Approach . In Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS, ISBN 978-989-758-187-8, pages 174-179. DOI: 10.5220/0005868401740179


in Bibtex Style

@conference{iceis16,
author={Faran Ahmed and Kemal Kilic},
title={Comparison of Fuzzy Extent Analysis Technique and its Extensions with Original Eigen Vector Approach},
booktitle={Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS,},
year={2016},
pages={174-179},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005868401740179},
isbn={978-989-758-187-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS,
TI - Comparison of Fuzzy Extent Analysis Technique and its Extensions with Original Eigen Vector Approach
SN - 978-989-758-187-8
AU - Ahmed F.
AU - Kilic K.
PY - 2016
SP - 174
EP - 179
DO - 10.5220/0005868401740179