DOI QR코드

DOI QR Code

Normalizing interval data and their use in AHP

구간데이터 정규화와 계층적 분석과정에의 활용

Kim, Eun Young;Ahn, Byeong Seok
김은영;안병석

  • Received : 2016.06.07
  • Accepted : 2016.06.13
  • Published : 2016.06.30

Abstract

Entani and Tanaka (2007) presented a new approach for obtaining interval evaluations suitable for handling uncertain data. Above all, their approach is characterized by the normalization of interval data and thus the elimination of redundant bounds. Further, interval global weights in AHP are derived by using such normalized interval data. In this paper, we present a heuristic method for finding extreme points of interval data, which basically extends the method by Entani and Tanaka (2007), and also helps to obtain normalized interval data. In the second part of this paper, we show that the solutions to the linear program for interval global weights can be obtained by a simple inspection. In the meantime, the absolute dominance proposed by the authors is extended to pairwise dominance which makes it possible to identify at least more dominated alternatives under the same information.

Keywords

Normalization;Interval local and global weights;Interval priority weights;Extreme points;Pairwise dominance

References

  1. Ahn, B. S. and H. C. Park, "Establishing Dominance between Strategies with Interval Judgments of State Probabilities," Omega, Vol.49, No.12(2014), 53-59. https://doi.org/10.1016/j.omega.2014.05.007
  2. Ahn, B. S., "Multiattribute Decision Aid with Extended ISMAUT," IEEE Transactions on Systems, Man, and Cybernetics-Part A, Vol.36, No.3(2006), 507-520. https://doi.org/10.1109/TSMCA.2005.851346
  3. Arbel, A., "Approximate Articulation of Preference and Priority Derivation," European Journal of Operational Research, Vol.43, No.3(1989), 317-326. https://doi.org/10.1016/0377-2217(89)90231-2
  4. Campos, L., J. Huete and S. Moral, "Probability Intervals: A Tool for Uncertain Reasoning," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.2, No.2(1994), 167-196. https://doi.org/10.1142/S0218488594000146
  5. Entani, T. and H. Tanaka, "Interval Estimations of Global Weights in AHP by Upper Approximation," Fuzzy Sets and Systems, Vol.158, No.17(2007), 1913-1921. https://doi.org/10.1016/j.fss.2007.04.007
  6. Li, D. Q., J. Y. Wang and H. X. Li, "Note on On the Normalization of Interval and Fuzzy Weights," Fuzzy Sets and Systems, Vol.160, No.18(2009), 2722-2725. https://doi.org/10.1016/j.fss.2009.03.009
  7. Pavlacka, O., "On Various Approaches to Normalization of Interval and Fuzzy Weights," Fuzzy Sets and Systems, Vol.243, No.5(2014), 110-130. https://doi.org/10.1016/j.fss.2013.07.026
  8. Sugihara, K., H. Ishii and H. Tanaka, "Interval Priorities in AHP by Interval Regression Analysis," European Journal of Operational Research, Vol.158, No.3(2004), 745-754. https://doi.org/10.1016/S0377-2217(03)00418-1
  9. Tanaka, H., K. Sugihara and Y. Maedab, "Non-additive Measures by Interval Probability Functions," Information Sciences, Vol.164, No.1-4(2004), 209-227. https://doi.org/10.1016/j.ins.2003.06.001
  10. Wang, Y. M. and T. M. S. Elhag, "On the Normalization of Interval and Fuzzy Weights," Fuzzy Sets and Systems, Vol.157, No.18(2006), 2456-2471. https://doi.org/10.1016/j.fss.2006.06.008