Abstract
The optimal priority method of the grey interval preference relation (GIPR) is proposed. In this chapter, based on the proposed multiplicative consistent conditions of GIPR, we construct three optimal models to get the priority of the GIPR. This method can reduce the information distortion of the operations of grey intervals. It is illustrated by a numerical example to show the feasibility and effectiveness of the proposed method.
The work is supported by the National Natural Science Foundation of China (No.70901043,No.70873063,No.60804047), Qing Lan Project (No.0911), Humanities and Social Sciences Foundation of Ministry of Education of China, Philosophical and Social Science Foundation of Higher Education of Jiangsu Province of China under Grant (09SJB630043,09SJD630059), Foundation of Nanjing University of Information Science and Technology (SK20080114, 20070122), Research Program of Humanities and Social Sciences at Universities of Anhui Province (2008SK180). Meteorological Soft Science Foundation of China Meteorological Administration (GQR2009023).
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References
Dubois, D., Prade, H.: Operations on fuzzy numbers. International Journal Systems Science 6, 613–626 (1978)
Gong, Z.W.: Least square method to priority of the fuzzy preference relation with incomplete information. International Journal of Approximate Reasoning 47, 258–264 (2008)
Gong, Z.W., Liu, S.F.: Research on consistency and priority of interval number complementary judgment matrix. Chinese Journal of Management Science 14, 64–68 (2006)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)
Lin, Y., Chen, M.-Y., Liu, S.-F.: Theory of grey systems: capturing uncertainties of grey information. Kybernetes: The International Journal of Systems and Cybernetics 33(2), 196–218 (2004)
Lin, Y., Liu, S.F.: Solving Problems with incomplete information: a grey systems approach. In: Advances in Imaging and Electron Physics, vol. 141, pp. 77–174. Elsevier, Oxford (2006)
Liu, S.F., Lin, Y.: Grey Information: Theory and Practical Applications. Springer, London (2006)
Liu, S.F., Guo, T.B., Dang, Y.G.: The Grey System Theory and Applications. Science Press, Beijing (2000)
Moore, R.E.: Interval Analysis. Prentice-Hall, Enblewood Cliffs (1966)
Qin, J.Y., Lv, Y.J.: The concepts and the nature of weak consistency, consistency in the gray-AHP. Systems Engineering Theory & Practice 28, 159–165 (2008)
Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Sugihara, K., Ishii, H., Tanaka, H.: Interval priorities in AHP by interval regression analysis. European Journal of Operational Research 158, 745–754 (2004)
Wang, L.F., Xu, S.B.: The Introduction to Analytic Hierarchy Process. China Renmin University Press, Beijing (1990)
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Gong, Z., Yao, T., Cao, J., Li, L. (2010). On the Priority Models of the Grey Interval Preference Relation. In: Liu, S., Forrest, J.YL. (eds) Advances in Grey Systems Research. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13938-3_2
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DOI: https://doi.org/10.1007/978-3-642-13938-3_2
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