Abstract
In AHP, there exists the problem of pair-wise consistency where evaluations by pair-wise comparison are presented with crisp value. We propose the interval AHP model with interval data reflecting Rough Set concept. The proposed models are formulated for analyzing interval data with two concepts (necessity and possibility). According to necessity and possibility concepts, we obtain upper and lower evaluation models, respectively. Furthermore, even if crisp data in AHP are given, it is illustrated that crisp data should be transformed into interval data by using the transitive law. Numerical examples are shown to illustrate the interval AHP models reflecting the uncertainty of evaluations in nature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Satty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Cheng, C.H., Mon, D.L.: Evaluating weapon system by Analytical Hierarchy Process basedon fuzzy scales. Fuzzy Sets and System 63, 1–10 (1994)
Onishi, S., Imai, H., Kawaguchi, M.: Evaluation of a stability on weights of fuzzy analytic hierarchy process using a sensitivity analysis. J. of Japan Society for Fuzzy Theory and Systems 9(1), 140–147 (1997) (in Japanese)
Pawlak, Z.: Rough Sets -Theoretical Aspects of Reasoning about Data. Kluwer Academic Publichers, Dordrecht (1991)
Tanaka, H., Guo, P.: Possibilistic Data Analysis for Operations Research. Physica- Verlag(A Springer-verlag Company), Heidelberg (1999)
Maeda, Y., Tanaka, H.: Non-additive probability measures with interval density functions. J. of Japan Society for Fuzzy Theory and Systems (to appear) (in Japanese)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sugihara, K., Maeda, Y., Tanaka, H. (1999). Interval Evaluation by AHP with Rough Set Concept. In: Zhong, N., Skowron, A., Ohsuga, S. (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. RSFDGrC 1999. Lecture Notes in Computer Science(), vol 1711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48061-7_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-48061-7_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66645-5
Online ISBN: 978-3-540-48061-7
eBook Packages: Springer Book Archive