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Effects of normalization on the entropy-based TOPSIS method
Abstract
Abstract In this paper, the frequently used normalization methods for the entropy method (EM) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) when these two methods are used in combination with each other are summarized. Taking information entropy (IE) as an indicator to measure the diversity of attribute data (DAD), the effects of normalization on the entropy-based TOPSIS method are analyzed. It is found that normalization can affect the decision result by affecting the DAD, while the DAD affects the contribution of attributes to the distance of each alternative from the ideal solution and the negative ideal solution, manifested in that the higher the DAD is, the bigger the contribution of the attribute will be. It is proved that vector normalization (VN) and sum normalization (SN) will not change the DAD, whereas min-max normalization (MMN) not only will change the DAD, but also may cause the appearance of numerous zero values, finally resulting in the fact that the calculated results of IE cannot represent the diversity of raw data. Therefore, normalization is not suggested for the EM, and VN is suggested for TOPSIS method. Some discussions on the combinability between the EM and TOPSIS method are also given as well as the applicability of different normalization methods in TOPSIS method.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
The Analytic Hierarchy Process
SAATY, T. L., & KEARNS, K. P. (1985) · Analytical Planning · doi:10.1016/b978-0-08-032599-6.50008-8 · Cited by 15,357
Multiple Attribute Decision Making: Methods and Applications
Chen, S.-J. J., Hwang, C. L., Beckmann, M. J., & Krelle, W. E. (1981) · Medical Entomology and Zoology · Cited by 8,207
Extensions of the TOPSIS for group decision-making under fuzzy environment
Chen, C.-T. (2000) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(97)00377-1 · Cited by 3,844
Determining objective weights in multiple criteria problems: The critic method
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995) · Computers & Operations Research · doi:10.1016/0305-0548(94)00059-h · Cited by 3,413
A state-of the-art survey of TOPSIS applications
Behzadian, M., Khanmohammadi Otaghsara, S., Yazdani, M., & Ignatius, J. (2012) · Expert Systems with Applications · doi:10.1016/j.eswa.2012.05.056 · Cited by 2,690
The Analytic Hierarchy Process: Structuring, Measurement, and Synthesis
Wang, J., Chakraborty, C., & Ouyang, H. (2011) · Encyclopedia of Decision Making and Decision Support Technologies · doi:10.4018/9781599048437.ch003 · Cited by 1,328
Linear Programming Techniques for Multidimensional Analysis of Preferences
Srinivasan, V., & Shocker, A. D. (1973) · Psychometrika · doi:10.1007/bf02291658 · Cited by 681
Fuzzy TOPSIS method for ranking renewable energy supply systems in Turkey
Şengül, Ü., Eren, M., Eslamian Shiraz, S., Gezder, V., & Şengül, A. B. (2015) · Renewable Energy · doi:10.1016/j.renene.2014.10.045 · Cited by 557
Comparative analysis of MCDM methods for the assessment of sustainable housing affordability
Mulliner, E., Malys, N., & Maliene, V. (2016) · Omega · doi:10.1016/j.omega.2015.05.013 · Cited by 529
Cited by
Ufa State Petroleum Technological University, U., & Mukhametzyanov, I. (2021) · Decision Making: Applications in Management and Engineering · doi:10.31181/dmame210402076i · Cited by 343
Metadata
- Authors
- Chen, P.
- Venue
- Expert Systems with Applications
- Publisher
- Elsevier BV
- Published
- 2019-12
- Volume
- 136
- Pages
- 33-41
- ISSN
- 0957-4174 (ISSN-L)
- OpenAlex
- W2950458763
- Cited by
- 404
- References
- 24
- FWCI
- 26.29
- Type
- journal article
- Language
- en
- Open access
- closed
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