I used different methods for generating the criteria’s weight in MCDM methods. Results demonstrate that the rate of changing in the weight of the criteria in the Shannon entropy method is negligible (changing the weight of the results are very low). does anyone know about the reason for the results?
http://www.mdpi.com/1099-4300/17/7/4664/pdf
https://arxiv.org/pdf/1609.00110
Dear Farzin,
I suggest you to see links and attached file in subject.
-Entropy | Free Full-Text | Objective Weights Based on Ordered Fuzzy ...
www.mdpi.com/1099-4300/19/7/373/htm -evaluation of sustainable development indicators ... - Semantic Scholar
https://pdfs.semanticscholar.org/.../a7945981f5ee44fa4fb24200c9...
-Hamming Distance Method with Subjective and Objective ... - NCBI - NIH
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3977101/
Best regards
Dear Farzin
Interesting question. I have been thinking about it and I don't have an answer, but simply some reasoning that may help to understand the difference
Weights from eigenvalues or by geometric mean belong to the domain if linear algebra.
Weights from Shannon entropy come from using logarithms of probabilities.
In addition to that is the meaning of values obtained from both methods.
Weights from eigenvalue represent trade-offs, and they are not weights for criteria.
Values from entropy are related with the quantity of information contained in a message, and they are not weights for criteria
In MCDM entropy measures the quantity of information content in a message or in a series of numbers in a criterion.
From this point of view entropy measures the dispersion or discrimination of values in a criterion, which is the only way for a criterion to evaluate an alternative.
Your question of why entropy produces negligible differences when varying data lies, in my humble opinion, in the very structure and definition of logarithms
http://www.mdpi.com/1099-4300/17/7/4664/pdf
https://arxiv.org/pdf/1609.00110
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