Date of Award
Master of Science (MS)
Mathematics and Statistics
James C. Byden
David S. Watkins
Since the introduction of Shannon's Entropy Function in a non-probabilistic setting [l], there has been an expectancy that it will provide a useful measure for the fuzzy cluster validity problem. We hope to demonstrate here (empirically) by Monte Carlo simulation that the entropy Hc(U) of fuzzy c-partitions (U) defined below has expectaction
E(Hc(U)) = ∑ck=2 1/k
Var(Hc(U)) = 1/n(∑ck=2 1/k2 - (c-1)/(c+1)(π2/6) - 1).
Furthermore, for sufficiently large n, that H is approximately normal.
In this report we propose a method which generates the required fuzzy matrix needed for the simulation. After we finish the simulation, we shall study the empirical distribution of Hc(U) at c=2 and 3 using statistical hypothesis testing.
Fu-Charo, Pan, "On the Sampling Distribution of Entropy Function" (1979). All Graduate Plan B and other Reports. 1174.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .