Date of Award
1979
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Committee Chair(s)
James C. Byden
Committee
James C. Byden
Committee
David S. Watkins
Abstract
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
and variance
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.
Recommended Citation
Fu-Charo, Pan, "On the Sampling Distribution of Entropy Function" (1979). All Graduate Plan B and other Reports, Spring 1920 to Spring 2023. 1174.
https://digitalcommons.usu.edu/gradreports/1174
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