Page 234 - Data Science Algorithms in a Week

218 Abdulrahman Albar, Ahmad Elshennawy, Mohammed Basingab et al.

The final fuzzy rules for subsystem IV are provided in Appendix D. These rules will
become an essential part of the knowledge base for subsystem IV.
The results presented in this section are a critical component of this research, as they
provide validation for the design intent of the framework, and show that the consensus
rates for rule assessments are good, necessitating only seven re-evaluations among the
initial 137 rules. The average consensus rate was 72% or better between each of the four
subsystems, which further highlights the consistency of results. It was observed that the
average consensus rate decreased noticeably in subsystems where there were either an
increase in assessment classes, more rules, or more complex rules with more conditions
for experts to evaluate. These factors contributed to each subsystem’s complexity,
contributing to the overall decrease in average consensus rate. The assessed fuzzy rules
will build upon the designed fuzzy system by feeding the four different fuzzy engines
from subsystems I-IV with supporting information to link the inputs to the outputs.

FUZZY SYSTEM RESULTS

The fuzzy logic toolbox of Matlab R2015b (Version 2.2.22) was used to construct
and simulate each fuzzy subsystem individually, with data gathered from experts. A
series of 3-D surface plots were generated relating the inputs of each subsystem to their
respective outputs. This was accomplished through the products of the proposed
architecture, including the development of membership functions from quantitative data
collected from experts, and the expert subjective assessment of rules. These generated
surface plots allow for a clearer view of how the different fuzzy subsystems function, and
it makes the relation between inputs more visually accessible. Additionally, the surface
plots allow for determining the outputs of the subsystems in a straightforward manner by
only using inputs, bypassing lengthy calculations. This section provides the results from
the fuzzy logic subsystems and presents the surface plots for the output of the
subsystems.
Figure 21 illustrates the surface of subsystem I, defined by two input axes, patient
complexity and patient demand, and one output axis, ED demand. The values for ED
demand on the surface plot range from 8 to 92, resulting from the centroid method used
for defuzzification. Generally speaking, it can be observed on the surface that ED
demand will increase with patient complexity if patient demand is held constant, and
similarly ED demand will increase with patient demand if patient complexity is held
constant. Interestingly, when patient demand is approaches a value of 1, the ED demand
plateaus when patient complexity is between 1 and 2, unless patient complexity increases.
The step-like structure occurring for patient demand higher than 1 resembles another
local step structure for patient complexity higher than 4, where ED demand cycles
between plateaus and increases until it plateaus near its maximum value. For patient