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Managing Overcrowding in Healthcare using Fuzzy Logic 201

functions; “Inadequate”, “Partially adequate”, and “Adequate”, which are assessed on the
intervals [0, 0.32], and [0, 50], respectively, with trapezoidal functions. With these
membership functions, the total number of fuzzy rules in this subsystem will be 9 rules
2
(3 ). The output of the fuzzy subsystem two is ED staffing status. The output is
represented by the same three membership functions; “Inadequate”, “Partially adequate”,
and “Adequate”, and is evaluated on a trapezoidal function with the interval [0, 100]. The
ED staffing status is an intermediate variable that feeds the third fuzzy subsystem with a
crisp value, which will serve as another variable for the assessment of the ED workload.
Finally, the ED workload will feed into the fourth fuzzy subsystem.

Figure 6: Fuzzy logic subsystem I. Figure 7: Fuzzy logic subsystem II.

The third fuzzy logic subsystem evaluates the ED workload. The three inputs of this
fuzzy subsystem are ED staffing level, ER occupancy rate, and average complexity of
patients who are being treated in the emergency room. It should be noted that the third input
shares the same characteristics of the second input of subsystem one, with the difference
being that the populations of these similar inputs are separate. Figure 8 illustrates the
components of fuzzy subsystem III. The ED staffing status, input one, is the output from
subsystem II, and is represented by three membership functions; “Inadequate”, “Partially
adequate”, and “Adequate”. Using the same membership function, this input is evaluated with
a trapezoidal function on the interval [0, 100]. The ER occupancy rate, which is an
independent input, is characterized by four membership functions; “Low”, “Medium”,
“High”, and “Very High”. The occupancy rate is evaluated with a trapezoidal function in the
interval [0, 100]. The third input, patient complexity shares characteristics from the second
input to the fuzzy subsystem I, as previously mentioned. Therefore, this third input is
represented by three membership functions; “Low”, “Medium”, and “High”, and is evaluated
with a trapezoidal function in the interval [1, 5]. With the three sets of membership indicators
2
in this subsystem, the number of fuzzy rules will now reach 36 rules (3 ×4). The single output
of the third fuzzy logic subsystem is the ED workload. It is represented by four membership
functions; “Low”, “Medium”, “High”, and “Very High”. As other outputs are evaluated in