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Managing Overcrowding in Healthcare using Fuzzy Logic 209

These results identify underlying differences between the evaluations of subject
matter experts, which may lead to the introduction of bias when relying on only one
perspective to implement a solution. The expert panel members who responded to each
survey question have different backgrounds and experience rooted in different areas of
emergency departments. These experts view the ER from their different perspective, as
internal and external stakeholders. Relying on only one perspective can lead to
overestimated or underestimated interval values, as seen in some cases such as the one
discussed in question two. The variation in the experts’ responses create foggy areas in
the collected data, which can be modeled by fuzzy logic. Without considering these
variations, data from experts can lead to biased conclusions.

Membership Functions

The database for subsystem I consists of membership functions for both inputs and
the output, and are structured according to the data from Table 6. Variable one, or the
demand status, consists of four trapezoidal membership functions, while variable two,
patient complexity, consists of three trapezoidal membership functions, and variable
three, the ED demand, is the output of the subsystem and has five triangular membership
functions.
The membership function representing patient demand in Figure 11 is constructed
using the fuzzy number intervals and linguistic classes provided in Table 6. For the “low”
linguistic class interval, the minimum value in the upper bound of the low class (as
observed in Table 1) is 0.2 meaning that there is 100% agreement among experts between
the values of 0 and 0.2 for “low”. The maximum value in the upper bound of the low
class is 0.5, yet the minimum value of the lower bound in the medium class is 0.2,
meaning that some experts varied in assigning the term “low” and “medium” between the
interval [0.2, 0.5]. In Figure 11, this accounts for the structure of the low class, where the
core exists between 0 and 0.2, and the support exists between 0.2 and 0.5, overlapping the
support of the medium class. The boundary for the medium class began at 0.2 and ended
at 0.8, while the boundary for the high class was between 0.6 and 1.2, and the boundary
for the very-high class was between 0.92 and 2. The core structures of the medium and
high class are small, compared to the low and very-high classes.
The membership function for patient complexity in Figure 12 was constructed from
the data provided by an expert using reverse interval estimation method. This was done
due to the need for an expert possessing medical expertise in the triage process and
familiarity with the emergency severity index. This expert directly constructed the
membership function, providing data for the three linguistic classes. Patients rated with a
value of 2 or 1 were considered “low” average complexity, and supports of this
membership function consist of patients rated between 2 and 2.5, meaning the boundary