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Managing Overcrowding in Healthcare using Fuzzy Logic 211

partially adequate class has the smallest core area, and the supports for all classes are
similar in size relative to each other.

Figure 13: Membership function of ED demand. Figure 14: Membership function of physician
staffing.

The second input in subsystem II, nurse staffing, is represented by the membership
functions in Figure 15. The inadequate class boundaries are at 0 and 0.18, with the core
structure representing full membership existing between 0 and 0.8. The partially adequate
class lies between boundaries of 0.8 and 0.32, while the core area exists between 0.18 and
0.24. For the adequate class, the boundaries lie at 0.24 and 0.5, with the core structure
existing between 0.32 and 0.5. It is apparent that the adequate class has the largest core
area, meaning that the adequate linguistic term was given the widest variety of interval
values for full membership, while values that defined the partially adequate class were
more restrictive.
Figure 16 contains the membership functions for the output of the subsystem ED
staffing. The membership functions are trapezoidal, but the intervals are assigned to
create similarly sized membership classes. In this figure, the boundaries for the
inadequate class lie between 0 and 35, with the core existing between 0 and 25,
representing a full degree of membership. The boundaries for the partially adequate class
are 25 and 75, with the core existing between 35 and 65. For the adequate class, the
boundaries are 65 and 100, with the core area defined between 75 and 100. It can be
noted that the midpoint between the boundaries for the partially adequate class lies at 50,
which is the halfway point on the ED staffing axis, further demonstrating the uniformity
in the membership functions.

Figure 15: Membership function of nurse staffing. Figure 16: Membership function of ED staffing.