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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
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