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a close relationship between people or things that
have similar qualities, structures, properties,
appearances or features. In this paper we call it
indirect affinity. Simply speaking, affinity represents
the closeness/distances between any two objects. We
only use the direct affinity modelling to predict the
time series generated by actual arrival of emergent
patient, and the performance of affinity model is
compared with that of neural network (NN) model
(Kim and Han, 2000). Interestingly, the errors of
affinity model are smaller than those of the NN
model. Thus, exploring and developing affinity
models are valuable in the very near future.
This paper is organized as follows: in Section 2, we
show the technical background for this study,
including the necessary affinity definitions. In
Section 3, an actual example of emergent patient
arrival is presented. Two types of models: NN model
and affinity model are both used to predict the time
series; furthermore, their performances are
compared. Finally, conclusions and
recommendations are in Section 4.
2 TECHNICAL BACKGROUND
In this section, we will simply review two prediction
models: affinity model and NN model.
2.1 Basic Concepts of Affinity
Here, the basic definitions are shortly reviewed
(Larbani and Chen, 2006).
Definition 2.1. Affinity Function.
Let e be an object and A be an affinity set,
respectively. The affinity between e and A is
represented by a function that we call affinity
function.
e
A
M ( . ): [0,+
] → [0,1]
t
→
e
A
M (t)
The value
e
A
M (t) expresses the degree or
strength of the affinity between object e the affinity
set A at time t. When
e
A
M (t) = 1 this means that the
object e satisfies completely the affinity that
characterizes A. When
e
A
M (t) = 0 this means that e
doesn’t satisfy the affinity characterizing A at all at
times t. When 0 <
e
A
M (t) < 1, this means that e
satisfies partially the affinity characterizing A at
time t.
Definition 2.2. The Universal Affinity Set.
The universal affinity set, denoted by U, is the
affinity set defined by the fundamental principle of
existence, that is,
e
U
M (t)=1, for all existing objects
at time t, and for all times t, that is, past present and
future.
Often in real problems the complete affinity
satisfaction
e
A
M (t)=1 may not be reached in real-
world situations for a given affinity set A and an
object e.
Definition 2.3. k-t-Core of a Affinity Set.
Let A be an affinity set and
]1,0[∈k . We say that
an object/element e is in the k-t-core of the affinity
set A at time t, denoted by k-t-core(A), if
e
A
M (t) ≥
k, that is, the k-t-core of A at time t is the traditional
set k-t-core(A)=
kte
e
≥)(M|
A
. When k =1, the
1-t- core(A) is simply called the core of A at time t,
denoted by t-core(A). The content of an affinity set
can be defined at any time by its membership
function. Let us give a formal definition of this
function. The k could be pre-decided or be viewed
as a decision value according to various problems.
Definition 2.4. Function Defining an Affinity Set.
Let A be a affinity set then the affinity defining A
can be characterized by the following function
R
A
(., .): U×[0, +∞] → [0,1] (1)
(e, t) → R
A
(e, t)=
e
A
M (t)
called affinity function.
In general, in real world situations, some
traditional referential set V, such that when an object
e is not in V,
e
A
M (t)=0 for all t, can be
determined, then the affinity defining A can be
defined by the following function
R
A
(., .): V×[0, +∞[→ [0,1]
(e, t) → R
A
(e, t)=
e
A
M (t)
We had larned earlier in Section 1 there are two
types of affinity : indirect affnity and direct affinity.
In this study, we only use the direct affinity for
modelling, which are briefly introduced as follows.
Definition 2.5. Let V and I be a referential set and a
subset of the time axis [0, +
∞ [ respectively. A time
dependent fuzzy relation R such that
(.)R
.) , (.
]1,0[V)(VI: →
(2)
)(R)),(,(
),(
tset
se
→
is called direct affinity on the referential V.
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