B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 139

regarded as B cells that are interacting with one another through stimulation and
suppression functions. Training algorithm uses same operations as defi ned in the
earlier model.

5.2.3.3 Fuzzy Immune Network Model

Nasraoui et al. (2002) proposed an IN model that deals with uncertainty and
fuzziness inherent in the matching process between antibodies and antigens, which
is called a fuzzy artifi cial immune system (AIS), and is based on the AINE model
of Timmis et al. (2002). In AINE, an IN consists of a set of interconnected ARBs,
where each ARB is composed of identical B cells. Also, each ARB represents a
single n -dimensional data item that may be stimulated by an antigen or another
ARB. A link between two ARBs is created if the a nity between them is below a
NAT, which is defi ned as the average distance between all the antigen items in the
dataset provided as input to the training process. Antigen-ARB matching and the
matching between ARBs are computed using an Euclidean distance. Also, when an
ARB gets stimulated above the threshold, it undergoes some cloning and mutation
processes. In addition, in AINE, the ARBs compete for a fi nite number of resources
(B cells); thus, resources are allocated to ARBs as a function of their stimulation
levels. Besides, ARBs that are not given any resources (i.e., have low stimulation
level) are removed from the network. h e purpose of the ARB concept is to reduce
the granularity of the model. However, the ARB population grows at a prolifi c rate
and it tends to converge rather prematurely to a network where a small number of
internal images of the antigens overtake the entire population due to the resource
allocation mechanism (Nasraoui et al., 2002).
In contrast to ARB, a fuzzy ARB does not represent a single data item but
a fuzzy set over a universe of discourse defi ned by the input training data. h e
membership function associated to the fuzzy set is a radial-basis-type of function,
which decreases with the distance to the point that represents the center of the
ARB. In contrast to AINE, each fuzzy ARB is allowed to have its own radius of
infl uence, denoted as σ . Particularly, the membership function associated to an
ARB i is defi ned as

( ) ( )

2 2

dx,c i ( ) 2

(5.19)

fx () e

i

i

where c i is the center of the ARB, x an antigen, and d ( x , c i ) the distance from x
to c i . h us, the stimulating level of ARB i produced by an antigen set X , denoted
as s i ( X ), is computed as

∑

fx ()

i

(5.20)

xX
i

∈

sX ()

i

2