Computational Intelligence - August 2012 - 38
FSs
Words
Encoder
CWW Engine
FSs
Recommendation
Decoder
+ Data
FIGURE 1 Architecture for the Perceptual Computer (Per-C).
applications, whereas others are not. This article explains what
the obstacles are and how they were overcome. The ones that
are application-dependent are explained in the context of three
specific applications: Investment decision making, social judgment making, and distributed decision-making. These applications are explained in more detail in Section III.
Definition 1: The centroid of an IT2 FS Au , C Au , is an interval
of numbers [c l, c r ] , where
/ Ni = 1 x i n (x i)
cl =
min
6n (x ) ! [ n (x ), n (x )]
/ Ni = 1 n (x i)
/ Ni = 1 x i n (x i)
cr =
max
.
6n (x ) ! [ n (x ), n (x )]
/ Ni = 1 n (x i)
i
i
Au
u
A
i
i
Au
Au
c Au = (c l + c r ) /2. X
(1)
II. Application-Independent Challenges
and How They Were Overcome
To operate the Per-C shown in Fig. 1, one needs to be able to
construct the encoder, the CWW engine and the decoder, all
of which pose some application-independent challenges. Next
we will explain these challenges and how they were overcome.
A. Encoder
i
i
c l and c r are computed by the KM [4] or EKM [28] Algorithms. The more uncertainty in Au (i.e., the more area in its
FOU), the wider the centroid. The average centroid (center of
centroid) of Au is defined as
Box 2: Interval Type-2 Fuzzy Sets
u is described by its footAn interval type-2 fuzzy set (IT2 FS) A
u ) (Fig. 2), which can be thought of
print of uncertainty FOU (A
as the blurring of a type-1 membership function (MF). The FOU
is completely described by its two bounding functions, a lower
u ) = n u (x) and an upper
membership function (LMF) LMF (A
A
u ) = nr Au (x) , both of which
membership function (UMF) UMF (A
are type-1 FSs. Consequently, it is possible to use type-1 FS
mathematics to characterize and work with IT2 FSs. For lots
more information about IT2 FSs, see, e.g. [2], [11], [15].
Our first challenge (all challenges are summarized in Table 6) in
implementing the Per-C was how to transform words into IT2
FSs, i.e., the encoding problem. Our solution requires: (1) a
continuous scale for each variable of interest, and (2) a vocabulary of words that covers the entire scale. Our methods are
described for the continuous scale numbered 0-10. One begins
by establishing a vocabulary of application-dependent words
that is large enough so a person will feel linguistically comfortable interacting with the Per-C. This vocabulary must include
subsets of words that feel, to each subject, like they will collecu i , in the
tively cover the scale 0-10. The collection of words, W
u i) , constitutes a
vocabulary and their IT2 FS models, FOU (W
codebook for an application ( A ), that is, Codebook ( A )=
u i, FOU (W
u i)), i = 1, ..., N A} .
{(W
We then randomize the words in the vocabulary and survey a group of subjects to provide end-point data for the
words on the scale. The subjects are asked the following question: On a scale of 0-10, what are the end-points of an interval that
you associate with the word -? Once enough data intervals (e.g.,
30) have been obtained, they can be processed by the Interval
Approach (IA) ([7]; see also Box 3) to obtain an IT2 FS model
for each word.
B. CWW Engine
u
~
A
~
UMF (A)
1
~
FOU (A)
~
LMF (A)
x
FIGURE 2 FOU for an IT2 FS Au .
38
IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2012
Next we consider how to construct the CWW engine, which
maps IT2 FSs into IT2 FSs. There are different kinds of CWW
engines, e.g.,
1) The novel weighted average (NWA) [19]. Aggregation of
numerical subcriteria (data, features, decisions, recommendations, judgments, scores, etc.) obtained by using a
weighted average of those numbers is quite common
and widely used. In many situations, however, providing
a single number for either the subcriteria or weights is
problematic (there could be uncertainties about them),
and it is more meaningful to provide uniformly-weighted intervals, non-uniformly-weighted intervals (T1 FSs),
Table of Contents for the Digital Edition of Computational Intelligence - August 2012
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