Computational Intelligence - August 2012 - 41
❏ The importance that I attach to the investment criterion c j is
_____ ?
His ratings and weights use words and therefore are linguistic.
The problem facing the individual investor is how to aggregate
the linguistic information in Tables 1 and 2 so as to arrive at his
preferential ranking of the five investments.
1) Encoder for the IJA: We will use the codebook for liquidity
as an example. Initially, the following 11 words were chosen to rate liquidity:
Very bad, more or less bad, somewhat bad, bad, somewhat fair,
fair, very fair, more or less good, somewhat good, good, very good.
During the first four months of 2008 a word survey was conducted and data were collected from 40 adult (male and
female) subjects. The IA was applied to the data collected to
compute the FOUs; however, we observed that when an individual was given the opportunity to choose a word from the
full 11-word codebook and then changed the words to the
ones either to the left or to the right of them, there was almost
no change in the outputs of the IJA. The individuals who tested the IJA did not like this because they were expecting to see
changes when they changed the words. This made the IJA not
"user-friendly." This "human factor" was surprising to us
because we have always advocated providing the individual
who will interact with the Per-C with a large vocabulary in
order to make this interaction "user-friendly." So, the challenge
was how to trim a large codebook down to size so that it is
more user-friendly, i.e., how to provide an individual with
vocabularies that contain sufficiently dissimilar words so that
when a change is made from one word to another there is a
noticeable change in the output of the IJA.
According to several researchers [20], [22], a codebook for
making preference judgments should have 5-9 words. In order
to accomplish this, the similarity matrix for the 11 words
were computed using the Jaccard similarity measure, as shown
in Table 3. Our solution was to start from the left column of
the similarity matrix and to remove all of the words to which
it is similar to degree > 0.6. Beginning with Very Bad, observe
that it is not similar to any word with degree > 0.6; so, it is
kept in the user-friendly codebook and we move to the next
word Bad. Observe that it is similar to More or Less Bad to
degree 0.78; hence, More or Less Bad is eliminated. There are
no other words in the row for Bad for which the similarity is
> 0.6; hence, no other words are eliminated, Bad is kept in the
user-friendly codebook, and we move next to the word Somewhat Bad. Focusing on the elements on the right-hand side of
the diagonal element in the row for Somewhat Bad, observe
that Somewhat Bad is not similar to any other words to degree
> 0.6; hence, no words are eliminated, Somewhat Bad is kept
in the user-friendly codebook, and we move next to the word
Fair. Proceeding in this way through the rest of the similarity
matrix, the following user-friendly seven-word codebook
was obtained:
Very bad, bad, somewhat bad, fair, somewhat good, good, very
good.
2) CWW Engine for the IJA: The IJA uses an LWA to aggregate the results for each of the rows in Table 1. Observe
that two of the investment criteria have a positive connotation-amount of profit received and liquidity-and two have a
negative connotation-risk of losing capital and vulnerability
to inflation. "Positive connotation" means that an investor
generally thinks positively about amount of profit received and
liquidity (i.e., the more the better) whereas "negative connotation" means that an investor generally thinks negatively
about risk of losing capital and vulnerability to inflation (i.e., the
less the better). The challenge here was how sub-criteria
which have negative connotations and whose inputs are
words are handled.
Our solution was that a small-sounding word should be
replaced by a large-sounding word, and vice versa. This kind of
word replacement is essentially the well-known idea of an antonym [5]. In this article the most basic antonym definition is
used [5], i.e.,
n 10 - A (x) = n A (10 - x), 6x ,
(2)
where 10 - A is the antonym of the T1 FS A, and 10 is the
right end of the domain of all FSs used for the application. The
definition in (2) can easily be extended to IT2 FSs, i.e.,
TABLE 3 Similarity matrix for the 11-word vocabulary. The words that are similar to degree > 0.6 are underlined,
starting from the left-most word VB.
WORD
VB
B
MLB
SB
F
SF
VF
SG
MLG
G
VG
VERY BAD (VB)
1
.29
.27
.17
.04
.03
.03
0
0
0
0
BAD (B)
.29
1
.78
.56
.15
.14
.14
.03
.01
.01
0
MORE OR LESS BAD (MLB)
.27
.78
1
.54
.11
.11
.11
.01
0
0
0
SOMEWHAT BAD (SB)
.17
.56
.54
1
.23
.22
.22
.06
.03
.02
0
FAIR (F)
.04
.15
.11
.23
1
.88
.87
.49
.35
.30
.1
0
SOMEWHAT FAIR (SF)
.03
.14
.11
.22
.88
1
.99
.58
.43
.38
VERY FAIR (VF)
.03
.14
.11
.22
.87
.99
1
.59
.44
.38
0
SOMEWHAT GOOD (SG)
0
.03
.01
.06
.49
.58
.59
1
.64
.53
.28
MORE OR LESS GOOD (MLG)
0
.01
0
.03
.35
.43
.44
.64
1
.81
.4
GOOD (G)
0
.01
0
.02
.30
.38
.38
.53
.81
1
.5
VERY GOOD (VG)
0
0
0
0
.15
.21
.21
.28
.49
.54
1
AUGUST 2012 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE
41
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