Computational Intelligence - August 2012 - 43

THEN there is _____ flirtation," three different consequents were obtained: none to very little, some, and large.
A gap exists between some and large amount. Let
G 1 = {none to very little, some} and G 2 = {l arg e amount} .
Because G 1 has considerably more responses than G 2 , it is
passed to the next step of data pre-processing and G 2
is discarded.
❏ Outlier processing: Outlier processing uses a Box and Whisker
test [24]. Outliers are points that are unusually too large or
too small. A Box and Whisker test is usually stated in terms
of first and third quartiles and an interquartile range. The
first and third quartiles, Q (0.25) and Q (0.75) , contain 25%
and 75% of the data, respectively. The inter-quartile range,
IQR, is the difference between the third and first quartiles;
hence, IQR contains 50% of the data between the first and
third quartiles. Any datum that is more than 1.5 IQR above
the third quartile or more than 1.5 IQR below the first
quartile is considered an outlier [24]; however, rule consequents are words modeled by IT2 FSs, thus the Box and
Whisker test cannot be directly applied to them. So, the
challenge is how to perform the Box and Whisker test on
IT2 FSs. In our solution, the Box and Whisker test is applied
to the set of centers of centroids formed by the centers of
centroids of the rule consequents. Focusing again on Rule
2, the centers of centroids of the consequent IT2 FSs NVL,
S, MOA, LA and MAA are first computed, and are 0.48,
4.50, 4.95, 8.13 and 9.68, respectively. Then the set of centers of centroids is
{ 0.48, f, 0.48, 4.50, f, 4.50} ,
144
4244
43 144
4244
43
33
12

(4)

where each center of centroid is repeated a certain number
of times according to the number of respondents after bad
data processing. The Box and Whisker test is then applied to
this crisp set, where Q (0.25) = 0.48 , Q (0.75) = 4.50 , and
1.5 IQR = 6.03 . For Rule 2, no data are removed in this
step. On the other hand, for Rule 1, the three responses to
some and the two responses to moderate amount are removed.
❏ Tolerance limit processing: Let m and v be the mean and standard deviation of the remaining histogram data after outlier
processing. If a datum lies in the tolerance interval
[m - kv, m + kv] , then it is accepted; otherwise, it is
rejected [24]. k is determined such that one is 95% confident that the given limits contain at least 95% of the available data. For Rule 2, tolerance limit processing is
performed on the set of centers of centroids in (4), for which
m = 1.55 , v = 1.80 and k = 2.41. No word is removed
for this particular example; so, two consequents, none to very
little and some, are accepted for this rule.
The final pre-processed responses for the histograms in the
top half of Table 4 are given in its bottom half. Observe that
most responses have been preserved; however, most rule consequents are still histograms instead of a single word. The next
challenge was how to use a histogram of consequent words in
rulebase construction. Our solution was to preserve the distri-

NVL

MOA

Y˜ 3

FIGURE 4 Yu 3 obtained by aggregating the consequents of R 31 - R 34 .

butions of the responses for each rule by using an NWA to
obtain the rule consequents, as illustrated by the following:
Example: Observe from the bottom half of Table 4 that
when the antecedent is MOA there are four valid consequents, so that the following four rules will be fired:
R 31 : IF touching is MOA,THEN flirtation is NVL.
R 32 : IF touching is MOA,THEN flirtation is S.
R 33 : IF touching is MOA,THEN flirtation is MOA.
R 34 : IF touching is MOA,THEN flirtation is LA.
These four rules should not be considered of equal importance because they have been selected by different numbers
of respondents. An intuitive way to handle this is to assign
weights to the four rules, where the weights are proportional to the number of responses, e.g., the weight for R 31 is
12/46, and the weight for R 32 is 16/46. The aggregated
consequent Yu 3 is
Yu 3 = 12NVL + 16S + 15MOA + 3LA .
12 + 16 + 15 + 3
Yu 3 is computed by the NWA. The result is shown in Fig. 4.
Observe that the shape of Yu 3 looks like the shape of MOA;
however, it is shifted somewhat leftwards along the flirtation-level axis, so Yu 3 is not the same as MOA.
3) CWW Engine and Decoder: Once the rulebase is constructed, the next step is to compute the output for a new input
word. We use Perceptual Reasoning (see Section II-B).
Consider single-antecedent rules of the form
R i : If x is Fu i, Then y is Yu i

i = 1, f, N ,

where Fu i and Yu i are words modeled by IT2 FSs. In PR, the
Jaccard similarity measure is used to compute the firing levels
of the rules, f i , i = 1, f, N. Then, the output FOU of the
SJA is computed as
YuC =

/ Ni = 1 f i Yu i
.
/ Ni = 1 f i

The subscript C in YuC stands for consensus because YuC is
obtained by aggregating the survey results from a population of
people, and the resulting SJA is called a Consensus Flirtation
Advisor. YuC is then mapped to the most similar word in the
10-word codebook using the Jaccard similarity measure.
4) How to Use the Flirtation Advisor: A flirtation adviser could
be used to train a person to better understand the relationship between touching and flirtation, so that they reach
correct conclusions about such a social situation. Their perception of flirtation for each of the 10 words for touching

AUGUST 2012 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

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