Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

Both models are created of the basis of data received
from the group of people or a group of technical measurement
machines for classification. Classifiers can be a form of
2 people, 3 people … a group of people or the population of
a whole country etc. On the basis of empirical or declared results
we receive average individual model of group from
which the data was taken or average individual model of the
person of the group [5].
Group model is usually used when we do not know from
whom exactly the linguistic information is received. We only
know that the information comes from of the group (population)
which the person belongs to. The model represents the
whole group of people (the whole population). Whereas the
average individual model of a person of group represents only
the average person of the group (population), it does not represent
the whole group of people (the whole population).
Average individual probability
classification functions from the group
of people (population)
In the group of people classification function of particular
members are usually a bit different. For example in the group
of 3 people each of them can differently understand the concept
“medium” (Fig. 1).
The question arises, what does the average individual classification
function of one typical person of the group look like,
in other words the most frequently found person in the group?
Classification function of such person are most similar to
the function of the majority of people in the examined population.
Similarly the height of majority of people in a population
is usually close to medium height. It means classification function
of the majority people in the population are most similar
to the function of the average person in the group.
In the example presented in Fig. 1 the average individual
classification function is drown in thick line.
Average individual classification probability function answers
the question: what is the probability the average (most
frequently found) person in the group qualifies numerical value
to the given linguistic concept.
The different between the group classification function of
linguistic concept and the average individual classification
function is that the group function expresses the average value
of classification probability by the whole group and the average
individual classification function expresses the average classification
probability by the average person from the group.
Next the method of the identification of the average individual
classification function to linguistic quantifiers is presented.
In this methods the support of the linguistic concept are divided
to the equal number of interval, then the integral of the
function on every of support interval is computed (area on the
interval limited by classification function and axis x). Next the
average area for i-th interval of n linguistic concept is computed.
where: n - the number of individual linguistics concept, f k (x) -
classification function of individual linguistic concept, e.g.
“small probability”.
Average individual classification probability function will be
created from average support intervals and the average area
in the particular interval. The support and the area of the average
individual classification probability function will be the
mean of individual classification function. In the last stage having
computed all the average quantifiers included in the dictionary
of classification probability function we normalized
them, so that the sum of all quantifiers is one. In many cases
the normalization does not change anything because the sum
of quantifiers is already one.
Example 1. In the below example we will look into two
quantifiers of classification function. For better understanding
of the method the quantifiers are in the form of step function,
Fig. 2. On the basis of the given quantifiers the average
individual quantifier of classification function will be determined,
using (1).
The points of the support F_aver are the average points
which divide the supports F1 and F2 (dotted line):
The surface area of rectangles which create the function
F_aver are the average surface area marked with doted line
rectangles in F1 and F2, respectively, thus the heights of the
rectangles are:
(1)
(2)
(3)
Fig. 1. The illustration of the sense of average individual classification
probability function (thick line)
Rys. 1. Ilustracja przeciętnej indywidualnej funkcji klasyfikacji
(linia pogrubiona)
Fig. 3, 4 and 5 presents application of method of determining
the average individual probability classification function using
individual probability classification function received on the
basis of the experiment which was carried out by the authors.
Individual classification function show the models of individual
people taking part of the experiment.
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