Information Technology Reference
In-Depth Information
m
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.
The semantic spaces with the membership functions being in line with the
formulated requirements are called complete orthogonal semantic spaces (COSS).
The requirement 1 means that each concept (term) has at least one standard,
which is the typical representative (level of expert gradational confidence of a
typical representative's membership to corresponding concept is equal to unity). If
there are several standards, all of them are located closely, instead of being
scattered over a universal set.
l
1
Fig. 1.7
Membership functions of COSS term-set “inlet steam pressure” of the “high
pressure preheater”
The requirement 2 says that if units are "close" to each other in universal set,
they also are "close" by a membership to a certain concept.
The requirement 3 ensures a possibility of simultaneous processing of fuzzy
and precise information from unified positions because regular characteristic
functions can be used as membership functions.
The requirement 4 ensures, for each unit from universal set, availability of at
least one concept which describes this unit with nonzero grade of membership.
Besides, it ensures the discriminability of concepts generating semantic space and
excludes the use of synonyms or semantically close terms.
An example is a complete orthogonal semantic space which term-set
membership functions are shown in Fig. 1.7.
The formulated requirements to functions of COSS term-set allow defining
degree of its fuzziness [28]
1
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