I would say that roughly_2 or about_2 are vague. Most often they model
uncertainty regarding the exact definition of a interval centred about 2.
This certainly would corresponds to vagueness according to the 'uncertainty of
definition' definition. On the other hand the restriction (X is roughly_2)
also conveys uncertainty regarding the exact value of the random variable
X. Indeed you have both types of uncertainty present here. This situation
is best modelled according a theory of the probability of fuzzy events.
More specifically, the contraint (X is roughly_2) induces a conditional
(posterior) probability distribution on X i.e Pr(X|X is roughly_2). This
distribution would take into account the prior distribution on X. Given
this distribution we can then make inferences regarding another fuzzy
event say (X is f) by determining Pr( X is f|X is roughly_2). This is
essentially how the semantic unification method in FRIL works.
Regarding your point about the usefullness of fuzzy intervals of precise
ones to say partition a universe, I completely agree that the former give a
degree of interpolation to your model absent when using the latter.
However, it seems to me that this comes directly from the uncertainty
regarding their exact definition i.e their vagueness
Regards
Jonathan
-- Dr Jonathan Lawry, AI Group, Dept. Engineering Mathematics, University of Bristol, Queens Building, University Walk, Bristol, BS8 1TR, UKEmail:j.lawry@bristol.ac.uk Tel:+44 117 928 8184
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