Tesis
Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista
Date
20120820Registration in:
COSTA, Claudilene Gomes da. Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista. 2012. 159 f. Tese (Doutorado em Automação e Sistemas; Engenharia de Computação; Telecomunicações)  Universidade Federal do Rio Grande do Norte, Natal, 2012.
Author
Costa, Claudilene Gomes da
Institutions
Abstract
The idea of considering imprecision in probabilities is old, beginning with the Booles
George work, who in 1854 wanted to reconcile the classical logic, which allows the modeling
of complete ignorance, with probabilities. In 1921, John Maynard Keynes in his
book made explicit use of intervals to represent the imprecision in probabilities. But only
from the work ofWalley in 1991 that were established principles that should be respected
by a probability theory that deals with inaccuracies.
With the emergence of the theory of fuzzy sets by Lotfi Zadeh in 1965, there is another
way of dealing with uncertainty and imprecision of concepts. Quickly, they began to propose
several ways to consider the ideas of Zadeh in probabilities, to deal with inaccuracies,
either in the events associated with the probabilities or in the values of probabilities.
In particular, James Buckley, from 2003 begins to develop a probability theory in which
the fuzzy values of the probabilities are fuzzy numbers. This fuzzy probability, follows
analogous principles to Walley imprecise probabilities.
On the other hand, the uses of real numbers between 0 and 1 as truth degrees, as
originally proposed by Zadeh, has the drawback to use very precise values for dealing with
uncertainties (as one can distinguish a fairly element satisfies a property with a 0.423 level
of something that meets with grade 0.424?). This motivated the development of several
extensions of fuzzy set theory which includes some kind of inaccuracy.
This work consider the Krassimir Atanassov extension proposed in 1983, which add
an extra degree of uncertainty to model the moment of hesitation to assign the membership
degree, and therefore a value indicate the degree to which the object belongs to the set
while the other, the degree to which it not belongs to the set. In the Zadeh fuzzy set
theory, this non membership degree is, by default, the complement of the membership
degree. Thus, in this approach the nonmembership degree is somehow independent of
the membership degree, and this difference between the nonmembership degree and the
complement of the membership degree reveals the hesitation at the moment to assign a
membership degree. This new extension today is called of Atanassov s intuitionistic fuzzy
sets theory. It is worth noting that the term intuitionistic here has no relation to the term
intuitionistic as known in the context of intuitionistic logic.
In this work, will be developed two proposals for interval probability: the restricted
interval probability and the unrestricted interval probability, are also introduced two notions
of fuzzy probability: the constrained fuzzy probability and the unconstrained fuzzy
probability and will eventually be introduced two notions of intuitionistic fuzzy probability:
the restricted intuitionistic fuzzy probability and the unrestricted intuitionistic fuzzy
probability
Subjects
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