Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista

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 non-membership degree is somehow independent of the membership degree, and this difference between the non-membership 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

Dinâmica de reprodução e comportamento reprodutivo de branchoneta Dendrocephalus brasiliensis Pesata, 1921 como incremento na produção de alimento vivo para peixes ornamentais

Reproductive behavior of Dendrocephalus brasiliensis Pesta, 1921(Crustacean: Anostracan). The reproductive behavior of fresh water Anostracan has been poorly investigated in carcinology specialized literature, specifically in relation to Dendrocephlaus brasiliensis Pesta, 1921, with abundant data just about the geographical distribution of that Anostracan. The objective of this work was to know the reproductive behavior of this Anostracan, in different seasons (dry and raine). For this, ripe individuals of both sexes were collected in four pond of the of Fish farming Station of Paulo Afonso (EPPA), through monthly captures in each ponds, from December 2004 to November 2005. The type of reproduction was observed after the placing in aquariums (a) of then with males and (b) other on individually, at the nauplii phase, where they stayed for 15 days until the reproductive age. The sexual proportion was calculated through the relative frequencies of males and females, every month, for the whole collection period during 10 days. the production of cysts was related to the size of the female. The male: female ratio in the study period was 1 male:1,07 female. The proportion male:female was from 48,25% : 51,75% along the year. Concerning the type of reproduction, it was observed that this specie is characteerized by sexual reproduction