Abstract: We present a solution to the Maxmin u/E parameters
estimation problem of possibility distributions in m-dimensional
case. Our method is based on geometrical approach, where minimal
area enclosing ellipsoid is constructed around the sample. Also we
demonstrate that one can improve results of well-known algorithms
in fuzzy model identification task using Maxmin u/E parameters
estimation.
Abstract: In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.
Abstract: In this paper, we propose a fuzzy aggregate
production planning (APP) model for blending problem in a brass
factory which is the problem of computing optimal amounts of raw
materials for the total production of several types of brass in a
period. The model has deterministic and imprecise parameters
which follows triangular possibility distributions. The brass casting
APP model can not always be solved by using common approaches
used in the literature. Therefore a mathematical model is presented
for solving this problem. In the proposed model, the Lai and
Hwang-s fuzzy ranking concept is relaxed by using one constraint
instead of three constraints. An application of the brass casting
APP model in a brass factory shows that the proposed model
successfully solves the multi-blend problem in casting process and
determines the optimal raw material purchasing policies.
Abstract: This paper investigates the issue of building decision
trees from data with imprecise class values where imprecision is
encoded in the form of possibility distributions. The Information
Affinity similarity measure is introduced into the well-known gain
ratio criterion in order to assess the homogeneity of a set of
possibility distributions representing instances-s classes belonging to
a given training partition. For the experimental study, we proposed an
information affinity based performance criterion which we have used
in order to show the performance of the approach on well-known
benchmarks.
Abstract: This paper proposes a new decision making approch
based on quantitative possibilistic influence diagrams which are
extension of standard influence diagrams in the possibilistic framework.
We will in particular treat the case where several expert
opinions relative to value nodes are available. An initial expert assigns
confidence degrees to other experts and fixes a similarity threshold
that provided possibility distributions should respect. To illustrate our
approach an evaluation algorithm for these multi-source possibilistic
influence diagrams will also be proposed.
Abstract: If a possibility distribution and a probability distribution
are describing values x of one and the same system or process
x(t), can they relate to each other? Though in general the possibility
and probability distributions might be not connected at all, we
can assume that in some particular cases there is an association linked
them.
In the presented paper, we consider distributions of bloodstream
concentrations of physiologically active substances and propose that
the probability to observe a concentration x of a substance X can be
produced from the possibility of the event X = x .
The proposed assumptions and resulted theoretical distributions
are tested against the data obtained from various panel studies of the
bloodstream concentrations of the different physiologically active
substances in patients and healthy adults as well.