Catálogo de publicaciones - libros

Production planning consists of the simultaneous determination of the production, inventory and capacity levels of a company on a finite planning horizon with the objective of minimizing the total costs generated by production plans. Fuzzy set theory has been used to model systems that are difficult to define accurately (Bellman and Zadeh 1970; Dubois and Prade 1980; Zimmermann 1996). This theory represents an attractive tool to support the production planning research when the dynamics of the manufacturing environment limits the specification of the model objectives, constraints and parameters. Guiffrida and Nagi (1998) provide an exhaustive literature survey on the fuzzy set theory applications in production management research.

Proportional bounding quantifiers like “Between 1 and 2 percent” are potentially useful for expressing linguistic summaries of data. Given 1, 2, existing methods for data summarization based on fuzzy quantifiers can be used to assign a quality score to the summary.

Dynamics, or variability over time, is crucial in virtually all real world processes. Among many formal approaches to the description of dynamic behavior is the use of time series, notably those composed of a sequence of real numbers that represent how values of a quantity, variable, etc. evolve over time. Time series are then used for many diverse purposes exemplified by decision making, prediction, etc. However, in all these situations first we have to grasp the very meaning of a particular time series in the sense of what is going on with the quantity or variable whose values it represents.

Modelling of fuzzy temporal quantified statements is of great interest for real time systems. In [1] use of fuzzy proportional quantifiers to model temporal statements (sentences involving occurrence of events within a time framework) has been proposed. By using these proportional quantifiers a semantics can be associated to expressions like “”. , as “”. We will see how evaluation of these similarity or correlation expressions between two signals can be modelled by using similarity quantifiers.

In this paper, a theory of conditional coherent lower previsions for arbitrary random quantities, including unbounded ones, is introduced, based on Williams’s [13] notion of coherence, and extending at the same time unconditional theories studied for unbounded random quantities known from the literature. We generalize a well-known envelope theorem to the domain of all contingent random quantities. Finally, using this duality result, we prove equivalence between maximal and Bayes actions in decision making for convex option sets.

We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets – the extreme lower probabilities – can be calculated and we give an illustration of our results.

We establish an intimate connection between Bayesian and credal nets. Bayesian nets are precise graphical models, credal nets extend Bayesian nets to imprecise probability. We focus on traditional belief updating with credal nets, and on the kind of belief updating that arises with Bayesian nets when the reason for the missingness of some of the unobserved variables in the net is unknown. We show that the two updating problems are formally the same.

We shall present a first explorative study of the variation of the parameter of the imprecise Dirichlet model when it is used to build classification trees. In the method to build classification trees we use uncertainty measures on closed and convex sets of probability distributions, otherwise known as credal sets. We will use the imprecise Dirichlet model to obtain a credal set from a sample, where the set of probabilities obtained depends on . According to the characteristics of the dataset used, we will see that the results can be improved varying the values of .

We review a recently introduced nonparametric predictive approach for comparison of groups of proportions data, using interval probability. We particularly focus on cases where groups have zero of few successes. These inferences are for events that ≥ 1 future observations from a particular group will include more successes than future observations from each other group.

Several methods for the practical representation of imprecise probabilities exist such as Ferson’s p-boxes, possibility distributions, Neumaier’s clouds, and random sets. In this paper some relationships existing between the four kinds of representations are discussed. A cloud as well as a p-box can be modelled as a pair of possibility distributions. We show that a generalized form of p-box is a special kind of belief function and also a special kind of cloud.