This paper discusses some models of Imprecise Probability Theory obtained by propagating uncertainty in risk analysis when some input parameters are stochastic and perfectly observable, while others are either random or deterministic, but the information about them is partial and is represented by possibility distributions. Our knowledge about the probability of events pertaining to the output ...

Monte Carlo simulation (MCS) has been widely used for the uncertainty propagations of building simulation tools. In general, most unknown inputs for the MCS are regarded as single probability distributions based on experts’ subjective judgements and assumptions, when simulation information and measured data are inaccurate and insufficient. However, this can lead to meaningless and untrustworthy...

-In this work we present the methods of creating the knowledge bases by using the theory of fuzzy systems as well as the probability and stochastic processes theory. We show that such knowledge-based systems can be applied in different diagnostic tasks. The structure of the reason-result fuzzy model is predefined by experts at the beginning of the task. The notion of probability of fuzzy events...

In this paper, two kinds of portfolio selection models are proposed based on fuzzy probabilities and possibility distributions, respectively, rather than conventional probability distributions in Markowitz’s model. Since fuzzy probabilities and possibility distributions are obtained depending on possibility grades of security data o ered by experts, investment experts’ knowledge can be re ected...

Exact small-sample methods for discrete data use probability distributions that do not depend on unknown parameters. However, they are conservative inferentially: the actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article surveys ways of reducing or even eliminating the conservatism. Fuzzy inference is a recent innovation that enables ...

Data are frequently not precise numbers but more or less non-precise, also called fuzzy. Moreover a-priori information in Bayesian inference is usually not available as a precise probability distribution. In case of fuzzy data and fuzzy a-priori information Bayes' theorem has to be generalized. There are different approaches for a generalization of Bayes' theorem but most of them don't keep the...

This paper describes an extended relational database model based on probability theory and possibility theory. Fuzzy information and probabilistic information are incorporated into the relational databases simultaneously to represent fuzzy probability of events in the real-world applications. The tuples in such a relation are associated with a possibility distribution, and their attribute value...

Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possi...

There are a lot of problems in engineering which are connected with the necessity not to neglect the influence of uncertainties in parameters (these are for example seismic vibrations, wind loaded structures and imperfection sensitive structures). Fuzzy numbers and possibility theory are used for problems where uncertainties in definition of input data do not allow for a treatment by means of p...

Anew integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, whichmight be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to...