in applications there occur different forms of uncertainty. the twomost important types are randomness (stochastic variability) and imprecision(fuzziness). in modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. however, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.since many years t...

Given fuzzy data the concept of histograms has to be extended to so-called fuzzy histograms in order to incorporate fuzziness into considerations. For these fuzzy histograms the height over a class itself is fuzzy. Based on this the extension of classical probability distributions to so-called fuzzy probability distributions on arbitrary σ-algebras is described, the main properties of fuzzy pro...

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develo...

Fuzzy probabilities have been widely used in the areas of risk assessment and decision making. Here, we propose a system based on fuzzy probabilities for assessing the intensity of pedestrian collisions and levels of injury. The proposed approach uses possibility probability distributions for demonstrating fuzzy probabilities. A composition of possibility probability distributions (fuzzy probab...

this article proposes composition of fuzzy sets theory with discrete-event simulation and puts it into application in order to model uncertain activity duration in simulating a real-world system. the purpose of this paper is to assess the usefulness of fuzzy simulation for modeling uncertain activity duration, especially when insufficient or no sample data is available. in this research, fuzzy ...

In fuzzy Decision Support Systems, methods are strongly required for eliciting knowledge in the form of interpretable fuzzy sets from numerical data. In medical settings, statistical data are often available, or can be obtained from rough data, typically in the form of probability distributions. Moreover, since physicians are used to think and work according to a statistical interpretation of m...

In this paper we consider the maximum entropy principle with imprecise side-conditions, where the imprecise side-conditions are modeled as fuzzy sets. Our solution produces fuzzy discrete probability distributions and fuzzy probability density functions.

In the present investigation, we deal with the reliability characteristics of a repairable system consisting of two independent operating units, by incorporating the coverage factor. The probability of the successful detection, location and recovery from a failure is known as the coverage probability. The reboot delay and common cause shock failure are also considered. The times to failure of t...

In this paper, two types of fuzzy probability spaces will be introduced and their possible applications in methods of decision-making under risk will be described. First, a fuzzy probability space that generalizes the classical probability space ( ,Bn, p) to the situation of fuzzy random events will be studied. It can be applied e.g. when given continuous probability distributions of risk facto...

This paper discusses hybrid probabilistic and fuzzy set approaches to propagating randomness and imprecision in risk assessment and fuzzy time series models. Stochastic and Computational Intelligence methods, such as Probability bounds analysis, Fuzzy -levels analysis, Fuzzy random vectors, Wavelets decomposition and Wavelets Networks are combined to capture different kinds of uncertainty. The...