-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...

Probabilistic safety assessment (PSA) which plays a crucial role in risk evaluation is a quantitative approach intended to demonstrate how a nuclear reactor meets the safety margins as part of the licensing process. Despite PSA merits, some shortcomings associated with the final results exist. Conventional PSA uses crisp values to represent the failure probabilities of basic events. This causes...

From a very broad point of view a Fuzzy System (FS) is any Fuzzy Logic – Based System, where Fuzzy Logic can be used either as the basis for the representation of various forms of knowledge systems, or to model the interactions and relationships among the system variables. Genetic Algorithms (GAs) are general purpose research algorithms which use principles inspired by natural genetics to evolv...

In real decision situations a decision maker (DM) is often confronted with the problem that the information which is necessary for constructing a classical decision model is not available, or the cost for getting this information seems too high. Subsequently, the DM abstains from constructing a decision model; the DM fears that this model is not an authentic image of the real problem. Fuzzy set...

This paper presents a proposition of the knowledge representation and the inference procedure including two types of uncertainty: probabilistic and fuzzy. Added weights to the fuzzy rule-based model state probabilities of fuzzy events in antecedents and consequents. The exemplary calculations are presented. Key-Words: Fuzzy sets, Knowledge representation, Inference procedure, Probability of fuz...

Representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. Fo-cusing on discounted cash flow analysis numerical results are presented, comparisons are made between alter-native modeling methods, and characteristics of the methods are discussed.

In this contribution we deal with the problem of doing computations with a Markov chain when the information about transition probabilities is expressed linguistically. This could be the case, for instance, if the process we are modeling is described by a human expert, for whom the use of linguistic labels is easier than being forced to give inexact numerical probabilities which, in turn, may y...

It is necessary and challenging to represent the probabilities of fuzzy events and make inferences between them based on a Bayesian network. Motivated by such real applications, in this paper, we first define the interval probabilities of type-2 fuzzy events. Then, we define weak interval conditional probabilities and the corresponding probabilistic description. The expanded multiplication rule...

Abstract: In this paper a non-repairable multi-state system with imprecise probabilities and performance rates are taken, representing imprecise probabilities by interval valued probabilities. These intervals are evaluated by computing bound of interval valued ordinary differential equation of the system. For imprecise performance rates random fuzzy variables are introduced. The proposed method...