Fuzziness and randomness are two distinct components of uncertainty. While fuzzy sets are a rigorous softening of random sets, many of the operations de ned in fuzzy logic lack a complete formalism, and are not strongly supported by experimental evidence. Causal Probabilistic Networks (CPN) or Bayesian networks provide an ultimately exible inference mechanism based on Bayesian probability princ...

Fuzziness is often regarded as a special form of uncertainty, possibly related to probability but not necessarily reducible to the latter. Indeed, all the mathematical techniques that have been proposed to model fuzziness are substantially different from probabilistic methods, albeit sometimes loosely similar. As shown in this paper, a particular form of fuzzy logic can be derived from probabil...

Due to the existing of various kinds of uncertainties, predicting structural performance is always a great challenge in practical applications. The reliability of structure under the probabilistic uncertainty has been well studied in the past decade. However, the randomness is not the only attribute of reality. This paper attempts to investigate approach for the structural reliability analysis ...

In the past few years, new applications of robots have increased the importance of robotic reliability and fault tolerance. Standard approaches of reliability engineering rely on the probability model, which is often inappropriate for this task due to a lack of su cient probabilistic information during the design and prototyping phases. Fuzzy logic o ers an alternative to the probability paradi...

In this paper we present a unified (probabilistic/possibilistic) model for resource-constrained project scheduling problem (RCPSP) with uncertain activity durations and a concept of a heuristic approach connected to the theoretical model. It is shown that the uncertainty management can be built into any heuristic algorithm developed to solve RCPSP with deterministic activity durations. The esse...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities...

The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such situations the mathematical tools of fuzzy set theory may be successfully used. It seems that the simple...

In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced p...