In this paper the theory of fuzzy logic is mixed with the theory of Markov systems and the abstraction of a Markov system with fuzzy states introduced. The notions such as fuzzy transient, fuzzy recurrent etc., were introduced. The results based on these notions are introduced.

Conventional approach to mathematical description of experiments applies probability theory. Here, another approach is used to express uncertainty based on probability, fuzzy sets, and evidence theory. The paper presents a new reliability model of an element working in different environmental and stress conditions. Fuzzy and probability descriptions are combined together using evidence theory t...

An incremental, nonparametric probability estimation procedure using a variation of the Fuzzy ARTMAP (FAM) neural network is introduced. The resulted network, called Fuzzy ARTMAP with Relevance factor (FAMR), uses a relevance factor assigned to each sample pair, proportional to the importance of that pair during the learning phase. We prove that our probability estimator is correct. The FAMR ca...

In this paper a network comprising alternative branching nodes with probabilistic outcomes is considered. In other words, network nodes are probabilistic with exclusive-or receiver and exclusive-or emitter. First, an analytical approach is proposed to simplify the structure of network. Then, it is assumed that the duration of activities is positive trapezoidal fuzzy number (TFN). This paper com...

In this paper, two kinds of fuzzy approaches are proposed for not only multiobjective stochastic linear programming problems, but also multiobjective fuzzy random linear programming problems through a probability maximization model. In a probability maximization model, it is necessary for the decision maker to specify permissible values of objective functions in advance, which have a great infl...

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...