Utilizing capacitor banks is very conventional in distribution network in order for local compensation of reactive power. This will be more important considering uncertainties including wind generation and loads uncertainty. Harmonics and non-linear loads are other challenges in power system which complicates the capacitor placement problem. Thus, uncertainty and network harmonics have been con...

Traditional and fuzzy control correspond to two different cases: traditional control is applicable when we have a precise knowledge of the controlled system, and possible uncertainties are described in probabilistic terms (as a noise). Fuzzy control (see, e.g., [S85, B91, L90]) is applicable in the situation when uncertainty is described in terms of natural language like “small”, “to some exten...

In this paper, we try the perceptive analysis of the optimal stopping problem in which both fuzzy and probabilistic uncertainty is accommodated. We establish the recursive equation for computing the expected value of the optimal stopped fuzzy perception reward. Also, a numerical example is given.

There exist techniques for decision making under speci c types of uncertainty, such as probabilistic, fuzzy, etc. Each of the corresponding ways of describing uncertainty has its advantages and limitations. As a result, new techniques for describing uncertainty appear all the time. Instead of trying to extend the existing decision making idea to each of these new techniques one by one, we attem...

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...

—Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval, probabilistic, and fuzzy uncertainty. We provide an overview of related algorithms, results, and remaining open problems.

This paper presents an adaptive fuzzy evidential reasoning approach, for segmenting multi-modality MR brain images. A novel fuzzy evidence structure model is proposed under the assumption that each information source provides two types of evidence: probabilistic evidence and fuzzy evidence. A new information measure, called hybrid entropy, is employed for evaluating the overall uncertainty cont...

Fuzzy control is based on approximate expert information, so its recommendations are also approximate. However, the traditional fuzzy control algorithms do not tell us how accurate are these recommendations. In contrast, for the probabilistic uncertainty, there is a natural measure of accuracy: namely, the standard deviation. In this paper, we show how to extend this idea from the probabilistic...

MM is one of the central ideas in the nowadays mathematics education. In an earlier paper applying ideas from fuzzy logic we have developed a model formalizing the MM process and we have used the total possibilistic uncertainty as a measure of students’ MM capacities. In the present paper we develop two alternative fuzzy measures for MM. The first of them concerns an adaptation for use in a fuz...