1. A random variable is a variable that takes specific values with specific probabilities. It can be thought of as a variable whose value depends on the outcome of an uncertain event. 2. We usually denote random variables by capital letters near the end of the alphabet; e.g., X,Y,Z. 3. Example: Let X be the outcome of the roll of a die. Then X is a random variable. Its possible values are 1, 2,...

In this paper, we propose a decentralized variable gain robust controller with guaranteed L2 gain performance for a class of uncertain large-scale interconnected systems with state delays. The proposed decentralized robust controller consists of a fixed gain and a variable gain tuned by parameter adjustment laws. In this paper, it is shown that sufficient conditions for the existence of the pro...

Wind power generation is variable and uncertain. In the power systems with high penetration of wind power, determination of equivalent operating reserve is the main concern of systems operator. In this paper, a model is proposed to determine operating reserves in simultaneous market clearing of energy and reserve by stochastic programming based on scenarios generated via Monte Carlo simulation ...

A normally distributed fuzzy variable is defined by a unimodal and symmetric membership function, and is proved to be the most uncertain one when expected value and variance are given. In this note, a lognormally distributed fuzzy variable is defined and the membership function, expected value and variance of this variable are discussed. Based on these results, some properties about geometric L...

Clustering on uncertain data, one of the essential tasks in mining uncertain data, posts significant challenges on both modeling similarity between uncertain objects and developing efficient computational methods. The previous methods extend traditional partitioning clustering methods like k-means and density-based clustering methods like DBSCAN to uncertain data, thus rely on geometric distanc...

Clustering uncertain data has emerged as a challenging task in uncertain data management and mining. Thanks to a computational complexity advantage over other clustering paradigms, partitional clustering has been particularly studied and a number of algorithms have been developed. While existing proposals differ mainly in the notions of cluster centroid and clustering objective function, little...

Because of inaccuracy of modeling and parameters measurement, the controlled systems are subjected by the inaccuracy inevitably and the control of uncertain systems is studied by many researchers. Uncertain nonlinear systems partial state variables control technique is developed, and applied to single pendulum systems. In order to make a certain state variable asymptotically stable and adaptive...

With the rapid development of transportation technology, public passenger traffic system construction investment is getting more and more expensive. Determining the development trend and make the optimal allocation of transportation investment becomes more and more important to the government. To describe the relationship and development trends of the integrated passenger transportation system ...

Real-life decisions are usually made in the state of uncertainty or risk. In this article we present the risk measuring techniques value at risk (VaR) and tail value at risk (TVaR) under uncertainty. Firstly, we introduce the VaR concept of uncertain variable based on uncertainty theory and examine its fundamental properties. Then, the TVaR concept is evolved and some fundamental properties of ...