Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin

Rough analysis in lattices

An outline of an algebraie generalization of the rough set theory is presented in the paper. It is shown that the majority of the basic concepts of this theory has an immediate algebraic generalization, and that some rough set facts are true in general algebraic structures. The formalism employed is that of lattice theory. New concepts of rough order, approximation space and rough (quantitative) approximation space are introduced and investigated. It is shown that the original Pawlak's theory of rough sets and information systems is a model of this general approach

Rough analysis in lattices.

An outline of an algebraie generalization of the rough set theory is presented in the paper. It is shown that the majority of the basic concepts of this theory has an immediate algebraic generalization, and that some rough set facts are true in general algebraic structures. The formalism employed is that of lattice theory. New concepts of rough order, approximation space and rough (quantitative) approximation space are introduced and investigated. It is shown that the original Pawlak's theory of rough sets and information systems is a model of this general approach.Rough set; Information system; Rough dependenee; Rough lattiee; Approximation spaee;

Characterisation of large changes in wind power for the day-ahead market using a fuzzy logic approach

Wind power has become one of the renewable resources with a major growth in the electricity market. However, due to its inherent variability, forecasting techniques are necessary for the optimum scheduling of the electric grid, specially during ramp events. These large changes in wind power may not be captured by wind power point forecasts even with very high resolution Numerical Weather Prediction (NWP) models. In this paper, a fuzzy approach for wind power ramp characterisation is presented. The main benefit of this technique is that it avoids the binary definition of ramp event, allowing to identify changes in power out- put that can potentially turn into ramp events when the total percentage of change to be considered a ramp event is not met. To study the application of this technique, wind power forecasts were obtained and their corresponding error estimated using Genetic Programming (GP) and Quantile Regression Forests. The error distributions were incorporated into the characterisation process, which according to the results, improve significantly the ramp capture. Results are presented using colour maps, which provide a useful way to interpret the characteristics of the ramp events

Geomorphic Change Detection Using Multi-Beam Sonar

The emergence of multi-beam echo sounders (MBES) as an applicable surveying technology in shallow water environments has expanded the extent of geomorphic change detection studies to include river environments that historically have not been possible to survey or only small portions have been surveyed. The high point densities and accuracy of MBES has the potential to create highly accurate digital elevation models (DEM). However, to properly use MBES data for DEM creation and subsequent analysis, it is essential to quantify and propagate uncertainty in surveyed points and surfaces derived from them through each phase of data collection and processing. Much attention has been given to the topic of spatially variable uncertainty propagation in the context of the construction of DEM and their use in geomorphic change detection studies. However little work has been done specifically with applying spatially varying uncertainty models for MBES data in shallow water environments. To address this need, this report presents a review of literature and methodology of uncertainty quantification in a geomorphic change detection study. These methods are then applied and analyzed in a geomorphic change detection study using MBES as the data collection technique