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

Kresge Foundation 2010-2011 Annual Report

Contains an introduction to Kresge's strategy; board chair's letter; president's letter; foundation timeline; program information; grant summary, including geographic distribution; grants lists; financial summary; and lists of board members and staff

The robust single machine scheduling problem with uncertain release and processing times

In this work, we study the single machine scheduling problem with uncertain release times and processing times of jobs. We adopt a robust scheduling approach, in which the measure of robustness to be minimized for a given sequence of jobs is the worst-case objective function value from the set of all possible realizations of release and processing times. The objective function value is the total flow time of all jobs. We discuss some important properties of robust schedules for zero and non-zero release times, and illustrate the added complexity in robust scheduling given non-zero release times. We propose heuristics based on variable neighborhood search and iterated local search to solve the problem and generate robust schedules. The algorithms are tested and their solution performance is compared with optimal solutions or lower bounds through numerical experiments based on synthetic data

San Francisco Disaster Food System Report

This analysis includes recommendations to advance food resiliency for low-income and vulnerable populations in the event of disaster. The report highlights the fragility of the disaster food pipeline in San Francisco, focuses on lessons learned from other disasters, and suggests opportunities for philanthropy to shore up the disaster food system

A software system for laboratory experiments in image processing

Laboratory experiments for image processing courses are usually software implementations of processing algorithms, but students of image processing come from diverse backgrounds with widely differing software experience. To avoid learning overhead, the software system should be easy to learn and use, even for those with no exposure to mathematical programming languages or object-oriented programming. The class library for image processing (CLIP) supports users with knowledge of C, by providing three C++ types with small public interfaces, including natural and efficient operator overloading. CLIP programs are compact and fast. Experience in using the system in undergraduate and graduate teaching indicates that it supports subject matter learning with little distraction from language/system learning

Edna McConnell Clark Foundation - 2003 Annual Report

Contains president's message, fund and program information, grants list, financial statements, grant guidelines, publications list, and lists of board members and staff