Monotonically improving approximate answers to relational algebra queries

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined

Evaluating aggregate functions on possibilistic data

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications, and are thus being supported by traditional languages like SQL or QUEL. This paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. These extensions are based on fuzzy set-theoretical concepts such as the extension principle, the sigma-count operation, and the possibilistic expected value. The consistency and completeness of the proposed operations is shown

Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses

A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses

Supporting Data mining of large databases by visual feedback queries

In this paper, we describe a query system that provides visual relevance feedback in querying large databases. Our goal is to support the process of data mining by representing as many data items as possible on the display. By arranging and coloring the data items as pixels according to their relevance for the query, the user gets a visual impression of the resulting data set. Using an interactive query interface, the user may change the query dynamically and receives immediate feedback by the visual representation of the resulting data set. Furthermore, by using multiple windows for different parts of a complex query, the user gets visual feedback for each part of the query and, therefore, may easier understand the overall result. Our system allows to represent the largest amount of data that can be visualized on current display technology, provides valuable feedback in querying the database, and allows the user to find results which, otherwise, would remain hidden in the database