Fuzzy orderings in flexible query answering systems

Abstract

This paper describes the benefits of using fuzzy orderings in flexible query answering systems. We provide a brief overview of those results from the theory of fuzzy orderings that are necessary to couple fuzzy orderings with flexible querying in a meaningful synergistic way. As one case study, we discuss a simple and pragmatic variant of a flexible query answering system -the so-called Vague query system (VQS). The integration of fuzzy orderings into that system is provided in full detail along with examples.Keywords Flexible query answering systems, Fuzzy orderings, Relational databases, Vague query system IntroductionFrom a naive viewpoint, databases are nothing else but means to store and retrieve data in an appropriately structured way. Conventional database systems available on the market offer powerful mechanisms to retrieve data according to complex criteria. A large majority of systems supports the structured query language (SQL) that has become a widely accepted standard.No matter how complex a query might be, SQL is based on logical expressions that a given record either fulfills or not. The use of classical binary logic for data retrieval poses severe limitations. Firstly, real-world data, in particular, numeric data, are often perturbed by noise or measurement errors. This may result in unstable behavior in the sense that minimal variations of the data can change the result of a query dramatically. Secondly, no structural information is available about how close a rejected record was to the fulfillment of the query. This loss of information is particularly harmful if the user would still be interested in potentially close records if the query gives an empty result. Thirdly, constructs that are closer to natural language, like vague and qualitative expressions, would mean a strong enrichment of a query interface in terms of usability and flexibility. SQL, however, does not support such kinds of elements.These fundamental needs have created an own discipline at the interface between database and fuzzy logic research. On the one hand, researchers in fuzzy logic have soon been interested in the question how to cope with imprecise and/or qualitative data and relations in database systems. The concepts developed in this direction are nowadays often subsumed under the term ''fuzzy databases' ' [6, 12, 32, 36]. A second branch of research, on the other hand, has been concerned with the problem how query interfaces to conventional databases with crisp data can be extended such that a flexible interpretation of queries is possible [7-10, 19, 22, 24, 25, 30, 33, 42, 43] -in particular, with the motivation to suggest alternatives which are close to matching the criteria in case that a query gives an empty result. This area is often referred to as ''flexible querying''. As recent overviews demonstrate [6,7,39], significant progress has been made in both directions.Fuzzy relations have a long tradition in flexible querying. In particular, fuzzy equivalence relations 1 have often been used for modeling the similar...

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