Information-theoretical characterization of fuzzy relational databases

TLDR

Fuzzy relational databases encode imprecise or aggregated subjective information, and measuring their precision is crucial for validating extreme fuzziness and assessing query discrimination. The authors develop entropy measures based on fuzzy and probabilistic attributes to evaluate these precision aspects. They apply these entropy measures to the two identified ends—extreme fuzziness and query discrimination.

Abstract

A fuzzy relational database is a medium capable of representing information that is inherently imprecise or is the aggregation of the subjective opinions of a number of individuals. Measuring the degree of precision or lack thereof is important for two reasons. First, if the measures themselves achieve extrema when conditions match what is intuitively recognized as maximum and minimum fuzziness, then confidence in the medium to faithfully represent the intervening range of precision is increased. Second, querying fuzzy information may result in ambiguous replies and measures of preciseness may fathom how well the query discriminated among the possible replies. Entropy measures based on the fuzzy and probabilistic attributes of databases are developed and applied to the two ends mentioned above.