About quotient and division of crisp and fuzzy relations |
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Authors: | P Bosc O Pivert D Rocacher |
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Affiliation: | (1) IRISA/ENSSAT, Lannion, France |
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Abstract: | The role and properties of the division are very well known in the context of queries addressed to regular relational databases.
However, Boolean queries whose result is expressed in terms of all or nothing may turn out to be too limited to answer certain
user needs and it is desirable to envisage extended queries by introducing preferences in the conditions. In this paper, two
lines of extension of the division operator are studied: (i) operand relations of the division are fuzzy relations (i.e.,
they are made of weighted tuples) and (ii) the universal quantifier underlying the division is weakened. Various approaches
to these extensions can be considered and one of our goals is to point out those which ensure that the resulting relation
is a quotient (in reference to the characterization of the quotient of two integers). So doing, a sound semantics for the
extended division is guaranteed. |
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Keywords: | Relational databases Preferences Flexible queries Fuzzy sets Division of relations Fuzzy quantifier |
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