On the approximate division of fuzzy relations

Abstract

Boolean queries may turn out to be too limited to answer certain users needs and it is desirable to envisage extended queries by introducing preferences in the conditions. In this paper, an extension of the division operator, called the approximate division, is studied where the operand relations are fuzzy ones (i.e., are made of weighted tuples) and the universal quantifier underlying the division is softened. The objective is twofold: i) to point out that fuzzy sets provide a convenient framework for the desired extension and ii) to show that the result of the approximate division is a quotient (in reference to the characterization of the quotient of two integers), which provides a well founded semantics. © Springer-Verlag Berlin Heidelberg 2005.