A General Technique to Measure Gradual Properties of Fuzzy Sets

This paper considers gradual set-oriented functions and their application to fuzzy sets. An example, taken in the context of flexible querying of databases, is provided by the condition “the average salary of \RXQJ employees is DURXQG ”. The evaluation of this condition leads to apply the gradual set-oriented property “the average salary is DURXQG ” to the fuzzy set made of \RXQJ employees. The contribution of this paper is to propose a general technique to achieve such computations which is a generalization of Sugeno fuzzy integral. The result is given in the form of a degree which has a clear meaning. Two examples of use of this technique in the area of regular relational databases serve to illustrate this proposal.