The aim of Knowledge Engineering, implementing human knowledge in computers, hardly depends on the modeling of uncertainty, imprecision and vagueness. Apart from qualitative methods, one of the most promising quantitative methods to deal with them is the so-called Fuzzy Logic (FL). This extended logic covers a wide range of models but can be presented as two main fields: the one which deals with vague, fuzzy predicates and degree of truth', and the other which is more involved with the modeling of uncertainty by the use of possibility theory.2 Often, imprecision and uncertainty resides together in knowledge-based systems. In such cases, FL provides an unified framework to deal with it.3 That is the power of Fuzzy Logic with respect to the other models.
This book gathers a collection of articles devoted to various applications of FL, particularly in database management systems and expert systems inference engines. It isn't possible to report widely on all the issues, however let us mention briefly the topic of each of them in order to stress on the most interesting feature of this book which is the practical way to implement FL to real problems.
Part I deals with the representation and the management of fuzzy information in database systems. Buckles, Petry and Sachar generalize the ordinary relational databases model by a similarity based model where equivalence relationship among domain value is replaced by a measure of "nearness." The fuzzy functional dependency is discussed. In a same way, Ruspini extends the Entity-Relationship model of Chen4 for dealing with imprecision and uncertainty by defining multivalued precision and certainty scales, extensions of the concepts of value-set and attribute, and some other special structures. Testemale proposes an extension of the basic operations of relational algebra to fuzzy and/or partially unknown attribute values. Single and multiple-valued attributes, treatment of irrelevant attributes, answer to a request in term of two fuzzy sets (the sets of items which certainly/possibly satisfy the query) are some interesting features of her article. Kacprzyk and Ziolkowski focus on queries involving linguistic quant i f i e r ~~ for nonfuzzy databases. A prototype expert system for information retrieval in unformatted full text databases is exposed by Tong. Rules with attached uncertainty imbedded description of what constitutes a document of interest. He defines a semantics and a calculus of relevance, a measure which estimates how *Senior Research Assistant at the National Fund for Scientific Research (Belgium).