392 Bulletin

some problems related to soft fuzzy probability spaces theory. The fol lowing results are obtained by now:

- a solution of the problem of joint observables for F-quantum spaces and their distribution (by A. Dvure~,enskij and B. Rie~,an); - a representation lemma for o-homomorphisms from the usual Borel field into o-complete lattices closed under nonincreasing involution (by A. Dvure~enskij and B. Rie~,an); - t h e individual ergodic theorem in F-quantum spaces (by B. Rie~an and B. Harman- VVT~ (~SSP, Liptovski Mikula~); - t h e Caratheodory extension theorem for P-measures on orthomodular lattices (by F. Chovanec and F. K6pka - VVT~ CSSP, Liptovski Mikula~); - some limit theorems in general ordered systems (by B. Rie~an); - a lemma representing P-measures on a Boolean algebra (by Z. Swi ta lsk i -Academy of Economy, Poznafi); - some equivalent definitions of a fuzzy P-measure (by myself); - properties of lower and upper probabilit ies generated by fuzzy P-measure (by myself).

The first meeting of people active in the above described area was held in June 1987 throughout the 11-th Mathematical Session of the Poznafi Circle. Therefore, some of the above mentioned results wi l l be published in the Proceedings thereof.

The second new area of my own research activity is an application of fuzzy sets theory in economics. I investigate a decision-making problem in econometric forecasting. Basing on some original assumptions given by the Polish economist Z. Czerwifiski for econometric models, I describe a forecast as a fuzzy subset in a space of informations. Thus, in the decision-making procedure considered by me, an optimal decision-maker's strategy is defined as a mapping from the family of fuzzy subsets in the space of informations into the family of fuzzy subsets in the space of actions. The first research results are obtained by now. I am very interested in exchange of results, experiences and remarks related to this subject.

Others problems in fuzzy set theory investigated by my colleagues from Poznafi Academy of Economy were presented in my first report. Unfortunately, not all of our investigations are supported by national research grant CPBR or a department grant such as many other research work in our country. Hence, purchasing foreign scientific literature and participation in international conferences are very troublesome for us. Therefore, all survey papers which are sent to us as free copies are an immense aid for our own studies. Many thanks for any assistance in this matter in advance.

Krzysztof Piasecki Department of Mathematics Academy of Economy ul. Marchlewskiego 146/150 60-967 Pozna~, Poland

3. B o o k R e v i e w : F u z z y Log ic in K n o w l e d g e E n g i n e e r i n g

This book edited by Henri Prade and Constantin Negoita is published by Verlag TUV Rheinland (1986).

As the flyleaf claims, this is the first edited volume dealing with the subject matter of its title. For that reason alone it is important. As with most edited volumes the quality is variable. The book is sensibly divided into three sections dealing with database and information system related issues, fuzzy inference and applications respectively. The applications section is by far the weakest, reflecting the newness of the subject. The other two sections are a treasure trove of useful and stimulating papers.

Bulletin 393

The opining contribution, by Buckles, Petry and Sachar, describes an interesting fuzzy version of relational albebra and calculus based on the central notions of similarity (crisp) relations and fuzzy functional dependencies. I felt that some effort to compare this approach with alternative ones would have been justified, but apart from this one criticism the paper is, like all the others in this section, a valuable source of inspiration and ideas for anyone working in the general area of vagueness in database systems or fuzzy retrieval. The next paper, by Ruspini, deals with proposed extensions to Chen's Entity-relationship model to permit the handling of imprecise facts. Again it contains many valuable insights. The third paper, by Testemale, contains a beautifully clear exposition of possibility theory applied to data base enquiry through an algebra-like language reminiscent of SQL.

Kacprzyk and Ziolkowski offer yet another fuzzy retrieval language. While this is by no means a criticism of this paper, I was beginning to feel by this stage the need to unify all the different methods on offer. Perhaps the most lasting contribution of this book will be that it stimulates such a unification. Next Tong has a brilliant paper describing the RUBIC retrieval system and Zemankova puts what seems to be emerging as the 'Tallahassee/Tennessee' view on the same subject, offering a description of a 'Fuzzy Intelligent Information System' FIIS.

Section Two kicks off with an interesting paper by Bandler and Kohout which offers a model (called for some obscure reason a 'paradigm') of the combination of decisions in the context of inference systems. Next, another technical paper on possibilistic inference by Dubois and Prade, followed by a paper on the use of Approximate Reasoning in knowledge acquisition. This latter paper describes a computer system called BIMBO which uses fuzzy set theory to assist rule induction. This is followed by two papers which discuss methods of inference in a medical diagnosis context, and two describing fuzzy production system tools. These are followed by an important paper by Baldwin and Crabtree on CRIL, an inference language based on conceptual graphs, which will be of interest to those who have followed Baldwin's earlier work.

As we have said the third section contains no real jewels, but does provide the starting point for those wishing to know about existing products and applications.

This book is highly recommended, despite the weaknesses associated with almost any collection of this kind.

lan Graham

4. Book Review: Applications of Fuzzy Set Theory in Human Factors

This book edited by W. Karwowski and A. Mital is published by Elsevier (1986). Another edited volume, and one even less homogeneous in quality than the one reviewed

above. To be fair, the editors say that the inclusion of such a hotch-potch of papers is deliberate policy, showing how much or how little fuzzy sets has to contribute to the field of human factors. The breadth of coverage of applications and disciplines is, in fact, one of the book's most impressive features.

The papers are organized into five sections, which are on: the concept of fuzziness in general, human-machine communication, operator judgement and reliability, work systems analysis and design and mental and physical workload stress. There is an appendix containing an interesting paper on fuzzy sets and acupuncture, although I could find no obvious reason for its inclusion, and a useful research guide with a comprehensive bibliography.

The introductory material is pretty much what one would expect, relating fuzzy sets to the existing human factors literature and focussing down to a paper on the measurement of membership functions - which is a theme implicit in some of the later papers.

The second section is a little disappointing in that its papers constantly return to the theme that fuzzy sets can be used to capture vague input, but rarely giving any experimental evidence for how good the suggested methods are. in this section, an interesting and well explained paper by Kacprzyk gives many ideas for further work, although the lines between