BOOKS Fuzzy Definitions Concepts in Chemistry-A Contemporary Challenge. Edited by D. H . Rouvray. John Wiley & Sons, Chichester, 1997. xvi, 420 pp., hardcover & 65.00.-ISBN 0-86380-200-1 The sixth in the series of Mathematical Chemistry Conferences was held on July 10-14, 1995, in Pitlochry, Scotland. The title of the conference was “Are the Concepts of Chemistry all Fuzzy?” Two books on mathematical chemistry have emerged from this meeting, both edited by one of the conference organizers, Professor Dennis H. Rouvray. One of them is under review here; the other is Fuzzy Logic in Chernisty (Academic Press, San Diego, 1997). Although the list of contributors is different in the two books, there is considerable overlap in the contents, with a very fuzzy dividing line between them. Thus it is curious that neither of the books makes explicit mention of the other. The original stimulus for the editor’s interest came from a dust jacket comment by Martin Gardner that “outside of mathematics and logic, all definitions are fuzzy.” A statement by H. A. Kramers in 1946 is repeatedly quoted: “. . . in physical science in particular, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning.” The 12 chapters of the book cover a wide range of topics and vary considerably in the depth of treatment of their subject matter. The introductory chapter by the editor, “Are the Concepts of Chemistry all Fuzzy?’, is followed by one on the partnership between mathematics and chemistry (N. Trinajstic). This chapter goes back to such fundamentals as the definition of science and the roots of new books received by theeditor. Book reviews are written by invitation from the editor Suggestions for books to be reviewed and for book reviewers are welcome. Publishers should send brochures or (better) books to the editorial office: Redaktion Angewdndte Chemie, Postfach 10 11 61, D-69451 Weinheim, Germany. The editor reserves the right of selecting which books will be reviewed Uninvited books not chosen for review will not be returned Angew. Cham 1171.Ed. Engl. 1997, 36, No. 22 K> mathematics and of chemistry, and also covers such recent events as the discovery of buckminsterfullerene. It defines mathematical chemistry as “that part of theoretical chemistry which is concerned with the application of mathematical methods in the chemical world.” The next two chapters also deal with broad conceptual topics, one with periodicity (E. V. Babaev and R. Hefferlin) and the other with chemical structure (J.L. Villaveces C. and E. E. Daza C.). The remaining eight chapters focus on more specific areas such as allotropic structures, aromaticity, ring currents, porous delocalization of superconductors, chirality (two chapters), complexity, and immunological recognition. Lest we judge the title of the book too pretentious, we must remember that the divergence of topics and depth of discussion derive from the conference program. There are conspicuous omissions from the point of view of the interplay between mathematics and chemistry, for example combinatorial chemistry and quasicrystals, both being recent hot topics. Nonetheless, what is presented here is a rich collection of interesting contributions. One section in the chapter “The Concept of Chemical Structure” does not do justice to the rest of the volume. There are some trivial points that could easily be corrected, for example electron diffraction is called “electronic diffraction”, and neutron diffraction is described as being performed on gases. Incidentally, electron diffraction is listed as a new experimental technique, quite a compliment for this 67year-old tool, even if only gas-phase studies are considered. However, one aspect that could be conceptually damaging is the discussion of differences in the form of structural information originating from different techniques. The authors state that “this situation has created a profusion of geometrical parameters that greatly complicate the definition of molecular geometry.” However, the complication may arise only from the lack of understanding of the physical origin of differences among these geometrical parameters. Decades ago, precision was generally too low to warrant concern about the difWILEY-VCH Verlag GmbH, D-69451 Weinheim. 1997 ferences in the physical meaning of the structural information originating from different techniques. Nowadays, however, a precise measurement or computation needs to be qualified by additional information as to its origin, so that one can assess its accuracy. To simply compare “experimental” and “computed” data, for example, is no longer acceptable because they may have a different physical basis. In addition to the difference in the physical phenomena utilized in various techniques, the extent of motion plays an important role in this, because of the very different ways in which the motional effects are averaged. The extent of motion also greatly influences the applicability of our model of chemical structure. We have to educate ourselves to an increased degree of rigor in these aspects, whether we are providers or users of structural information. This is a conceptual question, and this book missed an important opportunity to put it in proper perspective. All in all, however, this book, along with its companion volume, discusses contemporary questions of mathematical chemistry at a high level. It has the potential of making its topics- which to many appear esoteric-accessible to a broad circle of chemists. Therefore, I recommend it to graduate students and researchers interested in aspects of their field beyond the confines of their research projects. Istvan Hargittai Budapest Technical University and Hungarian Academy of Sciences Budapest (Hungary) Fuzzy Logic in Chemistry. Edited by D. H . Rouvray. Academic Press, San Diego, 1997. 364 pp., hardcover $ 80.00.-ISBN 0-12-598910-6 The review articles collected together in this book are extended versions of papers presented during a conference held in 1995 on the subject of fuzzy logic in chemistry. The contributions can be roughly divided into three categories: introductory articles of a scientific/philosophical nature, articles concerned with the intrinsic problem of uncertainty and/or with the potential applications of fuzzy methods, 0570-0833/97/3622-2525 S 17 50+ SO 0 2525 BOOKS ~~ and lastly those in which the mathematical techniques based on the theory of fuzzysets are used to solve chemical problems. Rather surprisingly, there is no contribution on fuzzy control methods. In the first article D. H. Rouvray explains how the motivation to develop a theory that can be applied to inexact quantities is a consequence of uncertainties that are inherent in the systems under investigation. Central to this is the philosophical question of the connection between knowledge, the degree of truth of that knowledge, and uncertainty. He gives a useful compilation of various definitions of uncertainty, emphasizing that there is no general agreement on this point. The title chosen by G. Klir for his contribution already betrays the fact that he approaches the task of giving a mathematical introduction to the subject only in a half-hearted way. Instead, his article too consists largely of a discussion of philosophical aspects. It would have been more useful to put a greater emphasis on reporting the forum discussions between mathematicians and chemists, so as to clarify the issues and concepts; for example, compare the conflicting statements of Klir and Bangov about the relationship between fuzzy set theory and probability theory. The next two articles belong to the second of the categories mentioned above. That by A. Amman sets out to provoke thought about the concept of chemical structure. Starting from quantum-mechanical considerations, he throws up a number of questions that can be expressed generally as follows: can deviations from classical behavior in chemistry be understood by treating strict classical behavior as a limiting case that corresponds to a crispset? According to this view, quantum-mechanical deviations from that situation, which result from a finite number of degrees of freedom or from finite masses, correspond instead to fuzzy sets. K. Mislow is thoroughly committed to the fuzzy concept in chemistry, and shows that in any case one does in fact think and express ideas in terms of fuzzy theories. In the main part of his article he gives a concise summary of his work on extending the concept of chirality. All the following articles are concerned with applications of fuzzy set theory to the solution of chemical problems. The 86page contribution by P. Mezey begins by discussing the relationship between fuzziness and resolution, and then deals with resolution-dependent chirality, symmetry, or measures of symmetry. In considering how to develop a fuzzy way of modeling electron density, Mezey uses the 2526 0 WILEY-VCH analogy between a-cuts and electron density levels, and also develops a generalization of the Hausdorff distance incorporating fuzziness. From this basis he then develops fuzzy generalizations of symmetry elements, measures of symmetry, and other classical concepts, which are used to describe the degree of correspondence of molecular form and size. He ends by describing various methods for calculating fuzzy electron density fragments, which are then stored in numerical databases and can be used as building blocks for constructing macromolecular electron density maps. J. Brickmann discusses the use of mutual matching methods for molecular recognition. The starting point for this is the classification problem involved in the lock-and-key principle. One stage of this concerns the transformation of numerical data into diagrams, which allows one to visually inspect the system under investigation. To test the compatibility of numerical data with abstract categories of human thought processes, Brickmann uses the concept of linguistic variables. Finally he applies membership functions to a description of a soft surface, and develops strategies for fuzzy pattern recognition on surfaces. The articles by J. Xu and I. Bangov are concerned with the use of fuzzy logic for interpreting spectra, with particular emphasis on applications involving 2D NMR techniques. Both authors set out to explain how fuzzy spectroscopic data can be correlated with fuzzy molecular graphs. Xu divides his method into two stages: first one evaluates the extent of agreement between the spin-spin couplings and the molecular topology, and secondly one evaluates the degree of similarity between the graphs by a fuzzy distance measurement. However, the explanation could have been improved by a better matching between the schematic examples that are given. The article ends by touching briefly on applications to IR spectroscopy and mass spectrometry. Bangov provides some well worked out examples of the use of fuzzy methods in computer-aided structure determination. However, Equation ( 5 ) contradicts Figure 1, and also appears to contain a printing error, as it implies that the number of spectral features available for determining the structure is equal to the number of atoms. Furthermore, on the basis of this equation the author derives some generalizations that are open to question. In the main part of the article Bangov gives a breadth-frist algorithm that can be used for generating structures, and allows the risk of a combinatorial explosion to be Verlag GmbH, D-69451 Weinheim, 1997 kept under control more effectively than in depth-first procedures. The article by D.-D. Dumitrescu is concerned with the classification of unknown samples using fuzzy cluster analysis. In the mathematical part he proposes an extension of Bezdek’s “fuzzy-c-means” algorithm. His approach to the “cluster validity” problem is based OR proving the existence of a hierarchical structure within the data, and for this purpose he introduces the degree of polarization of a fuzzy partition. The algorithm makes use of binary partitions (divisive hierarchical clustering) based on procedures analogous to fuzzy-c-means. Furthermore, by using fuzzy cross-classification, the author classifies the objects according to their variables and the variables according to the objects, and investigates their interrelationship in the partitions. Some examples of analytical applications of these methods are described. The fact that D. H. Rouvray has taken on the task of collecting together, for the first time, reports of work on the applications of fuzzy methods in chemistry-related research, is very much to be welcomed. Therefore, the uniqueness of this workat least for the present-is in itself sufficient reason for recommending Fuzzy Logic in Chemistry. It will be useful not only for specialists in the particular fields concerned to study how classical concepts are being extended, but also for everyone interested in these methods, as an overview showing how far the theory of fuzzy sets has already entered chemical research. Frank Ehrentreich Institut fur Analytische Chemie der Technischen Universitat Freiberg (Germany) Alkyl Polyglycosides. Technology, Properties and Applications. Edited by K. Hill, W von Rybinski and G. Stoll. VCH Verlagsgesellschaft, Weinheim, 1996. ix, 242 pp., hardcover DM 148.00.--ISBN 3-527-29451-1 The appearance of a monograph on the properties and uses of alkyl polyglycosides (APGs), a new and interesting class of surfactants, is a welcome development. It will be especially useful for chemists who are active in the field of surfactants and are seeking new areas of application. The painstaking work of compiling the first complete picture of the technology, the physical and chemical properties, and the many applications of APGs has been undertaken by 36 scientists of the Henkel research group. This 0570-083319713622-2526 $17.50+ .SO/O Angew. Chem. Int. Ed. Engl. 1997,36,No. 22

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