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Book Review Fuzzy Logic in Chemistry. Edited by D. H. Rouvray

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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
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
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
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
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
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
Frank Ehrentreich
Institut fur Analytische Chemie
der Technischen Universitat Freiberg
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
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Angew. Chem. Int. Ed. Engl. 1997,36,No. 22
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