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General System Theory: Essential Concepts and applications
Book
Multivariate regression and linear model. Inference on cqvariance matrices. 9. Discriminant analysis. 10. Distributions of characteristic roots and vectors. 11. Principal component analysis. 12. Canonical correlation analysis. 13. Selection of variables. Appendices A: Some results on matrices. B: Matrix derivation and Jacobians. C: Some specific computerprograms (70 pages). 7. 8.
I miss chapters about factor and cluster analysis. The book contains 70 pages of references (up to 1981).
115
Reviews
discussed in more general cases; hence, after studying the book, students are not able to understand the classical ‘Gaussian law of errors in physical measures’, which is in fact of a large use for everybody. It must be noted that the book contains two chapters introducing to elementary statistics, and one on artificial generation of random variables; and that many examples ‘and problems are presented, very well chosen, with discussions and short solutions. R. FORTET Laboratoire de Probabilitt!, Tour 56 75230 Paris, France
A.J. BOSCH Eindhoven University of Technology Eindhoven, Netherlands
Anatol RAPOPORT G.P. BEAUMONT Probability and Random Variables
Ellis Horwood, Chichester, 1986, 345 pages, 212.50
General System Theory: Essential Concepts and Applications
Volume 10 in: Cybernetics and Systems Series, Abacus, Tunbridge Wells, 1986, v+ 270 pages, E24.50
In schools and universities, there is often the. necessity of introducing to probability and statistics, students who have a limited background in mathematics. The present book is intended to face that uncomfortable situation. Of course, the exposition, however rigorous, does not pretend to full generality; for instance, the concept of continuous random variable is restricted, in order that computation of moments reduces to integrals of elementary Riemannian type. Incidentally, I qtiote that the author speaks of a probability density for discrete random variables, which is not really incorrect, but unusual. In a simple case only, the author deduces the law of large numbers from Tschebischev’s inequality; actually, he gets convergence in the quadratic mean, but reduces his proposition to the convergence in probability, without writing nor discussing the terms: law of large numbers, quadratic mean, in probability. Here, I point out that ordinary people-hence, ordinary students-expect to get some precise information about ‘law of large numbers’, which is a very popular term. Another point is that the central limit theorem, proved in the simplest case of identically distributed random variables, is not presented nor
“This new awareness of the fundamental relatedness of everything to everything else has been probably the most ‘practical’ result of the systems approach” (last sentence of the preface). “But prediction and control are not the only rewards of scientific cognition. Equally important, in fact, even more important in some areas are understanding and emancipation”.( ... . ). “Here General System Theory enters in its most important function, namely, making thinking in terms of analogies, the basis of all searching for ‘explanation’ (probably a basic human need) sharper, broader, and above all, disciplined, so as to satisfy the standards of scientific cognition. It is this input of GST into the ever growing storage of reliable and organized knowledge that ought to be regarded as the most valuable contribution of this approach” (last concluding remark, p. 259). The reader may expect that some work has to be done between these two sentences. A. Rapoport, mathematician and biologist, is surely one of the most informed authors to write about that work, since he has been with the G.S.T. since its foundation. But how is it done? “Since G.S.T. is not properly a ‘theory’ (this book, p. 220), nor does it provide an ‘inquiring
116
Book
system’, as a practitioner could hope, but represents an ‘outlook’, a ‘direction’, or ‘new way of thinking’, the reader is offered mainly a set of concepts, models, and contexts, and is educated in some relations and analogies which should enrich his or her views. This set is presented under four main headers, namely ‘the classical mathematical approach’, ‘recognition and preservation of identity’, ‘organization’, ‘goal-directedness’. In the ‘application’ chapter, we see first why the term ‘application’ does not properly.. . apply, then some relations between models and contexts which illustrate arguments about structural relatedness. It is true that one should broaden his. view about the too often narrow correspondencies between models and their field of usage, about causal and teleological explanation, about direct impact prediction and apprehension of complexity; in these respects, the book offers a valuable cultural contribution. However, as concerns the dicourse on ‘classical scientific’ against ‘system thinking’, the present writer highly prefers the book “Systems Thinking, Systems Practice” by P. Checkland (1981) . It is not surprising that, given the wide range of concern, the tenants of G.S.T. are more attracted by the structurally richer, and perhaps more pervasive, formulations of models, for example: dynamic models, state-transitions, catastrophes, entropy-based measures, factor analysis. Perhaps because these cope more directly with complexity in various contexts? In this case, G.S.T. would suffer an ‘instrumental bias’ . . . - and these topics are in fact dominant in the book. However, details weaken sometimes the contribution. For example (p. 28): “the formula (AX/x!) e- A represents equally well the fraction of time periods in which . . . “, and then a case of kicks of horses is reported. Apart from the ‘fraction of time’ questionable assertion, one would expect a higher level of consideration about a known stochastic process. Also (p. 241), “since correlations range from -1 to +l, they can be associated with cosines of angles that range from 180” to 0”” should not be surprising! Finally, the assertion: “Decision theory can be regarded as a branch of organization theory” (p. 7) is a debatable point of view. As a whole, the book opens to the already cultivated reader the road to mental freedom, and to other approaches to too narrowly-defined prob-
Reviews
lems. And this is, according to Bruce Lee (in “Tao Jeet Kun Do”) “a continuous state of inquiry without conclusion. . . “. Chr. de BRUYN University of Li&e LiSge, Belgium
Michio SUGENO (ed.) Industrial Applications of Fuzzy Control North-Holland, Amsterdam, pages, Dfl.150.00
1985,
viii + 269
This volume brings together 15 papers, mostly describing recent work aimed towards the practical application of Fuzzy Control; it highlights three important points. The main one is that there are still very few leports of fuzzy controllers applied to real systems; in this book, only five papers fall into this category. This is important since practical applications are the prerequisite for convincing the wider industrial community of the virtues of what is essentially an unorthodox, but attractively simple, approach to the control of complex, non-linear industrial systems. Secondly, this book reflects the fact that, at present, most of the work in this area appears to be done in Japan and Europe - Larkin’s paper on Air Flight Con-’ trol is the only one originating solely in North America. Thirdly, fuzzy controllers which are able to generate their own rules are still uncommon only 3 out of the 15 contributions consider such techniques. The paper by Yagishita et al. on the Water Purification Process provides a convincing real application of fuzzy control employing a nonlearning controller. A clearer description of the derivation of the rules base would have been welcome since this aspect is often the most difficult in rule-based systems. The robot ,paper by Scharf et al. is one of the few known practical cases where a learning heuristic generates the controller rules; the system also requires a high sampling rate of 50 Hz. The study by Murayama et al. uses 3 rules (2 fuzzy) to optimize, on-line, the fuel consumption rate vs. fuel injection timing performance of a diesel engine; this appears to be quite a simple algorithm which performs hill-climbing using two fuzzy decisions.
Multivariate regression and linear model. Inference on cqvariance matrices. 9. Discriminant analysis. 10. Distributions of characteristic roots and vectors. 11. Principal component analysis. 12. Canonical correlation analysis. 13. Selection of variables. Appendices A: Some results on matrices. B: Matrix derivation and Jacobians. C: Some specific computerprograms (70 pages). 7. 8.
I miss chapters about factor and cluster analysis. The book contains 70 pages of references (up to 1981).
115
Reviews
discussed in more general cases; hence, after studying the book, students are not able to understand the classical ‘Gaussian law of errors in physical measures’, which is in fact of a large use for everybody. It must be noted that the book contains two chapters introducing to elementary statistics, and one on artificial generation of random variables; and that many examples ‘and problems are presented, very well chosen, with discussions and short solutions. R. FORTET Laboratoire de Probabilitt!, Tour 56 75230 Paris, France
A.J. BOSCH Eindhoven University of Technology Eindhoven, Netherlands
Anatol RAPOPORT G.P. BEAUMONT Probability and Random Variables
Ellis Horwood, Chichester, 1986, 345 pages, 212.50
General System Theory: Essential Concepts and Applications
Volume 10 in: Cybernetics and Systems Series, Abacus, Tunbridge Wells, 1986, v+ 270 pages, E24.50
In schools and universities, there is often the. necessity of introducing to probability and statistics, students who have a limited background in mathematics. The present book is intended to face that uncomfortable situation. Of course, the exposition, however rigorous, does not pretend to full generality; for instance, the concept of continuous random variable is restricted, in order that computation of moments reduces to integrals of elementary Riemannian type. Incidentally, I qtiote that the author speaks of a probability density for discrete random variables, which is not really incorrect, but unusual. In a simple case only, the author deduces the law of large numbers from Tschebischev’s inequality; actually, he gets convergence in the quadratic mean, but reduces his proposition to the convergence in probability, without writing nor discussing the terms: law of large numbers, quadratic mean, in probability. Here, I point out that ordinary people-hence, ordinary students-expect to get some precise information about ‘law of large numbers’, which is a very popular term. Another point is that the central limit theorem, proved in the simplest case of identically distributed random variables, is not presented nor
“This new awareness of the fundamental relatedness of everything to everything else has been probably the most ‘practical’ result of the systems approach” (last sentence of the preface). “But prediction and control are not the only rewards of scientific cognition. Equally important, in fact, even more important in some areas are understanding and emancipation”.( ... . ). “Here General System Theory enters in its most important function, namely, making thinking in terms of analogies, the basis of all searching for ‘explanation’ (probably a basic human need) sharper, broader, and above all, disciplined, so as to satisfy the standards of scientific cognition. It is this input of GST into the ever growing storage of reliable and organized knowledge that ought to be regarded as the most valuable contribution of this approach” (last concluding remark, p. 259). The reader may expect that some work has to be done between these two sentences. A. Rapoport, mathematician and biologist, is surely one of the most informed authors to write about that work, since he has been with the G.S.T. since its foundation. But how is it done? “Since G.S.T. is not properly a ‘theory’ (this book, p. 220), nor does it provide an ‘inquiring
116
Book
system’, as a practitioner could hope, but represents an ‘outlook’, a ‘direction’, or ‘new way of thinking’, the reader is offered mainly a set of concepts, models, and contexts, and is educated in some relations and analogies which should enrich his or her views. This set is presented under four main headers, namely ‘the classical mathematical approach’, ‘recognition and preservation of identity’, ‘organization’, ‘goal-directedness’. In the ‘application’ chapter, we see first why the term ‘application’ does not properly.. . apply, then some relations between models and contexts which illustrate arguments about structural relatedness. It is true that one should broaden his. view about the too often narrow correspondencies between models and their field of usage, about causal and teleological explanation, about direct impact prediction and apprehension of complexity; in these respects, the book offers a valuable cultural contribution. However, as concerns the dicourse on ‘classical scientific’ against ‘system thinking’, the present writer highly prefers the book “Systems Thinking, Systems Practice” by P. Checkland (1981) . It is not surprising that, given the wide range of concern, the tenants of G.S.T. are more attracted by the structurally richer, and perhaps more pervasive, formulations of models, for example: dynamic models, state-transitions, catastrophes, entropy-based measures, factor analysis. Perhaps because these cope more directly with complexity in various contexts? In this case, G.S.T. would suffer an ‘instrumental bias’ . . . - and these topics are in fact dominant in the book. However, details weaken sometimes the contribution. For example (p. 28): “the formula (AX/x!) e- A represents equally well the fraction of time periods in which . . . “, and then a case of kicks of horses is reported. Apart from the ‘fraction of time’ questionable assertion, one would expect a higher level of consideration about a known stochastic process. Also (p. 241), “since correlations range from -1 to +l, they can be associated with cosines of angles that range from 180” to 0”” should not be surprising! Finally, the assertion: “Decision theory can be regarded as a branch of organization theory” (p. 7) is a debatable point of view. As a whole, the book opens to the already cultivated reader the road to mental freedom, and to other approaches to too narrowly-defined prob-
Reviews
lems. And this is, according to Bruce Lee (in “Tao Jeet Kun Do”) “a continuous state of inquiry without conclusion. . . “. Chr. de BRUYN University of Li&e LiSge, Belgium
Michio SUGENO (ed.) Industrial Applications of Fuzzy Control North-Holland, Amsterdam, pages, Dfl.150.00
1985,
viii + 269
This volume brings together 15 papers, mostly describing recent work aimed towards the practical application of Fuzzy Control; it highlights three important points. The main one is that there are still very few leports of fuzzy controllers applied to real systems; in this book, only five papers fall into this category. This is important since practical applications are the prerequisite for convincing the wider industrial community of the virtues of what is essentially an unorthodox, but attractively simple, approach to the control of complex, non-linear industrial systems. Secondly, this book reflects the fact that, at present, most of the work in this area appears to be done in Japan and Europe - Larkin’s paper on Air Flight Con-’ trol is the only one originating solely in North America. Thirdly, fuzzy controllers which are able to generate their own rules are still uncommon only 3 out of the 15 contributions consider such techniques. The paper by Yagishita et al. on the Water Purification Process provides a convincing real application of fuzzy control employing a nonlearning controller. A clearer description of the derivation of the rules base would have been welcome since this aspect is often the most difficult in rule-based systems. The robot ,paper by Scharf et al. is one of the few known practical cases where a learning heuristic generates the controller rules; the system also requires a high sampling rate of 50 Hz. The study by Murayama et al. uses 3 rules (2 fuzzy) to optimize, on-line, the fuel consumption rate vs. fuel injection timing performance of a diesel engine; this appears to be quite a simple algorithm which performs hill-climbing using two fuzzy decisions.