Showing papers in "International Journal of General Systems in 1978"

Synthesis of fuzzy models for industrial processes-some recent results

Abstract: Many industrial processes are examples of Zadeh's “principle of incompatibility” which states that as a system becomes more complex it becomes increasingly difficult to make mathematical statements about it which are both meaningful and precise. So that if a model of such a process is required then a fuzzy model may be the “best” that can be achieved. This paper considers the problems of building such models. It introduces a definition of a fuzzy model, discusses the assessment of its quality and outlines a systematic procedure for deriving a model from input-output data.

On the connection between the complexity and credibility of inferred models

Abstract: The connection between the simplicity of scientific theories and the credence attributed to their predictions seems to permeate the practice of scientific discovery. When a scientist succeeds in explaining a set of nobservations using a model Mof complexity c then it is generally believed that the likelihood of finding another explanatory model with similar complexity but leading to opposite predictions decreases with increasing nand decreasing c. This paper derives formal relationships between n, c and the probability of ambiguous predictions by examining three modeling languages under binary classification tasks: perceptrons, Boolean formulae, and Boolean networks. Bounds are also derived for the probability of error associated with the policy of accepting only models of complexity not exceeding c. Human tendency to regard the simpler as the more trustworthy is given a qualified justification.

Network synthesis and varela's calculus

Abstract: Network models are given for self-referential expressions in the calculus of indications (of G. Spencer Brown). A precise model is presented for the behavior of such expressions in time. The extension of Brown's calculus by F. Varela is then shown to describe behavior invariant properties of these networks. Network design is discussed from this viewpoint

Some foundational views on general systems and the hempel paradox

Abstract: Some concepts within general systems, like autonomy and self-reference, are difficult enough to raise foundational questions. Tarski's foundational work on meaning is reviewed and applied to explain some consistent forms of self-reference. The characteristic circularity is hereby unfolded. This suggests that explicable forms of autonomy and self-reference can always be eliminated in a language of sufficiently high order. Thus, in an explicatory sense, these concepts undoubtedly have a productive value The notion of relevance within theory-formation processes is another difficult concept, raised by the interdisciplinary character of general systems. For philosophy of science it has generated the paradox of Hempel. A foundational view is given that explains the paradox and provides a further insight into the concept of relevance (and support and confirmation).

Structuring the organization of partial models

Abstract: An organization of partial models is a system in which no one model can answer all questions about a real large-scale system, but where there is a means of determining whether there is a model appropriate to a given question and if so indicating which it is. The structuring of such an organization based on the theory of modelling and simulation is discussed.

Discrete and continuous models

Abstract: M. E. Van Valkenburg writes in the foreword to Steiglitz’s Introduction to Discrete Systems,1 that “Given the widespread availability of computers, there seems little doubt that the teaching of electrical engineering should undergo an evolution ... In the emerging pedagogical approach, equations should be written in discrete form as difference equations, instead of in continuous form as differential equations. Indeed, equations should seldom be used, since principles should be stated directly in algorithmic form.” Approaches having this character are increasingly being proposed not only in electrical engineering but in other fields where continuous mathematical methods have been traditional, and not only are pedagogical changes being suggested. Digital computing and discrete models are influencing our conception of real world systems and the role classical mathematical methods are to play in modelling them.

Input/output codings and transition functions in effective systems

Abstract: We study some aspects of what might be called a general theory of effective systems. First, we define the notion of a universal effective system and derive some theorems which give the connection of this notion with related concepts in recursive function theory. Then we characterize the class of transition functions and the sets of final states of universal effective systems. Finally, we exactly determine the role of input/output codings in effective systems and characterize the class of possible input and output codings in universal effective systems. We interpret our results in terms of computer science

Evolution of a hydrology model—an exercise in modelling strategy

Abstract: This paper is a case study of the application of modelling principles. Development of a forest watershed hydrology model, designed as a component of a forest ecosystem model, is followed through a series of developmental stages. Primary attention is given to the manner in which structural change was implemented in order to achieve coarse agreement with prescribed model behavior; little attention was given to Tine tuning. The modelling effort was terminated when it was recognized that further improvement required better definition of prescribed system behavior, more complete specification of couplings with other ecosystem components, and a better submodel for incidence of snow and snowmelt. The capacity to yield arbitrary prescribed behavior was demonstrated, with the exception of snow behavior. The FLEX modelling paradigm, developed from a base provided by Klirapos;s General System Theory, and implemented in a computer processor, FLEX2, was shown to be very useful in the structural evolution repo...

Foundations of the polynomial theory for linear systems

Abstract: This paper briefly presents the fundamental facts of the polynomial systems theory as applied by Rosenbrock, Wolovich and others. The theory utilizes an operator algebra which is a natural generalization of the usual operational calculus based on the Laplace and Z-transforms. It is shown how this operator algebra can be used in an efficient way for solving a number of typical problems relating to the analysis and synthesis of linear time-invariant feedback systems and estimators.

The characterization of binary relation homomorphisms

Abstract: A characterization theorem is derived for homomorphisms of one binary relation to another. The characterization theorem states that any homomorphism from one relation to another can be represented as the intersection of some basis relations. Furthermore, appropriate intersections of the basis relations define a relation homomorphism. The characterization theorem leads to an efficient algorithm for determining all the homomorphisms from one relation to another: first find the basis relations, and then use the basis relations to generate all single-valued relations which then will be all the homomorphisms from one relation to the other. Specialization of the procedure easily determines whether two relations or digraphs are isomorphic.

Review of: “SELF-ORGANIZATION IN NONEQUILIBRIUM SYSTEMS”, by G. Nicolis and I. Prigogine, John Wiley, New York, 1977, 491 pp.

Abstract: (1978). Review of: “SELF-ORGANIZATION IN NONEQUILIBRIUM SYSTEMS”, by G. Nicolis and I. Prigogine, John Wiley, New York, 1977, 491 pp. International Journal of General Systems: Vol. 4, No. 4, pp. 266-269.

Problems on feedback control of uncertain systems: a theoretical interpretation†

Abstract: The main problem in control theory is the definition of the optimal control law that must be applied to a physical system in order to obtain a desired behaviour. A general approach to this problem is developed, in order to explain the consideration of Rapoport that: “.feedback loops suggest that information is somehow fed into the system, or that the system obtains information about itself.” To this extent, the meanings of “system” and approximating “model” are properly clarified. The correct use of an observer, as the device which measures the uncertainty about the internal structure of the system and about the environmental influences on the system itself, is defined. The concept of “equilibrium” of a controlled system is introduced and some necessary and sufficient conditions in order that such an equilibrium may be reached, are stated.

On the strength of belief of dialectical belief systems

Abstract: This paper shows how the notion of the “strength of belief” of a purposeful individual in a “belief system” can be conceptualized in a manner fitting operationalization. We argue that the notion of “strength of belief” is to the behavioral sciences as the notion of “force” is to the physical sciences. The paper also shows how the distance between belief systems can be operationalized so that the analogue to the physical science concept of work can be measured as the product of (strength of belief” times (distance.” That is, the paper develops a formula for work or energy in the behavioral sense which is based on the integral of “strength of belief” through a distance. We show under which conditions the strength of belief in a belief system goes to zero as well as to infinity. The paper not only argues that the concept of the strength of belief is central to the social sciences but it also argues that the meaning of “law” is considerably different in the social sciences than it is in the physical ...

A completely arithmetic formulation of classical and special relativistic physics

Abstract: In this paper it is shown how classical Newtonian mechanics and special relativistic mechanics can be reformulated using only arithmetic. All the usual conservation laws are established in exactly the same form in which they appear in continuous mechanics. New, completely arithmetic models of physical phenomena emerge. Analysis of dynamical behavior requires the use of a modern digital computer.