REQUISITE VARIETY IN THE SYSTEMS AND CONTROL SCIENCES†

Trends in the systems and control sciences are discussed in relation to certain results in cybernetics. In particular, optimal control theory is reviewed in the light of practical engineering requirements and servomechanism theory is considered in the light of Ashby's law of requisite variety.     

ON THE REPRESENTATION OF ACTIVITY ARRAYS†

A general methodology for empirical investigaiion is described which consists of: (i) the selection of a system on the object of investigation with respect to the purpose and constraints of investigation, (ii) the gathering of data for the system and organizing them in the form of activity arrays, (iii) the processing of the data through which certain time-invariant properties representing the data are determined, (iv) the interpretation of these time-invariant data representations from the standpoint of the purpose of investigation.

It is shown that each activity array yields many different representations. A procedure through which the various representations can be obtained is described that consists of: (1) the selection of a mask specifying a pattern for sampling the data, (2) the sampling procedure through which certain types of time-invariant relations are determined for the given mask, (3) the simplification of the time-invariant relations, if necessary or desirable.

A basis for the objective comparison of possible representations and ascertainment of the representation with the highest possible degree of determinism, subject to given constraints, is developed.

The procedure is applicable to both well defined and fuzzy variables of any scale. No classification into input and output variables is required, although it is not prohibited.     

THE SYSTEMS APPROACH TO A NEW WORLD VIEW†

The use of the system approach in relation to an evaluation of man and society which will contribute to the emerging world civilization (a new worldview) is explored, with particular emphasis on the question of long range goals for mankind. Gerald Feinberg's The Prometheus Project is reviewed, together with the new trends which Willis Harman calls The New Copernican Revolution. Man is emerging as the creator of his own destiny, consciously or unconsciously, and man's image of the future is a key to that future coming into being.     

BEHAVIOUR IN CONTROLLING A COMBINATION OF SYSTEMS∗

The state of a manually controlled system or combination of systems depends upon a balance between the skill of the operator and the difficulty of his task. When the difficulty of the task is varied by increasing the number of systems which have to be controlled, some change in the pattern of performance can be expected. It is possible to identify the parameters of performance which can be adjusted to meet the increasing demands of such a situation, and to describe how they are related to each other and to overall performance.

This analysis has boon applied to a task in which the pointers of Several dials which tend spontaneously to deviate have to be kept as nearly in alignment as possible, and an experiment with this task has shown ways in which subjects adapt to changes in the number of dials (and controls) involved.     

THE DECISION PROCESS: A PERSPECTIVE†

Abstract

A decision process consists of all the subprocesses pertaining to the selection of a course of action, or a plan, and to its execution. Most of these subprocesses except some well formalized ones like decision analysis are covert processes taking place exclusively in someone's mind, and are hitherto paid relatively little attention. In order to have a better understanding of the organization of the whole process, and thus to upgrade it, these neglected aspects should be brought to attention. With that principle in mind, the topics like the following are discussed in this paper: hierarchical structure of multiple decision processes, learning mechanism to dispense with deliberate analytical information processing for minor decisions, cognitive simulators to generate decision trees, goal-setting and decision scope.     

SEMANTICS OF COMPLEX STRUCTURAL SYSTEMS—PRESENTATION AND REPRESENTATION: A SYNCHRONIC VISION OF LANGUAGE L( M T )

Abstract

In this paper, the authors continue developing a Linguistic Theory of the Complex Structural Models, but in terms of the Semantics. Each symbol (transformed function) is syntactically a lexeme, carrying associate a sememe or atomic semantic unit. Each sememe can be decomposed in semes or quantic semantic unities. They are studied the semantic systems, associated with the syntactic, and that serve them as suprastruc-ture, in terms of two levels: the quantic and the atomic. Also, it is demonstrated that for all model of the complex reality, will exist always a most complex model from the syntactic and semantic point of view.     

A NOTE ON “DECOMPOSITION PROBLEM OF FUZZY RELATIONS”

The decomposition problem of a fuzzy relation R ∈ F(X × X) can be stated as: “Given a fuzzy relation R∈F(X ×.X), to determine whether there exists a fuzzy relation Z∈f(X × X) such that R = Z [Odot] Z, where X is a finite set and “[Odot]” is the max-min composition of two fuzzy relations.” In particular, if R is a Boolean matrix, then this problem becomes to find the square root of a Boolean matrix, which is a well-known unsolved problem. In 1985, Di Nola et al. (A. Di Nola, S. Sessa and W. Pedrycz, Int J. General Systems,. 10, 1985, 123?133) had solved it in theory, and proposed a numerical algorithm, illustrated by a flowchart In this note, we first point out that the flowchart proposed by Di Nola et al. is in error and give a correct flowchart. Then we give a numerical example, which is also a counterexample of the flowchart given by Di Nola el al., to explain our flowchart.     

FUZZY SYSTEMS: BASIS FOR A MODELING METHODOLOGY?

Modeling becomes a key methodological issue when we have to deal with large, complex and ill-structured problems. The traditional analytic approach to modeling aims at capturing the aggregate logic of a problematic situation, which is taken to represent the essence of the problem. The aggregate logic does not, and should not, describe the full complexity of the modeling situation, but should give a sufficient basis for finding an optimal solution to the problem. In recent criticism, however, it is pointed out that the analytic approach does not give an adequate basis for solving complex and ill-structured problems, and a systems approach is recommended. Checkland finds that the so-called hard systems thinking is no better than the analytic approach and introduces a soft systems methodology. In this paper a fuzzy systems approach is found to be more flexible than the analytic and the hard systems methods, but more precise and easier to validate than the soft systems approach.     

A DIRECTED GRAPH ALGORITHM OF VARIATIONAL GEOMETRY BASED ON GEOMETRIC REASONING

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A STUDY OF SOIL CONSERVATION MONITORING INFORMATION SYSTEM BASED ON REMOTELY SENSED DATA FOR A CATCHMENT ON THE LOESS PLATEAU

The Soil Conservation Monitorins Information System (SCMIS) presented in this paper is oriented to soil erosion control, resources exploitation, utilization, planning and management for a small watershed (about 10 sq. km.) on the Loess Plateau. It sums up Remote sensing (RS), Geographical Information System (GIS) and Expert System (ES) and consists of a integrated system. As a basic level information system of Loess Plateau, its perfection and psreading will bring about a great advance in resources exploitation and management of Loess Plateau.     

A SET-THEORETIC VIEW OF BELIEF FUNCTIONS Logical operations and approximations by fuzzy sets†

A body of evidence in the sense of Shafer can be viewed as an extension of a probability measure, but as a generalized set as well. In this paper we adopt the second point of view and study the algebraic structure of bodies of evidence on a set, based on extended set union, intersection and complementation. Several notions of inclusion are exhibited and compared to each other. Inclusion is used to compare a body of evidence to the product of its projections. Lastly, approximations of a body of evidence under the form of fuzzy sets are derived, in order to squeeze plausibility values between two grades of possibility. Through all the paper, it is pointed out that a body of evidence can account for conjunctive as well as a disjunctive information, i.e. the focal elements can be viewed either as sets of actual values or as restrictions on the (unique) value of a variable.     

FUZZY MATHEMATICS IN DYNAMICAL SYSTEMS: IS THERE A PLACE FOR IT?

A critical evaluation is presented of current attempts to introduce a fuzzification into dynamical systems theory, and, in general, to physics. The applicability and interpretation of these fuzzification methods is analysed. A new heuristic approach is suggested and discussed, which is based on the idea of the finite resolution limit.     

TIME WINDOWS: AUTOMATED ABSTRACTION OF CONTINUOUS-TIME MODELS INTO DISCRETE-EVENT MODELS IN HIGH AUTONOMY SYSTEMS∗

This paper describes the automated generation of time windows from continuous system simulation models. Time windows can be used to automatically generate equivalent discrete-event models at a coarser granularity level and they are instrumental to the design of event-based control systems. The generation of time windows represents one facility in the knowledge-based multifacetted modeling and simulation environment. DEVS-Schemc. In this environment, continuous-time and discrete-event models can coexist and they can be amalgamated with AI techniques. The usefulness of these concepts will be demonstrated by means of a model of a robot controlled fluid handling laboratory for Space Station Freedom to be used for research in Life Sciences, Microgravity Sciences, and Space Medicine.     

A review of: “THE EFFICACY OF THE SYMBOLIC,VOLUME II: A SYSTEMS MODEL OF REPRESENTATION” (in French), by Norman Lacharité. University of Quebec,Montreal, 1987, 223 pp

Classification, a data mining technique, has widespread applications including medical diagnosis, targeted marketing, and others. Knowledge discovery from databases in the form of association rules is one of the important data mining tasks. An integrated approach, classification based on association rules, has drawn the attention of the data mining community over the last decade. While attention has been mainly focused on increasing classifier accuracies, not much efforts have been devoted towards building interpretable and less complex models. This paper discusses the development of a compact associative classification model using a hill-climbing approach and fuzzy sets. The proposed methodology builds the rule-base by selecting rules which contribute towards increasing training accuracy, thus balancing classification accuracy with the number of classification association rules. The results indicated that the proposed associative classification model can achieve competitive accuracies on benchmark datasets with continuous attributes and lend better interpretability, when compared with other rule-based systems.