MATHEMATICAL BIBLIOGRAPHY FOR INTERPRETIVE STRUCTURAL MODELING
John N. Warfield
ABSTRACT
For those who wish to study the mathematics, this annotated bibliography provides short descriptions of various relevant publications.
MATHEMATICAL BIBLIOGRAPHY FOR INTERPRETIVE STRUCTURAL MODELING John N. Warfield
Primarily a tutorial on the use of binary matrices in system modeling, this paper introduces a method for developing a binary matrix enroute to a structural model of a system, with a procedure that permits transitivity to be used in developing the matrix.
A requirement for structural modeling is that data be acquired and organized into a form from which a structural model can be developed. A reachability matrix is one such form, useful when the contextual relation being modeled is transitive and multilevel. The author shows how to order the elements of a system in such a way that much of the data required can be computed from supplied data (given transitivity).
A procedure is described for developing an interconnection matrix that specifies a cascade connection of two known digraphs to form a digraph. The solution of this form of the interconnection problem can be applied to complete the process of description of a binary relation initiated by the process of partitioning on elements described in a companion paper. It is assumed the contextual relation is transitive.
This book gives a mathematical basis for writing software which will put interpretive structural models into graphic form. This book is also available for check-out from the Fenwick Library circulating collection, using Call No. QA402 .W37.
Describes computer operations which assist in the interpretation of complex structural models. Several of these involve partitions on a reachability matrix, which describes a contextual relation among the elements of the system under study. When partitioning of the reachability matrix in various ways does not permit adequate interpretation, cycles are usually the source of difficulty. A weighting matrix applied to the elements of a maximal cycle set permits a set of digraphs to be developed.
In this paper the `bordering theorem' is reworked and completed, following its first appearance in incomplete form in 1974. The problem of interconnecting two multilevel subsystems models defined by binary matrices A and B and a common, transitive, contextual relation to form a system model defined by matrix M is solved.
A description of a unique methodology for coping with complexity - Interpretive Structural Modeling - which, with its efficient and rapid organization of knowledge, can become the basis for dramatic social gains. The book contains all of the theoretical and mathematical background for the ISM process. This book has been translated into the Chinese language, in a publication issued in 1992, Wuhan, China.
Techniques are introduced which are applicable to machine construction of digraph maps. See also IASIS File 77/004, for a software package based on this paper, written by R. R. Cline.
The mathematical theory of how to eliminate overlap among concepts, using Translatable Graphics, Structural Types, Problem Definitions, Block Representation of Sets, and Mapping Theory, can be helpful in replacing a set of overlapping goals with a set of relatively independent goals when constructing a usable planning or policy decision.
A description of a method for computer-assisted interpretation of graphical structural models, without requiring mathematical sophistication on the part of the working group using the model.
Techniques for correcting structural defects when using interpretive structural modeling.
Published 10 years after the invention of the ISM process, this paper describes the wide scope of its current applications, lists technical and procedural details for its efficient use, includes a review of the mathematical theory supporting its software programs and a response to critics.(In this version of the mathematical theory, the author used only algebraic explanations, excluding all matrices).
Peirce's ideas on symbolic logic and the organization of human knowledge are the foundation for Warfield's presentation of a model of information-gathering and processing which will reliably and incrementally increase humanity's storehouse of accurate, usable scientific knowledge. In part, this paper is a protest against current enshrinement of the superficial and insufficient `artificial intelligence'.
By designing a numerical measurement to designate complexity and usability of three computer languages (ADA, Pascal and ALGOL 60) the author demonstrates the relative benefits of the three.
SUPPLEMENTAL REFERENCES RELATED TO THE MATHEMATICS OF INTERPRETIVE STRUCTURAL MODELING
This report is an outline of a computer program used to augment the interpretive structural modeling process. Sections include an Overview, Protocol and Interactive Dialogue, Systems Structure, Process Structure, Data Structure and Hardware Considerations.
A methodology is described for exploration and systemic development of the basis for a coalition of two social units, using computer assistance in developing the structural character of the basis. A joint intent structure and a conflict structure form the basis for consideration of a coalition, with three types of cycles being of special concern in the exploration.
Current world-wide economic difficulties suggest that there is a need for methods that lend greater insight into what econometric models tell us. It is also desirable to find simple methods for solving such models. Methods drawn from interpretive structural modeling are shown to provide a very simple solution technique for a 52-equation econometric model, and a flexible, modular interpretation of the model.
The need for transitive interconnection of two transitive, multilevel structures occurs in interpretive structural modeling. The theory of such interconnection is given. Some implications for the modeling process are discussed.
A survey of the types of research, study and applications needed to bring the new tool of Interpretive Structural Modeling into its full potential. Suggestions by the author include more and better computer programs, training of session leaders, development of the theory of cycles, development of computerized graphical displays, increased help for the use of the process by the non-mathematical user.
After a trip to Japan in 1978 to attend the International Conference of the IEEE Systems Man and Cybernetics Society in Tokyo, Warfield added the names of numerous Japanese authors to his compilation of persons studying and using Interpretive Structural Modeling, and in 1980 the collected titles of all the papers he could discover became the basis for this first ISM bibliography.
A primer-introduction to understanding graphical models, addressed to students. This 16-page report is part of a large environmental education project sponsored by the Office of Environmental Education, and headquartered at the University of Virginia under direction of J. N. Warfield.
A supplement to the June 1980 bibliography of the same title, this report contains 22 additional titles, with annotations, of papers dealing with the topic of structural modeling, interpretative structural modeling, or significantly similar fields of study. Many of the papers are by Japanese authors.
Suggestions for improving the quality of computer language design, by use of complexity-reducing techniques, augmented by graphic representations of the languages. This paper was presented by the author at the Southeastern Symposium on System Theory held at Auburn, Alabama, on March 24-26, 1985.
Presented June 22, 1988 at a joint meeting of IEEE Chapters on Computers and Social Implications of Technology, Rosslyn, Virginia, this paper is a critique of the Defense Science Board Military Software Task Report, detailing the problems which the author foresees because of its implicit assumptions. The paper closes with a number of suggestions for improving the situation. |