Invariance and Nominal Value Mapping as Key Themes for Qualitative Simulation

  • Paul A. Fishwick
Part of the Advances in Simulation book series (ADVS.SIMULATION, volume 5)

Abstract

We discuss the purpose of qualitative studies in simulation modeling and analysis. The notions of invariance (with regard to system structures, input, and output) and nominal value mapping are seen as central concepts (or “themes”) to the variety of qualitative methods that currently exist in simulation. Thus, our purpose is to try to help unify the study of qualitative methods by relating them to each other using the key themes. In our work we have found that many different scientific and engineering disciplines have been doing simulation using qualitative methodology; our purpose, then, is to illustrate that these efforts are connected and that the collective concepts and methodology can be potentially utilized as a set of interdisciplinary tools. The thrust in qualitative methods is seen as a step toward making quantitative methods more accessible and usable by many different types of researchers and project managers. However, as we emphasize in the text, we must be extremely careful that qualitative approaches are carefully studied so that we do not fall into the trap of using ambiguous input to generate purely ambiguous results; results must, in the long term, be directly useful to decision makers that rely on simulation (among other tools) to make well-informed decisions. We also stress that the choice of which input, output, and model to use depends on the specific goals of the analyst. It is too easy, sometimes, either to create qualitative solutions that have no utility or to make qualitative an expression that has a more powerful quantitative equivalent.

Keywords

Expense Nism Kelly Prep Metaphor 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abraham, R.H., and Shaw, C.D. Dynamics—The Geometry of Behavior (Volume 1: Periodic Behavior). Aerial Press, Santa Cruz, Calif., 1982.Google Scholar
  2. 2.
    Abraham, R.H., and Shaw, C.D. Dynamics—The Geometry of Behavior (Volume 2: Chaotic Behavior). Aerial Press, Santa Cruz, Calif., 1983.Google Scholar
  3. 3.
    Abraham, R.H., and Shaw, C.D. Dynamics—The Geometry of Behavior (Volume 3: Global Behavior). Aerial Press, Santa Cruz, Calif., 1984.Google Scholar
  4. 4.
    Abraham, R.H., and Shaw, C.D. Dynamics—The Geometry of Behavior (Volume 4: Bifurcation Behavior). Aerial Press, Santa Cruz, Calif., 1988.Google Scholar
  5. 5.
    Alefeld, G., and Herzberger, J. Introduction to Interval Computations. Academic Press, New York, 1983.MATHGoogle Scholar
  6. 6.
    Allen, J.F. Maintaining knowledge about temporal intervals. Commun. ACM 26, 11 (Nov. 1983), 832–843.MATHCrossRefGoogle Scholar
  7. 7.
    Andronov, A.A., Vitt, A.A., and Khaikin, S.E. Theory of Oscillators. Pergammon Press (reissued by Dover in 1987), 1966.Google Scholar
  8. 8.
    Austin, W., and Khoshnevis, B. Intelligent simulation environments for system modeling. In Institute of Industrial Engineering Conference, May 1988.Google Scholar
  9. 9.
    Beck, H.W., and Fishwick, P.A. Incorporating natural language descriptions into modeling and simulation. Simulation J. 52, 3 (Mar. 1989), 102–109.CrossRefGoogle Scholar
  10. 10.
    Beck, H.W., La Raw Maran, Fishwick, P.A., and Li, L. Architectures for knowledge based simulation and their suitability for natural language processing. In Advances in AI and Simulation, Tampa, Fla, Mar. 1989, pp. 103–108.Google Scholar
  11. 11.
    Blalock, H.M. Theory Construction: From Verbal to Mathematical Formulations. Prentice-Hall, Englewood Cliffs, N.J., 1969.Google Scholar
  12. 12.
    Brauer, F., and Nohel, J.A. Qualitative Theory of Ordinary Differential Equations. W.A. Benjamin, Inc., 1969.Google Scholar
  13. 13.
    Bungay, H.R. Computer Games and Simulation for Biochemical Engineering. Wiley, New York, 1985.Google Scholar
  14. 14.
    Cellier, F.E. Qualitative simulation of technical systems using the general system problem solving framework. Int. J. Gen. Syst. 13, 4 (1987), 333–344.CrossRefGoogle Scholar
  15. 15.
    Cellier, F.E., and Yandell, D.W. SAPS-II: A new implementation of the systems approach problem solver. Int. J. Gen. Syst. 13, 4 (1987), 307–322.CrossRefGoogle Scholar
  16. 16.
    Devaney, R.L. An Introduction to Chaotic Dynamical Systems. 2nd ed. Addison-Wesley, Reading, Mass., 1989.MATHGoogle Scholar
  17. 17.
    Fishwick, P.A. The role of process abstraction in simulation. IEEE Trans. Syst., Man Cybern. 18, 1 (Jan./Feb. 1988), 18–39.CrossRefGoogle Scholar
  18. 18.
    Fishwick, P.A. A study of terminology and issues in qualitative simulation. Simulation J. 51, 7 (Jan. 1989), 5–9.CrossRefGoogle Scholar
  19. 19.
    Fishwick, P.A. Qualitative methodology in simulation model engineering. Simulation J. 52, 3 (Mar. 1989), 95–101.CrossRefGoogle Scholar
  20. 20.
    Fishwick, P.A. Utilizing natural language for simulation reporting, 1990. (In preparation for the 1990 SCS Eastern Simulation MultiConference.)Google Scholar
  21. 21.
    Forrester, J.W. Urban Dynamics. MIT Press, Cambridge, Mass., 1969.Google Scholar
  22. 22.
    Franksen, O.I., Falster, P., and Evans, F.J. Qualitative aspects of large scale systems. In Lecture Notes in Control and Information Sciences, Vol. 17, A.V. Balakrishnan and M. Thoma, Eds. Springer-Verlag, New York, 1979.Google Scholar
  23. 23.
    Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. Discovering Causal Structure. Academic Press, New York, 1987.MATHGoogle Scholar
  24. 24.
    Hale, R. Cambridge University (personal communication).Google Scholar
  25. 25.
    Hamming, R.W. Numerical Methods for Scientists and Engineers. McGraw-Hill, New York, 1962.MATHGoogle Scholar
  26. 26.
    Harary, F. Structural models and graph theory. In Computer-Assisted Analysis and Model Simplification, H.J. Greenberg and J.S. Maybee, Eds. Academic Press, New York, 1981, pp. 31–58.Google Scholar
  27. 27.
    Heidorn, G.E. English as a very high level language for simulation programming. In Proceedings of the Symposium on Very High Level Languages, vol. 9, SIG-PLAN Not. (ACM) (Apr. 1974), 91–100.Google Scholar
  28. 28.
    Hezemans, P., and van Geffen, L. Justified use of analogies in systems science. In Complex and Distributed Systems: Analysis, Simulation and Control. Elsevier North-Holland, Amsterdam, 1985, pp. 61–67. (Volume IV: IMACS Transactions on Scientific Computation-85.)Google Scholar
  29. 29.
    Franklin Institute. Special issue on physical structure in modeling. J. Franklin Inst. 319, 1–2 (1985).CrossRefGoogle Scholar
  30. 30.
    Iwasaki, Y., and Simon, H.A. Causality in device behavior. Artif. Intell. 29, 1 (July 1986), 3–32.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Jacquez, J.A. Compartmental Analysis in Biology and Medicine. 2nd ed. University of Michigan Press, 1985.Google Scholar
  32. 32.
    Kandel, A. Fuzzy Mathematical Techniques with Applications. Addison-Wesley, Reading, Mass., 1986.MATHGoogle Scholar
  33. 33.
    Kaufmann, A., and Gupta, M.M. Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand, 1985.Google Scholar
  34. 34.
    Klir, G.J. Architecture of Systems Problem Solving. Plenum Press, 1985.Google Scholar
  35. 35.
    Klir, G.J., and Folger, T.A. Fuzzy Sets, Uncertainty and Information. Prentice-Hall, Englewood Cliffs, N.J., 1988.MATHGoogle Scholar
  36. 36.
    Kosslyn, S.M. Ghosts in the Mind’s Machine. W.W. Norton and Company, 1983.Google Scholar
  37. 37.
    Kuipers, B. Qualitative simulation. Artif. Intell. 29, 3 (Sept. 1986), 289–338.MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Moszkowski, B. A temporal logic for multilevel reasoning about hardware. Computer 18, 2 (Feb. 1985), 10–19.CrossRefGoogle Scholar
  39. 39.
    Moszkowski, B. Executing Temporal Logic Programs. Cambridge Press, Cambridge, Mass., 1986.Google Scholar
  40. 40.
    Nguyen, H. Fuzzy methods in discrete event simulation. Master’s thesis, Univ. of Florida, Gainesville, 1989.Google Scholar
  41. 41.
    Odum, H.T. Systems Ecology: An Introduction. Wiley, New York, 1983.Google Scholar
  42. 42.
    Odum, H.T. Simulation models of ecological economics developed with energy language methods. Simulation J. 53, 2 (1989), 69–75.CrossRefGoogle Scholar
  43. 43.
    Puccia, C.J., and Levins, R. Qualitative Modeling of Complex Systems. Harvard University Press, 1985.Google Scholar
  44. 44.
    Richardson, G.P., and Pugh, A.L. Introduction to System Dynamics Modeling with DYNAMO. MIT Press, Cambridge, Mass., 1981.Google Scholar
  45. 45.
    Richmond, B., Peterson, S., and Vescuso, P. An Academic User’s Guide to STELLA. High Performance Systems, Lyme, N.H., 1987.Google Scholar
  46. 46.
    Roberts, F.S. Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs, N.J., 1976.MATHGoogle Scholar
  47. 47.
    Roberts, F.S. Structural models and graph theory. In Computer-Assisted Analysis and Model Simplification, H. J. Greenberg and J.S. Maybee, Eds. Academic Press, New York, 1981, pp. 59–67.Google Scholar
  48. 48.
    Roberts, N., Andersen, D., Deal, R., Garet, M., and Shaffer, W. Introduction to Computer Simulation: A Systems Dynamics Approach. Addison-Wesley, Reading, Mass., 1983.Google Scholar
  49. 49.
    Rosenberg, R.C., and Karnopp, D.C. Introduction to Physical System Dynamics. McGraw-Hill, New York, 1983.Google Scholar
  50. 50.
    Seydel, R. From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis. Elsevier, New York, 1988.MATHGoogle Scholar
  51. 51.
    Simon, H.A. On the definition of the causal relation. J. Philos. 44, 16 (1952), 517–528.CrossRefGoogle Scholar
  52. 52.
    Simon, H.A. Spurious correlation: A causal interpretation. In Causal Models in the Social Sciences, H.M. Blalock, Ed. Aldine, New York, 1985.Google Scholar
  53. 53.
    Thoma, J. Bond Graphs: Introduction and Application. Pergamon Press, 1975.Google Scholar
  54. 54.
    Weld, D.S., and DeKleer, J. Readings in Qualitative Reasoning about Physical Systems. Morgan Kaufmann, 1990.Google Scholar
  55. 55.
    Wright, S. Correlation and causation. J. Agricultural Res. 20, 7 (1921).Google Scholar
  56. 56.
    Wymore, A.W. A Mathematical Theory of Systems Engineering: The Elements. Krieger Publishing Co., 1977.Google Scholar
  57. 57.
    Zadeh, L.A. Fuzzy sets. Inf. Control 8 (1965), 338–353.MathSciNetMATHCrossRefGoogle Scholar
  58. 58.
    Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8 (1975), 199–249.MathSciNetCrossRefGoogle Scholar
  59. 59.
    Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8 (1975), 301–357.MathSciNetCrossRefGoogle Scholar
  60. 60.
    Zadeh, L.A. The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 9 (1975), 43–80.MathSciNetCrossRefGoogle Scholar
  61. 61.
    Zeigler, B.P. Towards a formal theory of modelling and simulation: Structure preserving morphisms. J. ACM 19, 4 (1972), 742–764.MathSciNetMATHCrossRefGoogle Scholar
  62. 62.
    Zeigler, B.P. Theory of Modelling and Simulation. Wiley, New York, 1976.MATHGoogle Scholar
  63. 63.
    Zeigler, B.P. Multi-Facetted Modelling and Discrete Event Simulation. Academic Press, New York, 1984.Google Scholar
  64. 64.
    Zeigler, B.P. Multifaceted systems modeling: Structure and behavior at a multiplicity of levels. In Individual Development and Social Change: Explanatory Analysis. Academic Press, New York, 1985, pp. 265–293.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Paul A. Fishwick

There are no affiliations available

Personalised recommendations