Skip to main content

The Entropy Theory as a Decision Making Tool in Environmental and Water Resources

  • Chapter
Entropy Measures, Maximum Entropy Principle and Emerging Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 119))

Abstract

Since the development of the entropy theory by Shannon in the late 1940s and of the principle of maximum entropy (POME) by Jaynes in the late 1950s, there has been a proliferation of applications of entropy in a wide spectrum of areas, including environmental and water resources. The real impetus to entropy-based modelling in environmental and water resources was however provided in the early 1970s, and a great variety of entropy-based applications have since been reported and new applications continue to unfold. Most of these applications have, however, been in the realm of modelling and a relatively few applications have been reported on decision making. This note revisits the entropy theory and emphasizes its usefulness in the realm of decision making in environmental and water resources, and is concluded with comments on its implications in developing countries.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aczel, J., 1984. Measuring information beyond communication theory-Why some generalized measures may be useful, others not. Aequationes Mathematice, Vol. 27, pp. 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  2. Aczel, J. and Daroczy, Z. 1975. On Measures of Informations and their Characterizations. Academic Press, New York.

    Google Scholar 

  3. Akaike, H., 1972. Information theory and an extension of the maximum likelihood principle. Proceedings, 2nd International Symposium on Information Theory, Supplement to Problems of Control and Information Theory, pp. 267281, Budapest, Hungary.

    Google Scholar 

  4. Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, Vol. AC-19, No. 6, pp. 716–723.

    Article  MathSciNet  Google Scholar 

  5. Akaike, H., 1985. Prediction and entropy. Chapter 1 in A Celebration of Statistics, edited by A.C. Atkinson and S.E. Fienberg, Springer Verlag, Heidelberg, Germany.

    Google Scholar 

  6. Alpaslan, N., Harmancioglu, N.B. and Singh, V.P., 1992. The role of entropy concept in design and evaluation of water quality mentoring networks. Entropy and Energy Dissipation in Water Resources, edited by V.P. Singh and M. Fiorentino, pp. 261–282, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  7. DeLuca, A. and Termini, S., 1972. A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, Vol. 20, pp. 301–312.

    Article  MathSciNet  Google Scholar 

  8. Forte, B., 1972. Information and Probability: Collectors and Compositivity. Symposia Mathematics, Vol. IX, pp. 121–129.

    Google Scholar 

  9. Forte, B., 1984. Entropies with and without probabilities: Application to questionnaires. Information Processing and Management, Vol. 20, No. 1, pp. 397405.

    Google Scholar 

  10. Forte, B. and Cictleo, H., 1979. Measures of uncertainty with the local property of order one and random variables. Journal of Combinatories, Information and System Science, Vol. 4, No. 3, pp. 179–204.

    Google Scholar 

  11. Goodman, J., 1985. Structural fragility and principle of maximum entropy. Structural Safety, Vol. 3, pp. 37–46.

    Article  Google Scholar 

  12. Harmancioglu, N.B., Alpaslan, N. and Singh, V.P.,1992a. Application of the entropy concept in design of water quality monitoring networks. Entropy and Energy Dissipation in Water Resources, edited by V.P. Singh and M. Fiorentino, pp. 283–302, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  13. Harmancioglu, N. B., Alpaslan. N and Singh, V.P., 1992b. Design of water quality monitoring networks. Geomechanics and Water Engineering in Environmental Management, edited by R.N. Chowdhury, Chapter 8, pp. 267–297, A.A. Balkema, Rotterdam, The Netherlands.

    Google Scholar 

  14. Harmancioglu, N.B., Alpaslan, N. and Singh, V.P., 1994. Assessment of the entropy principle as applied to water quality monitoring network design. Stochastic and Statistical methods in Hydrology and Environmental Engineering, Vol. 3, edited by K.W. Hipel, A.I. McLeod, U.S. Panu and V.P. Singh, pp. 135–148, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  15. Hramancioglu, N.B. and Singh, V.P., 1998. Entropy in environmental and water resources. In: Encyclopedia of Hydrology and Water Resources, edited by R.W. Herschy and R.W. Fairbridge, pp. 225–241, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Chapter  Google Scholar 

  16. Harmancioglu, N.B., Singh, V.P. and Alpaslan, N., 1992c. Versatile uses of the entropy concept in water resources. Entropy and Energy Dissipation in Water Resources, edited by V.P. Singh and M. Fiorentino, pp. 91–117, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  17. Horibe, Y., 1985. Entropy and correlation. IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-15, No. 5, pp. 641–642.

    Article  Google Scholar 

  18. Horowitz, A.R. and Horowitz, I., 1976. The real and illusory virtues of entropy-based measures for business and economic analysis. Decision Sciences, Vol. 7, pp. 121–136.

    Article  Google Scholar 

  19. Jaynes, E.T., 1957a. Information theory and statistical mechanics, I. Physical Review, Vol. 106, pp. 620–630.

    Article  MathSciNet  MATH  Google Scholar 

  20. Jaynes, E.T., 1957b. Information and statistical mechanics, II. Physical Review, Vol. 108, pp. 171–190.

    Article  MathSciNet  Google Scholar 

  21. Jaynes, E. T., 1961. Probability Theory in Science and Engineering. McGraw-Hill Book Company, New York.

    Google Scholar 

  22. Jaynes, E.T., 1978. When do we stand on maximum entropy. The Maximum Entropy Formalism, edited by R.D. Levine and M. Tribus, pp. 15–118, The MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  23. Jaynes, E.T., 1982. On the rationale of maximum entropy methods. Proceedings of the IEEE, Vol. 70, pp. 939–952.

    Article  Google Scholar 

  24. Kaplan, S. and Garrick, B.J., 1981. On the quantitative definition of risk. Risk Analysis, Vol. 1, No. 1, pp. 11–27.

    Article  Google Scholar 

  25. Kapur, J.N., 1983. Twenty-five years of maximum entropy principle. Journal of Mathematical and Physical Sciences, Vol. 17, No. 2, pp. 103–156.

    MathSciNet  MATH  Google Scholar 

  26. Kapur, J.N. and Kesavan, H.K., 1992. Entropy Optimization Principles with Applications. 408p., Academic Press, Inc., New York.

    Google Scholar 

  27. Kullback, S. and Leibler, R.A., 1951. On information and sufficiency. Annals of mathematical statistics, Vol. 22, pp. 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  28. Kvalseth, T.O., 1987. Entropy and correlation: Some comments. IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-17, No. 3, pp. 517–519.

    Article  Google Scholar 

  29. Levine, R.D. and Tribus, M., eds., 1978. The Maximum Entropy Formalism. 498p., The MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  30. Lewis, G.N., and Randall, M., 1961. Thermodynamics. 2nd edition revised by K.S. Pitzer and L. Brewer, McGraw-Hill, New York.

    Google Scholar 

  31. Linfoot, E.H., 1957. An informational measure of correlation. Information and control, Vol. 1, pp. 85–89.

    Article  MathSciNet  MATH  Google Scholar 

  32. Mukherjee, D. and Ratnaparkhi, M.V., 1986. On the functional relationship between entropy and variance with related applications. Communications in Statistical Theory and Methods, Vol. 15, No. 1, pp. 291–311.

    Article  MATH  Google Scholar 

  33. Pierce, J.G., 1978. A new look at the relation between information theory and search theory. The Maximum Entropy Formalism edited by R.D. Levine and M. Tribus, pp. 339–402, the MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  34. Prigogine, I., 1967. Introduction to Thermodynamics of Irreversible Processes. 3rd edition, John Wiley & Sons, New York.

    Google Scholar 

  35. Rajagopal, A.K., Teitler, S. and Singh, V.P., 1987. Some new perspectives on maximum entropy techniques in water resources research. Hydrologic Frequency Modeling, edited by V.P. Singh, pp. 247–366, D. Reidel Publishing Co., Dordrecht, The Netherlands.

    Google Scholar 

  36. Rajski, C., 1961. A metric system space of discrete probability distributions. Information and Control, Vol. 4, pp. 371–377.

    Article  MathSciNet  Google Scholar 

  37. Rosenkrantz, R.D., ed., 1983. E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics. 435 p., D. Reidel Publishing Company, Boston.

    Google Scholar 

  38. Shannon, C.E., 1948a. A mathematical theory of communications, I and II. Bell System Technical Journal, Vol. 27, pp. 379–443.

    MathSciNet  MATH  Google Scholar 

  39. Shannon, C.E., 1948b. A mathematical theory of communications, III-V. Bell System Technical Journal, Vol. 27, pp. 623–656.

    MathSciNet  Google Scholar 

  40. Singh, V.P., 1989. Hydrologic modeling using entropy. IE(I) Journal of the Institution of Engineers, Civil Engineering Division, Vol. 70, pp. 55–60.

    Google Scholar 

  41. Singh, V.P., 1992. Entropy-based probability distributions for modeling of environmental and biological systems. Structuring Biological Systems: A Computer Modeling Approach, edited by S.S. Iyengar, Chapter 6, pp. 167–208, CRC Press, Boca Raton, Florida.

    Google Scholar 

  42. Singh, V.P., 1997. The use of entropy in hydrology and water resources. Hydrological Processes, Vol. 11, pp. 587–626.

    Article  Google Scholar 

  43. Singh, V.P., 1998. Entropy-Based Parameter Estimation in Hydrology. Kluwer Academic Publishers, Boston.

    Google Scholar 

  44. Singh, V.P. and Fiorentino, M., 1992. A historical perspective of entropy applications in water resources. Entropy and Energy Dissipation in Water resources, edited by V.P. Singh and M. Fiorentino, pp. 155–173, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  45. Singh, V. P. and Rajagopal, A. K., 1986. A new method of parameter estimation for hydrologic frequency analysis. Hydrological Science and Technology, Vol. 2, No. 3, pp. 33–40.

    Google Scholar 

  46. Singh, V.P., and Rajagopal, A.K., 1987. Some recent advances in application of the principle of maximum entropy (POME) in hydrology. IAHS Publication No. 164, pp. 353–364.

    Google Scholar 

  47. Smith, C.R. and Grandy, Jr., W.T., editors, 1985. Maximum Entropy and Bayesian Methods in Inverse Problems. D. Reidel Publishing Company, Boston.

    Google Scholar 

  48. Tikochinsky, Y., Tishby, N.Z. and Levine, R.D., 1984a. Consistent inference of probabilities for reproducible experiments. Physical Review Letters, Vol. 52, No. 16, pp. 1357–1360.

    Article  Google Scholar 

  49. Tribus, M., 1963. The use of the maximum entropy in the estimation of reliability. Recent Developments in Information and Decesion Processes, edited by R.E. Machol and P. Gray, The Macmillan Company, New York.

    Google Scholar 

  50. Tribus, M., 1969. Rational Descriptions, Decisions and Designs. Pergamon Press, New York.

    Google Scholar 

  51. Tribus, M., Evans, R. and Crellin, C., 1964. The use of entropy in hypothesis testing. Proceedings of the 10th National Symposium on Reliability and Control, pp. 579–590.

    Google Scholar 

  52. Whitaker, E.T. and Robinson, G., 1944. The Calculus of Observations. 4th edition, p. 341, Blackie, Glasgow, U.K.

    Google Scholar 

  53. Yang, C.T., 1994. Variational theories in hydrodynamics and hydraulics. Journal of Hydraulic Engineering, Vol. 120,No. 6, pp. 737–756.

    Article  Google Scholar 

  54. Zurek, W.H., 1989. Algorithmic randomness and entropy. Physical Review A, Vol. 40, No. 8, pp. 4731–4751.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Singh, V.P. (2003). The Entropy Theory as a Decision Making Tool in Environmental and Water Resources. In: Karmeshu (eds) Entropy Measures, Maximum Entropy Principle and Emerging Applications. Studies in Fuzziness and Soft Computing, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36212-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-36212-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05531-7

  • Online ISBN: 978-3-540-36212-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics