Skip to main content
SpringerLink
Log in

Application of possibility-probability distribution in assessing water resource risk in Yiwu city

  • Water Resources Development: Economic and Legal Aspects
  • Published:
Water Resources Aims and scope Submit manuscript

Abstract

The possibility-probability risk calculated using the interior-outer set model is referred to as fuzzy risk. A fuzzy expected value of the possibility-probability distribution is a set with E α(x) and \(\bar E_\alpha \)(x) as its boundaries. The fuzzy expected values E α(x) and \(\bar E_\alpha \)(x) of a possibility-probability distribution represent the fuzzy risk values being calculated. Under such an α level, three risk values can be calculated: conservative risk value, venture risk value and maximum probability risk value. As α adopts all values throughout the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk can be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of Yiwu city’s water resource risk has been performed based on the interior-outer set model. We can get a conservative risk value (R C ) of 800 mm for Yiwu city’s water resource risk, a venture risk value (R V ) of 1020 mm, and a maximum probability risk value (R M ) of 988 mm for the α = 0.1 level cut set.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allahviranloo, T., Successive Over Relaxation Iterative Method for Fuzzy System of Linear Equations, Applied Mathematics and Computation, 2005, vol. 162, no. 1, pp. 189–196.

    Article  Google Scholar 

  2. Alsharif, K., Feroz, E.H., Klemer, A., and Raab, R., Governance of Water Supply Systems in the Palestinian Territories: A Data Envelopment Analysis Approach To the Management of Water Resources, Journal of Environmental Management, 2008, vol. 87, no. 1, pp. 80–94.

    Article  Google Scholar 

  3. Cazurra, T., Water Reuse of South Barcelona’s Wastewater Reclamation Plant, Desalination, 2008, vol. 218, nos. 1–3, pp. 43–51.

    Article  Google Scholar 

  4. Delgado, M., Vgay, J.L., and Vila, M.A., A Model for Linguistic Partial Information in Decision-Making Problems, Intern. Journal of Intelligent System, 1994, vol. 9, pp. 365–378.

    Article  Google Scholar 

  5. Dikmen, I., Birgonul, M.T., and Han, S., Using Fuzzy Risk Assessment to Rate Cost Overrun Risk in International Construction Projects, Intern. Journal of Project Management, 2007, vol. 25, no. 5, pp. 494–505.

    Article  Google Scholar 

  6. Elsalamony, G., A Note on Fuzzy Neighbourhood Base Spaces, Fuzzy Sets and Systems, 2006, vol. 157, no. 20, pp. 2725–2738.

    Article  Google Scholar 

  7. Feng, L.H. and Zhang, X.C., Quantitative Expression on Drought Magnitude and Disaster Intensity, Natural Hazards and Earth System Sciences, 2005, vol. 5, no. 4, pp. 495–498.

    Article  Google Scholar 

  8. Hajkowicz, S. and Higgins, A., A Comparison of Multiple Criteria Analysis Techniques for Water Resource Management, European Journal of Operational Research, vol. 184, no. 1, pp. 255–265.

  9. Huang, C.F., Concepts and Methods of Fuzzy Risk Analysis, Proc. of the First China-Japan Conference on Risk Assessment and Management, Beijing: Intern. Academic Publishers, 1998, pp. 12–23.

    Google Scholar 

  10. Huang, C.F., Moraga, C., and Chen, Z.F., A Simple Algorithm of Interior-Outer Set Model, Journal of Natural Disasters, 2004, vol. 13, no. 4, pp. 15–20.

    Google Scholar 

  11. Huang, C.F., and Shi, Y., Towards Efficient Fuzzy Information Processing—Using the Principle of Information Diffusion, Heidelberg: Physica-Verlag (Springer), 2002.

    Google Scholar 

  12. Joblonowski, M., Fuzzy Risk Analysis, Using AI Systems, AI Expert, 1994, vol. 9, no. 12, pp. 34–37.

    Google Scholar 

  13. Karimi, I. and Hullermeier, E., Risk Assessment System of Natural Hazards: A New Approach Based on Fuzzy Probability, Fuzzy Sets and Systems, 2007, vol. 158, no. 9, pp. 987–999.

    Article  Google Scholar 

  14. Machias, A.V. and Skikos, G.D., Fuzzy Risk Index of Wind Sites, IEEE Transactions on Energy Conversion, 1992, vol. 7, no. 4.

  15. Matos, M.A., Decision under Risk as a Multicriteria Problem, European Journal of Operational Research, 2007, vol. 181, no. 3, pp. 1516–1529.

    Article  Google Scholar 

  16. Moraga, C., and Huang, C.F., Learning Subjective Probabilities from a Small Data Set, Proc. of 33rd Intern. Sympos. on Multiple-Value Logic, IEEE Computer Society, Los Alamitos, 2003, pp. 355–360.

    Chapter  Google Scholar 

  17. Reyna, V.F., and Brainerd, C.J., Numeracy, Ratio Bias, and Denominator Neglect in Judgments of Risk and Probability, Learning and Individual Differences, 2008, vol. 18, no. 1, pp. 89–107.

    Article  Google Scholar 

  18. Riecan, B., On the Dobrakov Submeasure on Fuzzy Sets, Fuzzy Sets and Systems, 2005, vol. 151, no. 3, pp. 635–641.

    Article  Google Scholar 

  19. Schmucker, K.J., Fuzzy Sets, Natural Language Computations, and Risk Analysis, Rockvill: Computer Science Press, 1984.

    Google Scholar 

  20. Thavaneswaran, A., Thiagarajah, K., and Appadoo, S.S., Fuzzy Coefficient Volatility (FCV) Models with Applications, Mathematical and Computer Modeling, 2007, vol. 45, nos. 7–8, pp. 777–786.

    Article  Google Scholar 

  21. Wu, H.C., Using Fuzzy Sets Theory and Black-Scholes Formula to Generate Pricing Boundaries of European Options, Applied Mathematics and Computation, 2007, vol. 185, no. 1, pp. 136–146.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, Zhejiang Normal University, Jinhua, 321004, China

    L. H. Feng & G. Y. Luo

Authors
  1. L. H. Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Y. Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, L.H., Luo, G.Y. Application of possibility-probability distribution in assessing water resource risk in Yiwu city. Water Resour 38, 409–416 (2011). https://doi.org/10.1134/S009780781103002X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S009780781103002X

Keywords

Search

Navigation