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Mathematical Problems in Engineering
Volume 2013, Article ID 647569, 10 pages
Research Article

Applying an Extended Fuzzy Parametric Approach to the Problem of Water Allocations

1School of Civil & Environmental Engineering, Nanyang Technological University, Blk N1-01c-82, 50 Nanyang Avenue, Singapore 639798
2Earth Observatory of Singapore (EOS), Nanyang Technological University, Singapore 639798

Received 22 November 2012; Accepted 22 January 2013

Academic Editor: Songlin Nie

Copyright © 2013 T. Y. Xu and X. S. Qin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An extended fuzzy parametric programming (EFPP) model was proposed for supporting water resources allocation problems under uncertainty. EFPP deals with flexible constraints (i.e., fuzzy relationships) by allowing violation of constraints at certain satisfaction degrees (i.e., levels) and employs fuzzy ranking method to handle trapezoidal-shaped fuzzy coefficients. The objective function is defuzzified by using cuts and weighting factors. The applicability of EFPP was demonstrated by a numerical example and a water resources allocation case. A series of decision alternatives at various satisfaction degrees were obtained. Generally, the higher the level, the lower the system benefit. In comparison, the level in the objective function posed less sensitive impacts on both objective function and model solutions. The reliability of EFPP was tested by comparing its solutions with those from fuzzy chance constrained programming (FCCP). The results indicated that EFPP performed equally well with FCCP in addressing parameter uncertainties, but it demonstrated a wider applicability due to its extended capacity of handling fuzzy relationships in the model constraints.