Water Resources Management

, Volume 32, Issue 13, pp 4425–4443 | Cite as

An Entropy-Based Approach to Fuzzy Multi-objective Optimization of Reservoir Water Quality Monitoring Networks Considering Uncertainties

  • Shokoufeh Pourshahabi
  • Mohammad Reza Nikoo
  • Ehsan Raei
  • Jan Franklin Adamowski


In this study, a new fuzzy methodology for a multi-objective optimization of reservoir Water Quality Monitoring Stations (WQMS) was developed, based on Transinformation Entropy (TE), the IRanian Water Quality Index (IRWQI), and fuzzy social choice considering uncertainties. The approach was utilized in the Karkheh Dam reservoir in Iran. The objective functions were: 1) minimizing costs, 2) minimizing redundant information and uncertainties, and 3) maximizing the spatial coverage of the network. A CE-QUAL-W2 model was used for the simulation of water quality variables. The IRWQI was computed to reveal a complete picture of the reservoir water quality. The TE quantities were calculated for each pair of potential stations. The TE values were plotted against the spatial distances among potential WQMS to obtain the TE–Distance (TE–D) curve, and minimize redundant information among stations, while providing coverage of the entire network. A multi-objective Genetic Algorithm (NSGA-II) was applied to obtain Pareto-optimal solutions taking stakeholder preference into account. The most preferred solution was then obtained using fuzzy social choice approaches to achieve a consensus. The fuzziness embedded in the decision-making procedure, the uncertainty in the value of mutual information, and the uncertainty in identifying the optimal distance among WQMS were also investigated. Results indicated that the three fuzzy social choice approaches (Borda Count, Minimax, and Approval Voting) led to the same number of optimized WQMS in each fuzzy alpha-cut. Based on the fuzzy linguistic quantifiers method, the number of optimized WQMS was increased.


Water quality monitoring stations (WQMS) NSGA-II Transinformation entropy Fuzzy social choice IRWQI 



The authors would like to gratefully acknowledge Dr. Fariborz Masoumi at the University of Mohaghegh Ardabili for his valuable assistance with data and the calibration process of the CE-QUAL-W2 model.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Supplementary material

11269_2018_2073_MOESM1_ESM.docx (1 mb)
ESM 1 (DOCX 1051 kb)


  1. Afshar A, Saadatpour M (2009) Reservoir eutrophication modeling, sensitivity analysis, and assessment: application to Karkheh reservoir, Iran. Environ Eng Sci 26(7):1227–1238CrossRefGoogle Scholar
  2. Behmel S, Damour M, Ludwig R, Rodriguez MJ (2016) Water quality monitoring strategies — a review and future perspectives. Sci Total Environ.
  3. Caselton WF, Husain T (1980) Hydrologic networks: information transmission. J Water Resour Plan Manag 106(2):503–520Google Scholar
  4. Cole TM, Wells SA (2013) CE-QUAL-W2: a two-dimensional, laterally averaged, Hydrodynamic and Water Quality Model, Version 3.71, Department of Civil and Environmental Engineering, Portland State University, Portland, ORGoogle Scholar
  5. Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. International Conference on Parallel Problem Solving From Nature, Springer Berlin Heidelberg, p 849–858Google Scholar
  6. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  7. García-Lapresta JL, Martínez-Panero M (2002) Borda count versus approval voting: a fuzzy approach. Public Choice 112:167–184CrossRefGoogle Scholar
  8. Harmancioglu NB, Fistikoglu O, Ozkul SD, Singh VP, Alpaslan N (1999) Water quality monitoring network design. Kluwer Academic Publishers, Boston 299 ppCrossRefGoogle Scholar
  9. Harmancioglu NB, Yevjevich V (1987) Transfer of hydrologic information among river points. J Hydrol 91:103–118CrossRefGoogle Scholar
  10. Iranian water quality index, User’s Manual (2013) 5-13 (In Persian)Google Scholar
  11. Kacprzyk J, Fedrizzi M, Nurmi H (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst 49:21–31CrossRefGoogle Scholar
  12. Lee C, Paik K, Lee Y (2014) Optimal sampling network for monitoring the representative water quality of an entire reservoir on the basis of information theory. J Water Clim Change 5(2):151–162CrossRefGoogle Scholar
  13. Masoumi F, Kerachian R (2010) Optimal redesign of groundwater quality monitoring networks: a case study. Environ Monit Assess Springer 161(1-4):247–257. CrossRefGoogle Scholar
  14. Maymandi N, Kerachian R, Nikoo MR (2018) Optimal spatio-temporal design of water quality monitoring networks for reservoirs: application of the concept of value of information. J Hydrol 558:328–340CrossRefGoogle Scholar
  15. Memarzadeh M, Mahjouri N, Kerachian R (2013) Evaluating sampling locations in river water quality monitoring networks: application of dynamic factor analysis and discrete entropy theory. Environ Earth Sci 70(6):2577–2585. CrossRefGoogle Scholar
  16. Mogheir Y, de Lima JLMP, Singh VP (2004a) Characterizing the spatial variability of groundwater quality using the entropy theory: I. Synthetic data. J Hydrol Process 18:2165–2179CrossRefGoogle Scholar
  17. Mogheir Y, de Lima JLMP, Singh VP (2004b) Characterizing the spatial variability of groundwater quality using the entropy theory: II. Case study from Gaza Strip. J Hydrol Process 18:2579–2590CrossRefGoogle Scholar
  18. Mogheir Y, de Lima JLMP, Singh VP (2009) Entropy and multiobjective based approach for groundwater quality monitoring network assessment and redesign. Water Resour Manag 23(8):1603–1620CrossRefGoogle Scholar
  19. Mondal NC, Singh VP (2012) Evaluation of groundwater monitoring network of Kodaganar River basin from southern India using entropy. Environ Earth Sci 66:1183–1193CrossRefGoogle Scholar
  20. Nikoo MR, Pourshahabi S, Rezazadeh N, Shafiee ME (2017) Stakeholder engagement in multi-objective optimization of water quality monitoring network, case study: Karkheh dam reservoir. Water Sci Technol Water Supply 17(4):966–974. ws2016196. CrossRefGoogle Scholar
  21. Nurmi H (1981) Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets Syst 6:249–259CrossRefGoogle Scholar
  22. Ozkul S, Harmancioglu NB, Singh VP (2000) Entropy-based assessment of water quality monitoring networks. J Hydrol Eng 5(1):90–100CrossRefGoogle Scholar
  23. Pourshahabi S, Talebbeydokhti N, Rakhshandehroo G, Nikoo MR (2018) Spatio-temporal multi-criteria optimization of reservoir water quality monitoring network using value of information and transinformation entropy. Water Resour Manag 1-16Google Scholar
  24. Rezazadeh N (2012) Management of eutrophication and selecting appropriate discharge level of Karkheh Dam Reservoir with Mathematics Model (Master Dissertation) University of Tehran, Tehran, Iran (In Persian)Google Scholar
  25. Salark N, Sorman AU (2006) Evaluation and selection of streamflow network stations using entropy methods. Turkish J Eng Environ Sci 30:91–100Google Scholar
  26. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:623–656CrossRefGoogle Scholar
  27. Sheikhmohammady M, Madani K (2008) Bargaining over the Caspian Sea- the largest lake on the earth. Ahupua’a, World Environmental and Water Resources CongressCrossRefGoogle Scholar
  28. Talebbeydokhti N, Pourshahabi S, Rakhshandehroo GR, Nikoo MR, Amiri M (2017) Review of reservoir water quality monitoring and modelling. 4th International Conference on Long-Term Behaviour and Environmentally Friendly Rehabilitation Technologies of Dams (LTBD 2017), Tehran, IranGoogle Scholar
  29. Varol M, Gökot B, Bekleyen A, Şen B (2012) Spatial and temporal variations in surface water quality of the dam reservoirs in the Tigris River basin, Turkey. Catena 92:11–21CrossRefGoogle Scholar
  30. Yenilmez F, Düzgün S, Aksoy A (2015) An evaluation of potential sampling locations in a reservoir with emphasis on conserved spatial correlation structure. Environ Monit Assess 187Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringShiraz UniversityShirazIran
  2. 2.Department of Bioresource EngineeringMcGill UniversityMontrealCanada

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