Comparative study of fuzzy evidential reasoning and fuzzy rule-based approaches: an illustration for water quality assessment in distribution networks

  • E. Aghaarabi
  • F. Aminravan
  • R. Sadiq
  • M. Hoorfar
  • M. J. Rodriguez
  • H. Najjaran
Original Paper


This paper presents the use of two multi-criteria decision-making (MCDM) frameworks based on hierarchical fuzzy inference engines for the purpose of assessing drinking water quality in distribution networks. Incommensurable and uncertain water quality parameters (WQPs) at various sampling locations of the water distribution network (WDN) are monitored. Two classes of WQPs including microbial and physicochemical parameters are considered. Partial, incomplete and subjective information on WQPs introduce uncertainty to the water quality assessment process. Likewise, conflicting WQPs result in a partially reliable assessment of the quality associated with drinking water. The proposed methodology is based on two hierarchical inference engines tuned using historical data on WQPs in the WDN and expert knowledge. Each inference engine acts as a decision-making agent specialized in assessing one aspect of quality associated with drinking water. The MCDM frameworks were developed to assess the microbial and physicochemical aspects of water quality assessment. The MCDM frameworks are based on either fuzzy evidential or fuzzy rule-based inference. Both frameworks can interpret and communicate the relative quality associated with drinking water, while the second is superior in capturing the nonlinear relationships between the WQPs and estimated water quality. More comprehensive rules will have to be generated prior to reliable water quality assessment in real-case situations. The examples presented here serve to demonstrate the proposed frameworks. Both frameworks were tested through historical data available for a WDN, and a comparison was made based on their performance in assessing levels of water quality at various sampling locations of the network.


Fuzzy evidential reasoning Fuzzy rule-based systems Water distribution network Quality assessment Multi-criteria decision making (MCDM) 



Multi-criteria decision making


Water quality parameter


Water distribution network




Fuzzy rule-based system


Fuzzy Dempster–Shafer


Free residual chlorine


Heterotrophic plate counts


Disinfection by-products


Total trihalomethanes


Water distribution system


Basic probability assignment




Probability density functions


Analytic hierarchy process


  1. Abraham A, Vasant P, Bhattacharya A (2008) Neuro-fuzzy approximation of multi-criteria decision-making QFD methodology. In: Kahraman C (ed) Fuzzy multi-criteria decision making. Springer optimization and its applications, vol 16. Springer, US, pp 301–321Google Scholar
  2. Alim S (1989) Application of Dempster–Shafer theory for interpretation of seismic parameters. Struct Eng 114(9):2070–2084CrossRefGoogle Scholar
  3. Allen MJ, Edberg SC, Reasoner DJ (2004) Heterotrophic plate count bacteria—what is their significance in drinking water? Int J Food Microbiol 92(3):265–274CrossRefGoogle Scholar
  4. Aminravan F, Sadiq R, Hoorfar M, Rodriguez MJ, Francisque A, Najjaran H (2011a) Evidential reasoning using extended fuzzy Dempster–Shafer theory for handling various facets of information deficiency. Int J Intell Syst 26:731–758CrossRefGoogle Scholar
  5. Aminravan F, Hoorfar M, Sadiq R, Francisque A, Najjaran H, Rodriguez MJ (2011b) Interval belief structure rule-based system using extended fuzzy Dempster–Shafer inference. 2011 IEEE International Conference on Systems, Man, and Cybernetics, pp 3017–3022Google Scholar
  6. Attoh-Okine NO, Gibbons J (2001) Use of belief function in brownfield infrastructure redevelopment decision making. ASCE J Urban Plan Dev 127(3):126–143CrossRefGoogle Scholar
  7. Brettar I, Höfle MG (2008) Molecular assessment of bacterial pathogens—a contribution to drinking water safety. Curr Opin Biotechnol 19(3):274–280CrossRefGoogle Scholar
  8. Chang NB, Pongsanone NP, Ernest A (2011) Comparisons between a rule-based expert system and optimization models for sensor deployment in a small-scale drinking water distribution network. Expert Syst Appl 38:10685–10695CrossRefGoogle Scholar
  9. Chang NB, Ernest A, Pongsanone NP (2012a) A rule-based decision support system for sensor deployment in small drinking water networks. J Clean Prod 29:28–37CrossRefGoogle Scholar
  10. Chang NB, Pongsanone NP, Ernest A (2012b) Optimal sensor deployment in a large-scale complex drinking water distribution network: comparisons between a rule-based decision support system and optimization models. Comput Chem Eng 43:191–199CrossRefGoogle Scholar
  11. Chen HW, Chang NB (2001) Identification of river water quality using the fuzzy synthetic evaluation approach. J Environ Manage 63(3):293–305CrossRefGoogle Scholar
  12. Chen JK, Chen IS (2010) Aviatic innovation system construction using a hybrid fuzzy MCDM model. Expert Syst Appl 37(12):8387–8394CrossRefGoogle Scholar
  13. Dempster A (1968) A generalization of Bayesian inference. J R Stat Soc Ser B 30:205–247Google Scholar
  14. Dongale TD, Kulkarni TG, Kadam PA, Mudholkar RR (2011) Fuzzy model of thermistor. Int J Appl Eng Res 2(2):431–438Google Scholar
  15. Dubois D, Prade H (1992) On the combination of evidence in various mathematical frameworks. In: Flamm J, Luisi T (eds) Reliability data collection and analysis, vol 3. Springer, Netherlands, pp 213–241CrossRefGoogle Scholar
  16. Francisque A (2009) Strategies for improving the surveillance of drinking water quality in distribution networks: application of emerging modeling approaches. Ph.D. Thesis. Superior School of Urban Planning and Regional Development, Laval University, Quebec, Canada, p. 208Google Scholar
  17. Francisque A, Rodriquez MJ, Sadiq R, Miranda LF, Proulx F (2009a) Modeling of heterotrophic bacteria counts in a water distribution system. Water Res 43(4):1075–1087CrossRefGoogle Scholar
  18. Francisque A, Rodriguez MJ, Sadiq R, Miranda L, Proulx F (2009b) Prioritizing monitoring locations in a water distribution network: a fuzzy risk approach. J Water Supply Res Technol 58(7):488CrossRefGoogle Scholar
  19. Gorchev HG, Ozolins G (1984) WHO guidelines for drinking-water quality. WHO Chron 38(3):104–108Google Scholar
  20. Guo M, Yang JB, Chin KS, Wang HW, Liu XB (2009) Evidential reasoning approach for multiattribute decision analysis under both fuzzy and interval uncertainty. IEEE Trans Fuzzy Syst 17(3):683–697CrossRefGoogle Scholar
  21. Hall J, Zaffiro AD, Marx RB, Kefauver PC, Krishnan R, Haught ROYC, Herrmann JG (2007) On-line water quality parameters as indicators of distribution system contamination Reviewed work(s). J Am Water Works Assoc 99(1):66–77Google Scholar
  22. Health Canada (2000) Chlorinated disinfection by-products. Prepared for the Chlorinated Disinfection By-product Task GroupGoogle Scholar
  23. Health Canada (2009) Guidelines for Canadian drinking water Quality: Guideline technical document—chlorine. Water, Air and Climate Change Bureau, Healthy Environments and Consumer Safety Branch, Health Canada, Ottawa, OntarioGoogle Scholar
  24. IPCS (2000) Disinfectants and disinfectant by-products. International Programme on Chemical Safety, World Health Organization, Geneva, SwitzerlandGoogle Scholar
  25. Koo JK, Shin HS (1985) Application of fuzzy sets to water quality management. Water Supply 4:293–305Google Scholar
  26. Liu J, Yang JB, Wang J, Sii HS, Wang YM (2004) Fuzzy rule-based evidential reasoning approach for safety analysis. Int J Gen Syst 33(2–3):183–204. doi: 10.1080/03081070310001633536 CrossRefGoogle Scholar
  27. National Guide to Sustainable Municipal Infrastructure (NGSMI) (2004). Monitoring water quality in the distribution system. Federation of Canadian Municipalities and National Research CouncilGoogle Scholar
  28. Niskanen VA (2002) A soft multi-criteria decision-making approach to assessing the goodness of typical reasoning systems based on empirical data. Fuzzy Sets Syst 131(1):79–100CrossRefGoogle Scholar
  29. Ostfeld A, Uber JG, Salomons E, Berry JW, Hart WE, Phillips CA et al (2008) The battle of the water sensor networks (BWSN): a design challenge for engineers and algorithms. J Water Res Plan Manage, ASCE 134(6):556–568CrossRefGoogle Scholar
  30. Payment P (1999) Poor efficacy of residual chlorine disinfectant in drinking water. Can J Microbiol 45(8):709CrossRefGoogle Scholar
  31. Payment P, Waite M, Dufour A (2003) Introducing parameters for the assessment of drinking water quality. Improving approaches and methods, In Assessing microbial safety of drinking waterGoogle Scholar
  32. Raptis C, Siettos CI, Kiranoudis CT, Bafas GV (2000) Classification of aged wine distillates using fuzzy and neural network systems. J Food Eng 46:267–275CrossRefGoogle Scholar
  33. Reasoner DJ (2004) Heterotrophic plate count methodology in the United States. Int J Food Microbiol 92(3):307–315CrossRefGoogle Scholar
  34. Russo L, Albanese D, Siettos C, Matteo M, Crescitelli A (2012) A neuro-fuzzy computational approach for multicriteria optimisation of the quality of espresso coffee by pod based on the extraction time, temperature and blend. Int J Food Sci Technol 47:837–846CrossRefGoogle Scholar
  35. Saaty TL (1980) The Analytic Hierarchy Process. McGraw-Hill, New YorkGoogle Scholar
  36. Sadiq R, Rodriguez MJ (2004) Disinfection by-products (DBPs) in drinking water and predictive models for their occurrence: a review. Sci Total Environ 321(1–3):21–46CrossRefGoogle Scholar
  37. Sadiq R, Rodriguez MJ (2005) Interpreting drinking water quality in the distribution system using Dempster–Shafer theory of evidence. Chemosphere 59(2):177–188CrossRefGoogle Scholar
  38. Sadiq R, Kleiner Y, Rajani BB (2004) Aggregative risk analysis for water quality failure in distribution networks. J Water 53(4):241–261Google Scholar
  39. Sadiq R, Kleiner Y, Rajani B (2006a) Estimating risk of contaminant intrusion in water distribution networks using Dempster–Shafer theory of evidence. Civ Eng Environ Syst 23(3):129–141CrossRefGoogle Scholar
  40. Sadiq R, Najjaran H, Kleiner Y (2006b) Investigating evidential reasoning for the interpretation of microbial water quality in a distribution network. Stoch Environ Res Risk Assess 21(1):63–73CrossRefGoogle Scholar
  41. Sadiq R, Kleiner Y, Rajani B (2007) Water quality failures in distribution networks—risk analysis using fuzzy logic and evidential reasoning. Risk Anal 27(5):1381–1394CrossRefGoogle Scholar
  42. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonGoogle Scholar
  43. Smets P (2007) Analyzing the combination of conflicting belief functions. Inf Fus 8(4):387–412Google Scholar
  44. Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66:191–243CrossRefGoogle Scholar
  45. Tesfamariam S, Sadiq R, Najjaran H (2009) Decision making under uncertainty—An example for seismic risk management. Risk Anal 30(1):87–94Google Scholar
  46. U.S. Environmental Protection Agency (USEPA) (1999) Review Draft “Guidelines for Carcinogen Risk Assessment;” July 1999. NCEA-F-0644. National Center for Environmental Assessment, Office of Research & Development, Washington, DCGoogle Scholar
  47. USEPA (2006) Inorganic contaminant accumulation in potable water distribution systems. U.S. Environmental Protection Agency, Washington, DCGoogle Scholar
  48. USEPA (2009) Distribution system water quality monitoring: Sensor technology evaluation methodology and results. U.S. Environmental Protection Agency, Washington, DC, 600/R-09/076Google Scholar
  49. WHO (1995) Disinfectants and disinfection by-products. In: WHO seminar pack for drinking water quality. World Health Organization, Geneva, SwitzerlandGoogle Scholar
  50. WHO (2007) pH in drinking water. In: WHO seminar pack for drinking water quality. World Health Organization, Geneva, SwitzerlandGoogle Scholar
  51. Xu DL (2012) An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis. Ann Oper Res 195:163–187CrossRefGoogle Scholar
  52. Xu DL, Liu J, Yang JB, Liu GP, Wang J, Jenkinson I (2007) Inference and learning methodology of belief-rule-based expert system for pipeline leak detection. Expert Syst Appl 32(1):103–113CrossRefGoogle Scholar
  53. Yager RR (1982) Generalized probabilities of fuzzy events from belief structures. Inf Sci 28:45–62CrossRefGoogle Scholar
  54. Yager RR (1987) On the Dempster–Shafer framework and new combination rules. Inf Sci (11):93–137Google Scholar
  55. Yager RR (2004) On the determination of strength of belief for decision support under uncertainty—Part II: fusing strengths of belief. Fuzzy Sets Syst 142(1):129–142CrossRefGoogle Scholar
  56. Yager RR, Filev DP (1995) Including probabilistic uncertainty in fuzzy logic controller modeling using Dempster–Shafer theory. IEEE Trans Syst Man Cybern 25:1221–1230CrossRefGoogle Scholar
  57. Yang JB, Singh MG (1994) An evidential reasoning approach for multiple attribute decision making with uncertainty. IEEE Transactions on Systems, Man, and Cybernetics 24:1–18CrossRefGoogle Scholar
  58. Yang JB, Liu J, Wang J, Sii HS, Wang HW (2006) Belief rule-base inference methodology using the evidential reasoning approach—RIMER. IEEE Trans Syst Man Cybern Part A Syst Hum 36(2):266–285CrossRefGoogle Scholar
  59. Yang YJ, Goodrich JA, Clark RM, Sylvana YL (2008) Modeling and testing of reactive contaminant transport in drinking water pipes: chlorine response and implications for online contaminant detection. Water Res 42(6–7):1397–1412CrossRefGoogle Scholar
  60. Yen J (1990) Generalizing the Dempster–Shafer theory. In: Generalizing the Dempster-Shafer Theory to fuzzy set, pp 559–570Google Scholar
  61. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
  62. Zadeh LA (1999) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 100(1):9–34CrossRefGoogle Scholar
  63. Zhou ZJ, Hu CH, Yang JB, Xu DL, Chen MY, Zhou DH (2010) A sequential learning algorithm for online constructing belief rule based systems. Expert Syst Appl 37:1790–1799CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • E. Aghaarabi
    • 1
  • F. Aminravan
    • 1
  • R. Sadiq
    • 1
  • M. Hoorfar
    • 1
  • M. J. Rodriguez
    • 2
  • H. Najjaran
    • 1
  1. 1.Okanagan School of EngineeringThe University of British ColumbiaKelownaCanada
  2. 2.École supérieure d’aménagement du territoireUniversité LavalQuebec CityCanada

Personalised recommendations