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

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Abstract

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.

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Abbreviations

MCDM:

Multi-criteria decision making

WQP:

Water quality parameter

WDN:

Water distribution network

DS:

Dempster–Shafer

FRBS:

Fuzzy rule-based system

FDS:

Fuzzy Dempster–Shafer

FRC:

Free residual chlorine

HPC:

Heterotrophic plate counts

DBP:

Disinfection by-products

TTHM:

Total trihalomethanes

WDS:

Water distribution system

BPA:

Basic probability assignment

MC:

Monte–Carlo

PDF:

Probability density functions

AHP:

Analytic hierarchy process

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Authors and Affiliations

  1. Okanagan School of Engineering, The University of British Columbia, Kelowna, BC, Canada

    E. Aghaarabi, F. Aminravan, R. Sadiq, M. Hoorfar & H. Najjaran

  2. École supérieure d’aménagement du territoire, Université Laval, Quebec City, QC, Canada

    M. J. Rodriguez

Authors
  1. E. Aghaarabi
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  2. F. Aminravan
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  3. R. Sadiq
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  4. M. Hoorfar
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  5. M. J. Rodriguez
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  6. H. Najjaran
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Corresponding author

Correspondence to H. Najjaran.

Appendix

Appendix

Table 11 presents microbial input data, used in this paper, from Quebec City WDN briefly. Table 12 presents physicochemical input data, used in this paper, from Quebec City WDN briefly.

Table 11 Statistics of microbial water quality parameters as input data
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Table 12 Statistics of physicochemical water quality parameters as input data
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Aghaarabi, E., Aminravan, F., Sadiq, R. et al. Comparative study of fuzzy evidential reasoning and fuzzy rule-based approaches: an illustration for water quality assessment in distribution networks. Stoch Environ Res Risk Assess 28, 655–679 (2014). https://doi.org/10.1007/s00477-013-0780-4

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