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A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation

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Abstract

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining’s agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model’s execution time by a factor of 450.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Aghasian, K., Moridi, A., Mirbagheri, A., & Abbaspour, M. (2019). A conflict resolution method for waste load reallocation in river systems. International Journal of Environmental Science and Technology, 16, 79–88.

    Article  Google Scholar 

  • Ahmadisharaf, E., Camacho, R. A., Zhang, H. X., Hantush, M. M., & Mohamoud, Y. M. (2019). Calibration and validation of watershed models and advances in uncertainty analysis in TMDL studies. Journal of Hydrologic Engineering, 24(7), 03119001.

    Article  Google Scholar 

  • Ahour, M. (2006). Pollution management and monitoring of the KhoramAbad River. Iran’s Department of Environment.

    Google Scholar 

  • Albert, C. G., Callies, U., & von Toussaint, U. (2022). A Bayesian approach to the estimation of parameters and their interdependencies in environmental modeling. Entropy, 24(2), 231.

    Article  Google Scholar 

  • Alzarrad, M. A. (2020). Fuzzy Monte Carlo simulation to optimize resource planning and operations. In Concepts, Applications and Emerging Opportunities in Industrial Engineering. IntechOpen.

    Google Scholar 

  • Andik, B., & Niksokhan, M. H. (2020). Waste load allocation under uncertainty using game theory approach and simulation-optimization process. Journal of Hydroinformatics, 22(4), 815–841.

    Article  Google Scholar 

  • Burn, D. H., & Yulianti, J. S. (2001). Waste-load allocation using genetic algorithms. Journal of Water Resources Planning and Management, 127(2), 121–129.

    Article  Google Scholar 

  • Camacho, R. A., Martin, J. L., Diaz-Ramirez, J., McAnally, W., Rodriguez, H., Suscy, P., & Zhang, S. (2014). Uncertainty analysis of estuarine hydrodynamic models: an evaluation of input data uncertainty in the weeks bay estuary, alabama. Applied Ocean Research, 47, 138–153.

    Article  Google Scholar 

  • Cetin, L., Kemp, A., Alcorn, M., & Greg, V. (2022, January). Exploring uncertainty in predicting annual nutrient and sediment loads to port Phillip Bay. In Hydrology & Water Resources Symposium 2022 (HWRS 2022): The Past, the Present, the Future: The Past, the Present, the Future (pp. 326–336). Engineers Australia.

    Google Scholar 

  • Chadderton, R. A., Miller, A. C., & McDonnell, A. J. (1981). Analysis of waste load allocation procedures 1. JAWRA Journal of the American Water Resources Association, 17(5), 760–766.

    Article  Google Scholar 

  • Chaudhary, A., & Hantush, M. M. (2017). Bayesian Monte Carlo and maximum likelihood approach for uncertainty estimation and risk management: application to lake oxygen recovery model. Water Research, 108, 301–311.

    Article  CAS  Google Scholar 

  • Cho, J. H., & Lee, J. H. (2014). Multi-objective waste load allocation model for optimizing waste load abatement and inequality among waste dischargers. Water, Air, & Soil Pollution, 225, 1–17.

    Article  Google Scholar 

  • Cho, J. H., & Lee, J. H. (2020). Fuzzy optimization model for waste load allocation in a river with total maximum daily load (TMDL) planning. Water, 12(9), 2618.

    Article  Google Scholar 

  • Daylami, A. A., Shamsai, A., & Niksokhan, M. H. (2010). Model for waste load allocation in rivers: a cooperative approach. American-Eurasian Journal of Agricultural and Environmental Science, 8(6), 626–632.

    Google Scholar 

  • Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In Parallel Problem Solving from Nature PPSN VI: 6th International Conference Paris, France, September 18–20, 2000 Proceedings 6 (pp. 849–858). Springer.

    Chapter  Google Scholar 

  • Deng, Y., Sadiq, R., Jiang, W., & Tesfamariam, S. (2011). Risk analysis in a linguistic environment: a fuzzy evidential reasoning-based approach. Expert Systems with Applications, 38(12), 15438–15446.

    Article  Google Scholar 

  • Farjoudi, S. Z., Moridi, A., Sarang, A., & Lence, B. J. (2021). Application of probabilistic bankruptcy method in river water quality management. International Journal of Environmental Science and Technology, 1–18.

  • Fisher, R. (2000). Sources of conflict and methods of conflict resolution. International Peace and Conflict Resolution, School of International Service, The American University, 1965, 1–6.

    Google Scholar 

  • Fisher, R. J. (1972). Third party consultation: a method for the study and resolution of conflict. Journal of Conflict Resolution, 16(1), 67–94.

    Article  Google Scholar 

  • Gaines, B. R. (1978). Fuzzy and probability uncertainty logics. Information and Control, 38(2), 154–169.

    Article  Google Scholar 

  • Ganoulis, J. (2008). Engineering risk analysis of water pollution: probabilities and fuzzy sets. John Wiley & Sons.

    Google Scholar 

  • Ganoulis, J., Anagnostopoulos, P. and Mpimpas, H., 2003, August. Fuzzy numerical simulation of water quality. In Proceedings of the 30th IAHR congress, Thessaloniki, Greece, theme B (pp. 165-174).

  • Ghorbani Mooselu, M., Nikoo, M. R., & Sadegh, M. (2019). A fuzzy multi-stakeholder socio-optimal model for water and waste load allocation. Environmental Monitoring and Assessment, 191, 1–16.

    Article  Google Scholar 

  • Ghosh, S., & Mujumdar, P. P. (2010). Fuzzy waste load allocation model: a multiobjective approach. Journal of Hydroinformatics, 12(1), 83–96.

    Article  Google Scholar 

  • Haan, C. T. (1989). Parametric uncertainty in hydrologic modeling. Transactions of the ASAE, 32(1), 137–0146.

    Article  Google Scholar 

  • Hajek, P., Godo, L., & Esteva, F. (1995). Fuzzy logic and probability. Institute of Computer Science (ICS).

    Google Scholar 

  • Han, J. C., Shang, F., Li, P., Li, B., Zhou, Y., & Huang, Y. (2021). Coupling Bayesian-Monte Carlo simulations with substance flow analysis for efficient pollutant management: a case study of phosphorus flows in China. Resources, Conservation and Recycling, 169, 105550.

    Article  CAS  Google Scholar 

  • Herrero, C., & Villar, A. (2001). The three musketeers: four classical solutions to bankruptcy problems. Mathematical Social Sciences, 42(3), 307–328.

    Article  Google Scholar 

  • Hession, W. C., Storm, D. E., & Haan, C. T. (1996). Two-phase uncertainty analysis: an example using the universal soil loss equation. Transactions of the ASAE, 39(4), 1309–1319.

    Article  Google Scholar 

  • Hu, J., Sun, L., Li, C. H., Wang, X., Jia, X. L., & Cai, Y. P. (2018). Water quality risk assessment for the Laoguanhe River of China using a stochastic simulation method. Journal of Environmental Informatics, 31(2), 123–136.

    CAS  Google Scholar 

  • Janssen, H. (2013). Monte-Carlo based uncertainty analysis: sampling efficiency and sampling convergence. Reliability Engineering & System Safety, 109, 123–132.

    Article  Google Scholar 

  • Karmakar, S., & Mujumdar, P. P. (2006). Grey fuzzy optimization model for water quality management of a river system. Advances in Water Resources, 29(7), 1088–1105.

    Article  CAS  Google Scholar 

  • Katz, D. (1965). Nationalism and strategies of international conflict resolution. In H. C. Kelman (Ed.), International Behavior: A Social-Psychological Analysis (pp. 356–390). Holt, Rinehartand Winston.

    Google Scholar 

  • Kerachian, R., Fallahnia, M., Bazargan-Lari, M. R., Mansoori, A., & Sedghi, H. (2010). A fuzzy game theoretic approach for groundwater resources management: application of Rubinstein bargaining theory. Resources, Conservation and Recycling, 54(10), 673–682.

    Article  Google Scholar 

  • Kerachian, R., & Karamouz, M. (2007). A stochastic conflict resolution model for water quality management in reservoir–river systems. Advances in Water Resources, 30(4), 866–882.

    Article  Google Scholar 

  • Kerachian, R., Karamouz, M., & Naseri, A. V. (2005). River water quality management: application of stochastic genetic algorithm. In Impacts of Global Climate Change (pp. 1–12).

    Google Scholar 

  • Liu, Q., Jiang, J., Jing, C., Liu, Z., & Qi, J. (2019). A new water environmental load and allocation modeling framework at the medium–large basin scale. Water, 11(11), 2398.

    Article  Google Scholar 

  • Loginov, V. I. (1966). Probability treatment of Zadeh membership functions and their use in pattern recognition. Engineering Cybernetics, 2, 68.

    Google Scholar 

  • Madani, K., & Dinar, A. (2013). Exogenous regulatory institutions for sustainable common pool resource management: application to groundwater. Water Resources and Economics, 2, 57–76.

    Article  Google Scholar 

  • Madani, K., & Zarezadeh, M. (2012). Bankruptcy methods for resolving water resources conflicts. In World environmental and water resources congress 2012: Crossing boundaries (pp. 2247–2252).

    Chapter  Google Scholar 

  • Madani, K., Zarezadeh, M., & Morid, S. (2014). A new framework for resolving conflicts over transboundary rivers using bankruptcy methods. Hydrology and Earth System Sciences, 18(8), 3055–3068.

    Article  Google Scholar 

  • Mahjouri, N., & Abbasi, M. R. (2015). Waste load allocation in rivers under uncertainty: application of social choice procedures. Environmental Monitoring and Assessment, 187, 1–15.

    Article  Google Scholar 

  • McIntyre, N. R., Wagener, T., Wheater, H. S., & Yu, Z. S. (2003). Uncertainty and risk in water quality modelling and management. Journal of Hydroinformatics, 5(4), 259–274.

    Article  Google Scholar 

  • Meysami, R., & Niksokhan, M. H. (2020). Evaluating robustness of waste load allocation under climate change using multi-objective decision making. Journal of Hydrology, 588, 125091.

    Article  CAS  Google Scholar 

  • Moreno-Ternero, J. D., & Villar, A. (2006). The TAL-family of rules for bankruptcy problems. Social Choice and Welfare, 27(2), 231–249.

    Article  Google Scholar 

  • Mujumdar, P. P., & Sasikumar, K. (2002). A fuzzy risk approach for seasonal water quality management of a river system. Water Resources Research, 38(1), 5-1.

    Article  Google Scholar 

  • Naghdi, S., Bozorg-Haddad, O., Khorsandi, M., & Chu, X. (2021). Multi-objective optimization for allocation of surface water and groundwater resources. Science of the Total Environment, 776, 146026.

    Article  CAS  Google Scholar 

  • Nash, J. (1953). Two-person cooperative games. Econometrica: Journal of the Econometric Society, 128–140.

  • Nikoo, M. R., Beiglou, P. H. B., & Mahjouri, N. (2016). Optimizing multiple-pollutant waste load allocation in rivers: an interval parameter game theoretic model. Water Resources Management, 30, 4201–4220.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., Karimi, A., & Azadnia, A. A. (2013). Optimal water and waste-load allocations in rivers using a fuzzy transformation technique: a case study. Environmental Monitoring and Assessment, 185, 2483–2502.

    Article  Google Scholar 

  • Nikoo, M. R., Kerachian, R., Niksokhan, M. H., & Beiglou, P. H. B. (2011). A game theoretic model for trading pollution discharge permits in river systems. International Journal of Environmental Science and Development, 2(2), 162–166.

    Article  Google Scholar 

  • Niksokhan, M. H., Kerachian, R., & Amin, P. (2009a). A stochastic conflict resolution model for trading pollutant discharge permits in river systems. Environmental Monitoring and Assessment, 154, 219–232.

    Article  Google Scholar 

  • Niksokhan, M. H., Kerachian, R., & Karamouz, M. (2009b). A game theoretic approach for trading discharge permits in rivers. Water Science and Technology, 60(3), 793–804.

    Article  Google Scholar 

  • Novotny, V. (2002). Water quality: diffuse pollution and watershed management. John Wiley & Sons.

    Google Scholar 

  • Oftadeh, E., Shourian, M., & Saghafian, B. (2016). Evaluation of the bankruptcy approach for water resources allocation conflict resolution at basin scale, Iran’s Lake Urmia experience. Water Resources Management, 30, 3519–3533.

    Article  Google Scholar 

  • Patil, A., & Deng, Z. Q. (2011). Bayesian approach to estimating margin of safety for total maximum daily load development. Journal of Environmental Management, 92(3), 910–918.

    Article  CAS  Google Scholar 

  • Rajabi, M. M., & Ataie-Ashtiani, B. (2014). Sampling efficiency in Monte Carlo based uncertainty propagation strategies: application in seawater intrusion simulations. Advances in Water Resources, 67, 46–64.

    Article  Google Scholar 

  • Raquel, S., Ferenc, S., Emery, C., Jr., & Abraham, R. (2007). Application of game theory for a groundwater conflict in Mexico. Journal of Environmental Management, 84(4), 560–571.

    Article  Google Scholar 

  • Rehana, S., & Mujumdar, P. P. (2009). An imprecise fuzzy risk approach for water quality management of a river system. Journal of Environmental Management, 90(11), 3653–3664.

    Article  CAS  Google Scholar 

  • Ruzhong, L. I. (2010). Fuzzy modeling of water environmental capacity for a large river. Environmental Technology and Knowledge Transfer, 970.

  • Saadatpour, M., & Afshar, A. (2007). Waste load allocation modeling with fuzzy goals; simulation-optimization approach. Water Resources Management, 21, 1207–1224.

    Article  Google Scholar 

  • Saadatpour, M., Afshar, A., & Khoshkam, H. (2019). Multi-objective multi-pollutant waste load allocation model for rivers using coupled archived simulated annealing algorithm with QUAL2Kw. Journal of Hydroinformatics, 21(3), 397–410.

    Article  Google Scholar 

  • Saadatpour, M., Afshar, A., Khoshkam, H., & Prakash, S. (2020). Equilibrium strategy-based waste load allocation using simulated annealing optimization algorithm. Environmental Monitoring and Assessment, 192(9), 612.

    Article  Google Scholar 

  • Sadiq, R., Kleiner, Y., & Rajani, B. (2007). Water quality failures in distribution networks—risk analysis using fuzzy logic and evidential reasoning. Risk Analysis: An International Journal, 27(5), 1381–1394.

    Article  Google Scholar 

  • Sahoo, M. M., & Patra, K. C. (2020). River water quality modelling and simulation based on Markov Chain Monte Carlo computation and Bayesian inference model. African Journal of Science, Technology, Innovation and Development, 12(6), 771–785.

    Article  Google Scholar 

  • Sanjaa, B., & Tsoozol, P. (2007). October. Fuzzy and probability. In 2007 International Forum on Strategic Technology, IEEE. 141–143.

  • Sasikumar, K., & Mujumdar, P. P. (1998). Fuzzy optimization model for water quality management of a river system. Journal of Water Resources Planning and Management, 124(2), 79–88.

    Article  Google Scholar 

  • Sasikumar, K., & Mujumdar, P. P. (2000). Application of fuzzy probability in water quality management of a river system. International Journal of Systems Science, 31(5), 575–591.

    Article  Google Scholar 

  • Sharifazari, S., Sadat-Noori, M., Rahimi, H., Khojasteh, D., & Glamore, W. (2021). Optimal reservoir operation using Nash bargaining solution and evolutionary algorithms. Water Science and Engineering, 14(4), 260–268.

    Article  Google Scholar 

  • Shirmohammadi, A., Chaubey, I., Harmel, R. D., Bosch, D. D., Muñoz-Carpena, R., Dharmasri, C., Sexton, A., Arabi, M., Wolfe, M. L., Frankenberger, J., & Graff, C. (2006). Uncertainty in TMDL models. Transactions of the ASABE, 49(4), 1033–1049.

    Article  Google Scholar 

  • Streeter, H. W., & Phelps, E. B. (1958). A study of the pollution and natural purification of the Ohio River. US Department of Health, Education, & Welfare.

    Google Scholar 

  • Tabesh, M., Roozbahani, A., Hadigol, F., & Ghaemi, E. (2021). Risk assessment of water treatment plants using fuzzy fault tree analysis and Monte Carlo simulation. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 1–16.

  • Vemula, V. S., Mujumdar, P. P., & Ghosh, S. (2004). Risk evaluation in water quality management of a river system. Journal of Water Resources Planning and Management, 130(5), 411–423.

    Article  Google Scholar 

  • Wang, X., Zhang, Y., Zeng, Y., & Liu, C. (2013). Resolving trans-jurisdictional water conflicts by the Nash bargaining method: a case study in Zhangweinan canal basin in north China. Water Resources Management, 27, 1235–1247.

    Article  Google Scholar 

  • Yandamuri, S. R., Srinivasan, K., & Murty Bhallamudi, S. (2006). Multiobjective optimal waste load allocation models for rivers using nondominated sorting genetic algorithm-II. Journal of Water Resources Planning and Management, 132(3), 133–143.

    Article  Google Scholar 

  • Yu, P. S., Yang, T. C., & Chen, S. J. (2001). Comparison of uncertainty analysis methods for a distributed rainfall–runoff model. Journal of Hydrology, 244(1-2), 43–59.

    Article  Google Scholar 

  • Zadeh, L. (1965). Fuzzy sets. Inform Control, 8, 338–353.

    Article  Google Scholar 

  • Zadeh, L. A. (1995). Discussion: Probability theory and fuzzy logic are complementary rather than competitive. Technometrics, 37(3), 271–276.

    Article  Google Scholar 

  • Zare Farjoudi, S., Moridi, A., & Sarang, A. (2021). Multi-objective waste load allocation in river system under inflow uncertainty. International Journal of Environmental Science and Technology, 18, 1549–1560.

    Article  Google Scholar 

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Authors and Affiliations

  1. Islamic Azad University Science and Research Branch, Tehran, Iran

    Alireza Nouri & Ershad Oftadeh

  2. Islamic Azad University East Tehran Branch, Tehran, Iran

    Mohammadreza Bazargan-Lari

Authors
  1. Alireza Nouri
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Contributions

Dr. Alireza Nouri conceived and designed the research, gathered the required data and information, did the calculations of the methodology, and analyzed the results of the study. Dr. Mohammadreza Bazargan-Lari provided critical preliminary consultation and final feedback. Mr. Ershad Oftadeh provided consultation and feedback on the bankruptcy section of the research and wrote the manuscript.

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Correspondence to Alireza Nouri.

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Appendix. Nominations used in equations

Appendix. Nominations used in equations

D

Dissolve oxygen deficiency (mg/lit)

k 1

The BOD decay coefficient (1/day)

k 2

The reaeration coefficient (1/day)

\({L}_{c_0}\)

BOD at the entry of the reach

L c

BOD at the end of the reach

t

Spend time for the simulation reach

\(\tilde{x}\)

Fuzzy variable value of x

[x]α

Fuzzy variable of x in the α-cut

\({\left[x\right]}_{\upalpha}^{\textrm{l}}\)

Lower limit of Fuzzy value of x in the x α-cut

\({\left[x\right]}_{\upalpha}^{\textrm{u}}\)

Upper limit of Fuzzy value of x in the x α-cut

μW

Membership function of low water quality

c

Fuzzy arithmetic indicator

cU

Upper limit of unacceptable cil variable

cL

Lower limit of unacceptable cil variable

\(\tilde{W}\)

Low water quality in Fuzzy form

f

Distribution function of critical DO

\({\upmu}_{{\textrm{D}}_{\textrm{cr}}}\)

Membership function of critical DO

f i

Target function for stakeholder i

d i

The disagreement point for stakeholder i

H

Solution space

\(\textrm{BO}{\textrm{D}}_i^{\textrm{Max}}\)

The maximum dischargeable biochemical oxygen demand for stakeholder i

CEAi

WLA for unit i provided CEA Rule

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Nouri, A., Bazargan-Lari, M. & Oftadeh, E. A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation. Environ Monit Assess 195, 1254 (2023). https://doi.org/10.1007/s10661-023-11811-8

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