Skip to main content
SpringerLink
Log in

An interval-valued fuzzy linear programming with infinite α-cuts method for environmental management under uncertainty

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

In this study, an interval-valued fuzzy linear programming with infinite α-cuts (IVFLP-I) method is developed for municipal solid waste (MSW) management under uncertainty. IVFLP-I can not only tackle uncertainties expressed as intervals and interval-valued fuzzy sets, but also take all fuzzy information into account by discretizing infinite α-cut levels to the interval-valued fuzzy membership functions. Through adoption of the interval-valued fuzzy sets, IVFLP-I can directly communicate information of waste managers’ confidence levels over various subjective judgments into the optimization process. Compared to the existing methods in which only finite α-cut levels exist, IVFLP-I would have enhanced the robustness in the optimization efforts. A MSW management problem is studied to illustrate the applicability of the proposed method. Four groups of optimal solutions can be obtained through assigning different intervals of α-cut levels. The results indicate that wider intervals of α-cut levels could lead to a lower risk level of constraint violation associated with a higher system cost; contrarily, narrower intervals of α-cut levels could lead to a lower cost with a higher risk of violating the constraints. The solutions under different intervals of α-cut levels can support in-depth analyses of tradeoffs between system costs and constraint-violation risks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Arey MJ, Baetz BW (1993) Simulation modeling for the sizing of solid waste receiving facilities. Can J Civil Eng 20:220–227

    Article  Google Scholar 

  • Cai YP, Huang GH, Nie XH, Li YP, Tan Q (2007) Municipal solid waste management under uncertainty: a mixed interval parameter fuzzy-stochastic robust programming approach. Environ Eng Sci 24(3):338–352

    Article  CAS  Google Scholar 

  • Cai YP, Huang GH, Lu HW, Yang ZF, Tan Q (2009) I-VFRP: An interval-valued fuzzy robust programming approach for municipal waste-management planning under uncertainty. Eng Optim 41:399–418

    Article  Google Scholar 

  • Chang NB, Wang SF (1997) A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems. Eur J Oper Res 32(4):303–321

    Article  Google Scholar 

  • Chang NB, Chen YL, Wang SF (1997) A fuzzy interval multiobjective mixed integer programming approach for the optimal planning of solid waste management systems. Fuzzy Sets Syst 89:35–59

    Article  Google Scholar 

  • Chang NB, Davila E, Dyson B, Brown R (2005) Optimal design for sustainable development of a recycling facility in a fast-growing urban setting. Waste Manage 25:833–846

    Article  Google Scholar 

  • Chi GF, Huang GH (1998) Long-term planning of integrated solid waste management system under uncertainty. University of Regina Report submitted to the City of Regina, Saskatchewan, Canada

    Google Scholar 

  • Delgado M, Verdegay JL, Vila MA (1989) A general model for fuzzy linear programming. Fuzzy Sets Syst 29:21–29

    Article  Google Scholar 

  • Dubios D, Prade H (1978) Operations on fuzzy number. Int J Syst Sci 9:613–626

    Article  Google Scholar 

  • Dubios D, Prade H (1999a) A synthetic view of belief revision with uncertain inputs in the framework of possibility theory. Int J Approx Reason 17(2–3):295–306

    Google Scholar 

  • Dubios D, Prade H (1999b) On fuzzy interpolation. Int J General Syst 28(2):103–112

    Article  Google Scholar 

  • Dubios D, Prade H (1999c) Qualitative possibility theory and its applications to constraint satisfaction and decision under uncertainty. Int J Intell Syst 14(1):45–53

    Article  Google Scholar 

  • Dupacova J (1998) Reflections on robust optimization. Lecture Notes in Economics and Mathematical Systems, vol 458, pp 111–127

  • Fang SC, Puthenpura SC (1993) Linear Optimization and Extensions: Theory and Algorithms. Prentice Hall, Englewood Cliffs, N.J

    Google Scholar 

  • Fang SC, Hu CF, Wang HF (1999) Linear Programming with Fuzzy Coefficients in Constraints. Comput Math Appl 37:63–76

    Article  Google Scholar 

  • Huang GH, Chang NB (2003) The perspectives of environmental informatics and systems analysis. J Environ Inform 1:1–6

    Article  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1992) A grey linear programming approach for municipal solid waste management planning under uncertainty. Civil Eng Environ Syst 9:319–335

    Article  CAS  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1993) A grey fuzzy linear programming approach for municipal solid waste management planning under uncertainty. Civil Eng Environ Syst 10:123–146

    Article  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1994a) Grey dynamic programming for solid waste management planning under uncertainty. J Urban Plan Dev 120(3):132–156

    Article  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1994b) Grey chance-constrained programming: application to regional solid waste management planning. In: Hipel KW, Fang L (eds). Effective environmental management for sustainable development. Kluwer Academic

  • Huang GH, Baetz BW, Patry GG (1995a) Grey quadratic programming and its application to municipal solid waste management planning under uncertainty. Eng Optim 23:201–223

    Article  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1995b) Grey integer programming: An application to waste management planning under uncertainty. Eur J Oper Res 83:594–620

    Article  Google Scholar 

  • Huang GH, Sae-Lim N, Chen Z, Liu L (2001) Long-term planning of waste management system in the City of Regina–An integrated inexact optimization approach. Environ Model Assess 6:285–296

    Article  Google Scholar 

  • Huang YF, Baetz BW, Huang GH, Liu L (2002) Violation analysis for solid waste management systems: an interval fuzzy programming approach. J Environ Manage 65:431–446

    CAS  Google Scholar 

  • Inuiguchi M, Ichihashi H, Tanaka H (1990) Fuzzy programming: a survey of recent developments. In: Slowinski R, Teghem J (eds) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kluwer Academic Publishers, Dordrechts, pp 45–70

    Google Scholar 

  • Kunjur A, Krishnamurty S (1997) A robust multi-criteria optimization approach. Mech Mach Theory 32(7):797–810

    Article  Google Scholar 

  • Lee YW, Bogardi I, Stansbury J (1991) Fuzzy decision making in dredged-material management. J Environ Eng 117(2):614–628

    CAS  Google Scholar 

  • Li YP, Huang GH, Nie XH, Nie SL (2008) A two-stage fuzzy robust integer programming approach for capacity planning of environmental management systems. Eur J Oper Res 189(2):399–420

    Article  Google Scholar 

  • Li YP, Huang GH, Yang ZF, Chen X (2009) Inexact fuzzy-stochastic constraint-softened programming–A case study for waste management. Waste Manage 29:2165–2177

    Article  CAS  Google Scholar 

  • Liu L, Huang GH, Liu Y, Fuller GA (2003) A fuzzy-stochastic robust programming model for regional air quality management under uncertainty. Eng Optim 35(2):177–199

    Article  CAS  Google Scholar 

  • Lu HW, Huang GH, Lin YP, He L (2009a) A two-Step infinite α-cuts fuzzy linear programming method in determination of optimal allocation strategies in agricultural irrigation systems. Water Resour Manage 23:2249–2269

    Article  Google Scholar 

  • Lu HW, Huang GH, He L (2009b) A semi-infinite analysis-based inexact two-stage stochastic fuzzy linear programming approach for water resources management. Eng Optim 41:73–85

    Article  Google Scholar 

  • Luhandjula MK, Gupta MM (1996) On fuzzy stochastic optimization. Fuzzy Sets Syst 81:47–55

    Article  Google Scholar 

  • Luo B, Zhou DC (2007) Planning hydroelectric resources with recourse-based multistage interval-stochastic programming. Stoch Env Res Risk Assess 23:65–73

    Article  Google Scholar 

  • Maqsood I, Huang GH (2003) A two-stage interval-stochastic programming model for waste management under uncertainty. J Air Waste Manage Assoc 53:540–552

    Google Scholar 

  • Maqsood I, Huang GH, Huang YF, Chen B (2005) ITOM: an interval parameter two-stage optimization mode for stochastic planning of water resources systems. Stoch Env Res Risk Assess 19(2):125–133

    Article  Google Scholar 

  • Nie XH, Huang GH, Li YP, Liu L (2007) IFRP: A hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty. J Environ Manage 84(1):1–11

    Article  CAS  Google Scholar 

  • Vassiadou-Zeniou C, Zenios SA (1996) Robust optimization models for managing callable bond portfolios. Eur J Oper Res 91:264–273

    Article  Google Scholar 

  • Yeomans JS, Huang GH (2003) An evolutionary grey, hop, skip, and jump approach: Generating alternative policies for the expansion of waste management. J Environ Inform 1:37–51

    Article  Google Scholar 

  • Yeomans JS, Huang GH, Yoogalingam R (2003) Combining simulation with evolutionary algorithms for optimal planning under uncertainty: an application to municipal solid waste management planning in the Regional Municipality of Hamilton–Wentworth. J Environ Inform 2:11–30

    Article  Google Scholar 

  • Zeng Y, Trauth KM (2005) Internet-based fuzzy multicriteria decision support system for planning integrated solid waste management. J Environ Inform 6:1–15

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The research was supported by the Major State Basic Research Development Program of MOST (2005CB724207), and the Natural Sciences and Engineering Research Council of Canada. The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, SK, S4S 0A2, Canada

    S. Wang, G. H. Huang & H. W. Lu

  2. College of Urban and Environmental Sciences, Peking University, 100871, Beijing, China

    Y. P. Li

Authors
  1. S. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. W. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. P. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. H. Huang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, S., Huang, G.H., Lu, H.W. et al. An interval-valued fuzzy linear programming with infinite α-cuts method for environmental management under uncertainty. Stoch Environ Res Risk Assess 25, 211–222 (2011). https://doi.org/10.1007/s00477-010-0432-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-010-0432-x

Keywords

Search

Navigation