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A Methodology for Tracing the Rank Invariance Region in Multi-Criterion Selection Problems: Application to Negative Emission Technologies

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Abstract

It has been previously established that, for multi-criterion selection problems, over a finite set of options, solved via simple additive weighting, there exists a set of weights for which the optimal alternative remains the best choice. This invariance region in the n-dimensional hyperspace defined by the problem criteria contains the set of all weights for which the optimal solution is robust to preference changes. When the set of options is a continuum, there are no known invariance regions reported in the literature. In this work, we develop a procedure to characterize and trace this invariance region when the number of options is finite. The methodology is demonstrated on a case study involving a selection of negative emission technologies based on carbon sequestration potential, water footprint, energy demand, and cost.

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References

  • Cortés-Borda D, Guillén-Gosálbez G, Esteller LJ (2013) On the use of weighting in LCA: translating decision makers’ preferences into weights via linear programming. Int J Life Cycle Assess 18:948–957

    Article  Google Scholar 

  • Cruz JB, Almario EMR (2018) When is the Pareto choice from a finite set invariant to variations in weight and values of multiple performance criteria? Philipp Sci Lett 11:61–70

    Google Scholar 

  • Geldermann J, Spengler T, Rentz O (2000) Fuzzy outranking for environmental assessment. Case study: iron and steel making industry. Fuzzy Sets Syst 115:45–65

    Article  Google Scholar 

  • Graham DJ, Midgley NG (2000) Graphical representation of particle shape using triangular diagrams: an Excel spreadsheet method. Earth Surf Process Landf 25:1473–1477

    Article  Google Scholar 

  • Haszeldine RS, Flude S, Johnson G, Scott V (2018) Negative emissions technologies and carbon capture and storage to achieve the Paris Agreement commitments. Philos Trans R Soc A Math Phys Eng Sci 376:20160447. https://doi.org/10.1098/rsta.2016.0447

    Article  Google Scholar 

  • MacCrimmon KR (1968) Decision making among multiple attribute alternatives: a survey and consolidated approach. RAND Memorandum, RM-4823-ARPA

  • Maliene V, Dixon-Gough R, Malys N (2018) Dispersion of relative importance values contributes to the ranking uncertainty: sensitivity analysis of multiple criteria decision-making methods. Appl Soft Comput 67:286–298

    Article  Google Scholar 

  • Mathiess TH, Rubin DS (1980) A survey and comparison of methods for finding all vertices of convex polyhedral sets. Math Oper Res 5:167–185

    Article  MathSciNet  Google Scholar 

  • Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    MATH  Google Scholar 

  • Sikdar SK (2009) On aggregating multiple indicators into a single metric for sustainability. Clean Techn Environ Policy 11:157–161

    Article  Google Scholar 

  • Smith P, Haszeldine RS, Smith SM (2016) Preliminary assessment of the potential for, and limitations to, terrestrial negative emission technologies in the UK. Environ Sci: Processes Impacts 18:1400–1405

    Google Scholar 

  • Tan J, Low KY, Sulaiman NMN, Tan RR, Promentilla MAB (2016) Fuzzy analytic hierarchy process (FAHP) for multi-criteria selection of microalgae harvesting and drying processes. Clean Techn Environ Policy 18:2049–2063

    Article  Google Scholar 

  • Tseng M-L (2013) Modeling sustainable production indicators with linguistic preferences. J Clean Prod 40:46–56

    Article  Google Scholar 

Download references

Acknowledgements

The support of the Philippine Commission on Higher Education (CHED) via the Philippine Higher Education Research Network (PHERNet) Sustainability Studies Program at De La Salle University is gratefully acknowledged. The support of a NAST Research Fellowship is acknowledged by Jose B. Cruz, Jr. We also wish to thank Mark Wiley of the LINDO Systems, Inc. for providing us with software code for tracing the vertices of convex polytopes.

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Correspondence to Raymond R. Tan.

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Tan, R.R., Almario, E.M.R., Aviso, K.B. et al. A Methodology for Tracing the Rank Invariance Region in Multi-Criterion Selection Problems: Application to Negative Emission Technologies. Process Integr Optim Sustain 3, 533–536 (2019). https://doi.org/10.1007/s41660-019-00089-4

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  • DOI: https://doi.org/10.1007/s41660-019-00089-4

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