Abstract
When a mutual ranking of a selection of objects is wanted, an initial step is the development of a multi-indicator system (MIS). Many MCDA concepts, e.g., members of the ELECTRE-family or of the different PROMETHEE versions, are available for obtaining rankings from an MIS. On the one side, a major disadvantage applying these models is the need for additional parameters beyond the data matrix, whereas Partial Order Theory is a methodology that allows extracting ranking information from a data matrix without additional, often subjective and consequently questionable parameters. On the other side, additional parameters help decision-making by introducing knowledge for decision makers/stakeholders beyond the data matrix. The present study focuses on the question to what extent an MIS can be modeled within the framework of partial order theory to add knowledge similarly to the MCDA approaches. Of all the possible alternatives, applying weight intervals to the indicators system is here discussed.
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Notes
- 1.
In the present example, the single weight intervals are not overlapping but this is not a general requirement.
References
Annoni P, Bruggemann R, Saltelli A (2012) Random and quasi-random designs in variance-based sensitivity analysis for partially ordered sets. Reliab Eng Sys Safety 107:184–189
Annoni P, Bruggemann R, Carlsen L (2015) A multidimensional view on poverty in the European Union by partial order theory. J Appl Stat 42:535–554
Bartel H-G, Mucha H-J (2014) Measures of incomparabilities and of inequality and their application. In: Bruggemann R, Carlsen L, Wittmann J (eds) Multi-indicator systems and modelling in partial order. Springer, New York, pp 47–67
Brans JP, Vincke PH (1985) A preference ranking organisation method (The PROMETHEE Method for Multiple Criteria Decision - Making). Manag Sci 31:647–656
Bruggemann R, Carlsen L (2012) Multi-criteria decision analyses. Viewing MCDA in terms of both process and aggregation methods: some thoughts, motivated by the paper of Huang, Keisler and Linkov. Sci Total Environ 425:293–295
Bruggemann R, Carlsen L (2016) An attempt to Understand Noisy Posets. MATCH Commun. Math. Comput. Chem. 75:485–510
Bruggemann R, Patil GP (2011) Ranking and prioritization for multi-indicator systems - introduction to partial order applications. Springer, New York
Bruggemann R, Voigt K (2012) Antichains in partial order, example: pollution in a German region by Lead, Cadmium Zinc and Sulfur in the herb layer. MATCH Commun Math Comput Chem 67:731–744
Bruggemann R, Voigt K, Restrepo G, Simon U (2008) The concept of stability fields and hot spots in ranking of environmental chemicals. Environ Model Softw 23:1000–1012
Bruggemann R, Kerber A, Restrepo G (2011) Ranking objects using fuzzy orders, with an application to refrigerants. MATCH Commun Math Comput Chem 66:581–603
Bruggemann R, Restrepo G, Voigt K, Annoni P (2013) Weighting intervals and ranking. Exemplified by leaching potential of pesticides. MATCH Commun Math Comput Chem 69:413–432
Bruggemann R, Carlsen L, Voigt K, Wieland R (2014) PyHasse software for partial order analysis: scientific background and description of selected modules. In: Bruggemann R, Carlsen L, Wittmann J (eds) Multi-indicator systems and modelling in partial order. Springer, New York, pp 389–423
Carlsen L (2008) Hierarchical partial order ranking. Environ Pollut 155:247–253
Carlsen L, Bruggemann R (2014) The ‘Failed Nations Index’ offers more than just a simple ranking. Soc Indic Res 115:525–530
Carlsen L, Bruggemann R (2016) On the influence of data noise and uncertainty on ordering of objects, described by a multi-indicator system. A set of pesticides as an exemplary case. J Chemom 30(1):22–29
Carlsen L, Bruggemann R, Kenessova O, Erzhigitov E (2015) Evaluation of analytical performance based on partial order methodology. Talanta 132:285–293
Gomes LFAM, Rangel LAD (2009) An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res 193:204–211
Kerber A, Bruggemann R (2015) Problem driven evaluation of chemical compounds and its exploration. Match Commun Math Comput Chem 73:577–618
Munda G (2008) Social multi-criteria evaluation for a sustainable economy. Springer, Berlin
Peters ML, Zelewski S (2007) TOPSIS als technik zur effizienzanalyse. WiSt Jnuar 2007:9–15
Roy B (1990) The outranking approach and the foundations of the ELECTRE methods. In: Bana e Costa CA (ed) Readings in multiple criteria decision aid. Springer, Berlin, pp 155–183
Sailaukhanuly Y, Zhakupbekova A, Amutova F, Carlsen L (2013) On the ranking of chemicals based on their PBT characteristics: comparison of different ranking methodologies using selected POPs as an illustrative example. Chemosphere 90:112–117
Wieland R, Bruggemann R (2013) Hasse diagram technique and Monte Carlo simulations. MATCH Commun Math Comput Chem 70:45–59
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Bruggemann, R., Carlsen, L., Annoni, P. (2017). Incomparable: What Now, IV. Incomparabilities: A Modeling Challenge. In: Fattore, M., Bruggemann, R. (eds) Partial Order Concepts in Applied Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-45421-4_3
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