Deep Ranking Analysis by Power
Eigenvectors (DRAPE): A Study
on the Human, Environmental
and Economic Wellbeing of 154 Countries
Cecile Valsecchi and Roberto Todeschini
1 Introduction
Multi-criteria decision making (MCDM) is a decision process applicable in presence
of multiple criteria which are often in contrast with each other (Ivlev et al. 2015;
Kumar et al. 2017; Ho et al. 2010; Triantaphyllou 2000). A decision process consists
of (1) definition and structuring of the problem, (2) model development to compare
and rank the alternatives in a transparent way, (3) elaboration of an action plan.
In general, the main aim of a decision process is to generate information and
solutions in an effective way providing a good understanding of the problem. The
simplest approaches in a MCDM belong to the so-called scoring methods, such
as desirability/utility functions and simple average scoring (Pavan and Todeschini
2008a). Other methods comparing objects pairwise are called outranking methods,
such as dominance functions (Pavan and Todeschini 2008b). Furthermore, partial
order ranking methods, such as Hasse diagram technique, highlight the conflicting
information by identifying incomparable objects (Pavan and Todeschini 2009).
Recently, a new approach based on a development of the Power-Weakness
Ratio (PWR), called Deep Ranking Analysis by Power Eigenvectors (DRAPE) was
proposed (Todeschini et al. 2015, 2019). Indeed, this method is based on the PowerWeakness Ratio proposed by Sir Kendall in (Kendall 1955) and later implemented
by Ramanujacharyulu in (Ramanujacharyulu 1964) exploiting the ability of the
eigenvalue/eigenvector technique in ranking the objects by taking into account the
whole information present in the data.
C. Valsecchi · R. Todeschini ()
Milano Chemometrics and QSAR Research Group, Department of Earth and Environmental
Sciences, University of Milano-Bicocca, Milan, Italy
e-mail: roberto.todeschini@unimib.it
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_17
267
Eigenvectors (DRAPE): A Study
on the Human, Environmental
and Economic Wellbeing of 154 Countries
Cecile Valsecchi and Roberto Todeschini
1 Introduction
Multi-criteria decision making (MCDM) is a decision process applicable in presence
of multiple criteria which are often in contrast with each other (Ivlev et al. 2015;
Kumar et al. 2017; Ho et al. 2010; Triantaphyllou 2000). A decision process consists
of (1) definition and structuring of the problem, (2) model development to compare
and rank the alternatives in a transparent way, (3) elaboration of an action plan.
In general, the main aim of a decision process is to generate information and
solutions in an effective way providing a good understanding of the problem. The
simplest approaches in a MCDM belong to the so-called scoring methods, such
as desirability/utility functions and simple average scoring (Pavan and Todeschini
2008a). Other methods comparing objects pairwise are called outranking methods,
such as dominance functions (Pavan and Todeschini 2008b). Furthermore, partial
order ranking methods, such as Hasse diagram technique, highlight the conflicting
information by identifying incomparable objects (Pavan and Todeschini 2009).
Recently, a new approach based on a development of the Power-Weakness
Ratio (PWR), called Deep Ranking Analysis by Power Eigenvectors (DRAPE) was
proposed (Todeschini et al. 2015, 2019). Indeed, this method is based on the PowerWeakness Ratio proposed by Sir Kendall in (Kendall 1955) and later implemented
by Ramanujacharyulu in (Ramanujacharyulu 1964) exploiting the ability of the
eigenvalue/eigenvector technique in ranking the objects by taking into account the
whole information present in the data.
C. Valsecchi · R. Todeschini ()
Milano Chemometrics and QSAR Research Group, Department of Earth and Environmental
Sciences, University of Milano-Bicocca, Milan, Italy
e-mail: roberto.todeschini@unimib.it
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_17
267