Indicators in the Framework of Partial Order
27
2006), the task to derive from the Hasse diagrams easily understandable estimation
methods for Rkav is still an important object of research in the future (see also
Bruggemann and Annoni 2014; Bruggemann and Carlsen 2011, 2014; Bruggemann
et al. 2004). It should be noted that in the field of research of indicator systems the
pure rendering of results by an effective but hardly understandable method cannot
be satisfying, because finally it is of main importance to understand, i.e. to trace
back the reason, why certain objects under certain indicator systems get a certain
position in the ranking!
The extremal case (AC) throws another light on the idea that an indicator
system is more than its parts: The Hasse diagram is of no direct help as there
is no order relation among the objects. Nevertheless, the indicators themselves
have a different influence why order relations among objects are broken, thus
inducing new relations, namely among indicators (Bruggemann and Voigt 2011,
2012; Bruggemann and Carlsen 2014).
Even if the Hasse diagram is somewhere in the middle between AC and CC,
algebraic concepts (taken from universal algebra, Davey and Priestley 1990) such
as congruence, linear sums and separated sums, are providing powerful tools to
analyse the indicator system. Congruence, for instance provides a methodological
framework, as to how far a family of subsets of objects can be considered as a
CC-system, i.e. not the objects themselves can be ranked, but appropriate selected
subsets of objects (Carlsen and Bruggemann, Soc.Ind. Res., Febr., 2019 submitted).
References
Aguirre-Urreta, M. I., Rönkkö, M., & Marakas, G. M. (2016). Omission of causal indicators:
Consequences and implications for measurement. Measurement: Interdisciplinary Research
and Perspectives, 14(3), 75–97.
Alaimo, L. S. (2020). Complexity of social phenomena: Measurements, analysis, representations
and synthesis. Unpublished Doctoral Dissertation, University of Rome “La Sapienza”, Rome,
Italy.
Alaimo, L. S., & Maggino, F. (2018). Sviluppo sostenibile e differenze regionali. In E. di Bella,
F. Maggino, & M. Trapani (Eds.), AIQUAV 2018. V Convegno dell’Associazione Italiana per
gli Studi sulla Qualità della Vita. Libro dei Contributi Brevi (pp. 199–206). Genova: Genova
University Press.
Alaimo, L. S., & Maggino, F. (2020). Sustainable development goals indicators at territorial level:
Conceptual and methodological issues—The Italian perspective. Social Indicators Research,
147, 383–419. https://doi.org/10.1007/s11205-019-02162-4.
Bruggemann, R., & Annoni, P. (2014). Average heights in partially ordered sets. MATCH
Communications in Mathematical and in Computer Chemistry, 71, 101–126.
Bruggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partially
orders. MATCH Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Bruggemann, R., & Carlsen, L. (2014). Incomparable-what now? MATCH Communications in
Mathematical and in Computer Chemistry, 71, 699–714.
Bruggemann, R., & Kerber, A. (2018). Fuzzy logic and partial order; first attempts with the
new PyHasse-program L_eval. MATCH Communications in Mathematical and in Computer
Chemistry, 80, 745–768.
27
2006), the task to derive from the Hasse diagrams easily understandable estimation
methods for Rkav is still an important object of research in the future (see also
Bruggemann and Annoni 2014; Bruggemann and Carlsen 2011, 2014; Bruggemann
et al. 2004). It should be noted that in the field of research of indicator systems the
pure rendering of results by an effective but hardly understandable method cannot
be satisfying, because finally it is of main importance to understand, i.e. to trace
back the reason, why certain objects under certain indicator systems get a certain
position in the ranking!
The extremal case (AC) throws another light on the idea that an indicator
system is more than its parts: The Hasse diagram is of no direct help as there
is no order relation among the objects. Nevertheless, the indicators themselves
have a different influence why order relations among objects are broken, thus
inducing new relations, namely among indicators (Bruggemann and Voigt 2011,
2012; Bruggemann and Carlsen 2014).
Even if the Hasse diagram is somewhere in the middle between AC and CC,
algebraic concepts (taken from universal algebra, Davey and Priestley 1990) such
as congruence, linear sums and separated sums, are providing powerful tools to
analyse the indicator system. Congruence, for instance provides a methodological
framework, as to how far a family of subsets of objects can be considered as a
CC-system, i.e. not the objects themselves can be ranked, but appropriate selected
subsets of objects (Carlsen and Bruggemann, Soc.Ind. Res., Febr., 2019 submitted).
References
Aguirre-Urreta, M. I., Rönkkö, M., & Marakas, G. M. (2016). Omission of causal indicators:
Consequences and implications for measurement. Measurement: Interdisciplinary Research
and Perspectives, 14(3), 75–97.
Alaimo, L. S. (2020). Complexity of social phenomena: Measurements, analysis, representations
and synthesis. Unpublished Doctoral Dissertation, University of Rome “La Sapienza”, Rome,
Italy.
Alaimo, L. S., & Maggino, F. (2018). Sviluppo sostenibile e differenze regionali. In E. di Bella,
F. Maggino, & M. Trapani (Eds.), AIQUAV 2018. V Convegno dell’Associazione Italiana per
gli Studi sulla Qualità della Vita. Libro dei Contributi Brevi (pp. 199–206). Genova: Genova
University Press.
Alaimo, L. S., & Maggino, F. (2020). Sustainable development goals indicators at territorial level:
Conceptual and methodological issues—The Italian perspective. Social Indicators Research,
147, 383–419. https://doi.org/10.1007/s11205-019-02162-4.
Bruggemann, R., & Annoni, P. (2014). Average heights in partially ordered sets. MATCH
Communications in Mathematical and in Computer Chemistry, 71, 101–126.
Bruggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partially
orders. MATCH Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Bruggemann, R., & Carlsen, L. (2014). Incomparable-what now? MATCH Communications in
Mathematical and in Computer Chemistry, 71, 699–714.
Bruggemann, R., & Kerber, A. (2018). Fuzzy logic and partial order; first attempts with the
new PyHasse-program L_eval. MATCH Communications in Mathematical and in Computer
Chemistry, 80, 745–768.