Vita e Pensiero
Socio-economic evaluation with ordinal variables: integrating counting and poset approaches
digital
Year:
2011
The evaluation of material deprivation, quality of life and well-being very often requires to deal with multidimensional systems of ordinal variables, rather than with classical numerical datasets. This poses new statistical and methodological challenges, since classical evaluation tools are not designed to deal with this kind of data. The mainstream evaluation methodologies generally follow a counting approach, as in a recent proposal by Alkire and Foster pertaining to the evaluation of
multidimensional poverty. Counting procedures are inspired by the composite indicator approach
and share similar drawbacks with it, computing aggregated indicators that may be poorly reliable.
A recent and alternative proposal is to address the ordinal evaluation problem through partial order
theory which provides tools that prove more consistent with the discrete nature of the data. The
goal of the present paper is thus to introduce the two proposals, showing how the evaluation methodology based on partial order theory can be integrated in the counting approach of Alkire and Foster.
Keywords: Partial Order theory, Counting Approach, Evaluation, Material Deprivation, Quality of
Life
The bi-partial approach in clustering and ordering: the model and the algorithms
digital
Year:
2011
The paper outlines an approach, applicable to both the problem of clustering and to (‘‘optimum’’)
ordering, which starts from a formulation of the objective function and the constraints, equivalent to
a binary mathematical programming problem. This formulation, for both ordering and clustering,
represents a number of very positive features, like possibility of dealing with incomplete and inconsistent
data, while posing essential numerical difficulties. For clustering, it implies a globally optimal
solution in that both cluster content and cluster number are obtained. We reformulate this problem
by parameterising it and show that, under certain additional assumptions, an effective algorithm
can be deduced for both clustering and ordering, which suboptimises the objective function.
In the case of clustering, the algorithm is an analogue of the classical hierarchical merger procedures,
while in the case of ordering it relies on iterations, in which just one object is moved. Some
essential properties are given, along with a simple illustration. In spite of the analogy, the properties
of the approach and the respective algorithms are different for the two cases considered, i.e.
clustering and ordering.
Keywords: Clustering, Ordering, Mathematical Programming, Parameterisation, Suboptimisation Algorithms, Objective Functions.
Finding incomparable pairs of subsets by using Formal Concept Analysis
digital
Year:
2011
In the paper presented here, we use Formal Concept Analysis (FCA) to solve a problem that arises
when working with partially ordered sets (posets). In detail, the task here is to look for incomparable
subsets which are related to a given poset. A way to solve this problem is to use FCA based
on a context which can be derived in some steps from the _-matrix of the (simple directed) graph
corresponding to the given poset. The requested incomparable subsets result from the set of concepts
obtained from this context. For illustrative purposes, small toy data sets are presented. At the
end, a real data application to environmental chemistry is given in detail. The data consist of ten
chemicals found in the German river Main. As the result a set of twelve incomparable pairs of subsets are figured out.
Keywords: Bipartite Graph, Adjacency Matrix, Formal Concept Analysis, Partially Ordered Set, Incomparability of Sets.
The Copeland method as a relative and categorized ranking tool
digital
Year:
2011
This paper is concerned with introducing a modified Copeland method as a relative and categorized
ranking tool. Using the concept of partially ordered sets and the social choice theory, the Copeland
score ranking methodology is applied outside its usual political voting environment to rank objects
in the scientific field. The ranking methodology was assessed using 45 data sets with different number of objects and indicators and compared with other methods. Results show that the Copeland
method appears as a good and stable tool for ranking objects giving results comparable to the
Dominance and the Simple Additive Ranking methods with the advantage of lower sensitivity and
CPU time. Also, it solves the problem of isolated objects found in some Hasse diagrams.
Keywords: Copeland Method, Hasse Diagram, Categorized Ranking, Relative Ranking, Sensitivity.
Preliminary assessment of reliability importance measures using the Hasse Diagram Technique, Ordered Weighted Average and Copeland Scores
digital
Year:
2011
Importance Measures (IMs) are valuable tools that have been used to quantify and rank the components of a system with respect to their contribution to a considered measure of performance. For example,
IMs have been used for characterizing the importance of element failures with respect to the
overall system reliability. In general, different IMs based on different definitions may lead to different
importance rankings of the components within a system. This fact could affect a decision-maker
for achieving, for example, a better global performance level.
In this paper we propose the use of the Hasse Diagram Technique (HDT) to make a preliminary assessment
for detecting possible conflicts among IM and selecting, if required, a convenient combination
or aggregation of IMs, based on parametric or non-parametric techniques, such as Ordered
Weighted Average (OWA) or Copeland Score (CS). Numerical examples illustrate the assessment.
Keywords: Copeland Score, Hasse Diagram Technique, Importance Measures, Multi-Criteria Decision, Ordered Weighted Average (OWA).
Qualification of the DPSIR approach by partial order ranking
digital
Year:
2011
The DPSIR (Driving forces, Pressures, State, Impacts, Responses) framework takes into account a
chain of past and present situations as well as suggests future activities as responses aiming at improving
the environmental health. Thus, DPSIR constitutes an advantageous directive for integrated
environmental assessments. The driving forces are centered on economic sectors and human activities,
i.e. activities in the society that directly or indirectly are causing the pressures on the environment.
The pressures on the environment develop from the human activities that are associated with
the above mentioned ‘needs’ (driving forces). The state refers to the environmental and human
health as a result of the pressures. The impacts refer to environmental and economic factors changing
the physical, chemical or biological states of the environment as well as impacts on human
health. The responses comprise a priori the reactions by authorities, regulators or society in general
to the changes induced through the other element in the DPSIR chain. The paper will discuss the
qualification of the DPSIR approach by applying partial order ranking (POR) to the single stages
of the assessment, eventually applying the hierarchical partial ranking (HPOR) methodology in order
to select the more appropriate responses. Further the paper will describe the possible involvement
of expert groups in the assessment process applying a partial order based DPSIR approach.
Keywords: DPSIR, Integrated Environmental Assessment, Partial Order Ranking, Hasse Diagrams.
Risk assessment of chemicals in the river Main (Germany): application of selected partial order ranking tools
digital
Year:
2011
Assessments of the behavior and impact of chemicals in the environment typically require a multicriteria
approach as a multitude of parameters has to be taken into account in order to disclose the
full picture. In the present paper we demonstrate how selected partial order ranking tools can be
applied as decision support. As an illustrative example a series of 14 chemicals, belonging to 4 different
classes of chemicals, found in the river Main (Germany) have been assessed based on 3 parameters,
i.e. volatilization, sedimentation and advection, determinative for their exposure behavior.
In addition to ordinary partial order ranking more advanced tools as average ranks and dominance
analysis have been applied leading to conclusions as to which class of chemicals should receive primary
attention. Further, the analyses suggest directions for risk management such as pointing to
specific sources for the most problematic pollutants.
Keywords: Partial Order Ranking, Hasse Diagram Technique, Average Rank, Dominance Analysis,
Environmental Impact Assessment, EIA, River Main.
Ranking of coagulants for wastewater treatment using partial order theory
digital
Year:
2011
Jar-test is a useful tool for chemicals selection for physical–chemical wastewater treatment. The results
show the treatment efficiency in terms of suspended matter and organic matter removal. However,
in spite of having all these results, coagulant selection is not an easy task because one coagulant
can remove efficiently the suspended solids but at the same time increase the conductivity. In
this paper, the use of Partial Order Scaling Analysis (POSA) is proposed to help on the selection of
the coagulant and its concentration in a sequencing batch reactor (SBR). An evaluation of two commonly
used coagulation-flocculation aids was conducted and based on jar tests and POSA model,
Ferric Chloride (100 ppm) was the best choice.
Keywords: Coagulation, Jar Test, Partial Order Scaling Analysis, Treatment Selection.
Application of the PyHasse program features: Sensitivity,Similarity, and Separability for environmental health data
digital
Year:
2011
It has been evident for decades that many environmental chemicals pose an enormous risk to the
environment as well as to humans. There is increasing pressure to intensify the research and to
more efficiently evaluate the data on persistent and bioaccumulative chemicals in the environment
as well as in human bodies. An appropriate data analysis method is based on the theory of partially
ordered sets. The program PyHasse, developed by the third author, provides several features which
are useful for gaining information out of the data and drawing conclusions concerning the impact
of those chemicals and their prevention. In our data analysis approach we investigated data sets of
breast milk samples of women in Denmark and Finland which contained measurable levels of 32
persistent organic pollutants (POPs). Three important features of the PyHasse program are used:
The Sensitivity Analysis, the Similarity Analysis and the Separability Analysis. The aim of this discrete
mathematical approach is to find differences in the chemicals’ contamination between the
healthy boys and those boys who were suffering from congenital malformations (cryptorchidism).
Keywords: Environmental Health Data, Persistent Organic Pollutants (POPs), Cryptorchidism, Partial
Order, PyHasse Program.
More on M.M. Zenga’s new three-parameter distribution for nonnegative variables
digital
Year:
2011
SUMMARY
Recently Zenga (2010) has proposed a new three-parameter density function f (x : µ; α; θ), (µ > 0;
α > 0; θ > 0), for non-negative variables. The parameter µ is equal to the expectation of the distribution. The new density has positive asymmetry and Paretian right tail. For θ > 1, Zenga (2010) has obtained the expressions of: the distribution function, the moments, the truncated moments, the mean deviation and Zenga’s (2007a) point inequality A(x) at x = µ. In the present paper, as to the general case θ > 0, the expressions of: the distribution function, the ordinary and truncated moments, the mean deviations and Zenga’s point inequality A (µ) are obtained. These expressions are more complex than those previously obtained for θ > 1 by Zenga (2010). The paper is enriched with many graphs of: the density functions (0.5 ≤ θ ≤ 1.5), the Lorenz L(p) and Zenga’s I (p) curves as well as the hazard and survival functions.
Keywords: Non-Negative Variables, Positive Asymmetry, Paretian Right Tail, Beta Function, Lorenz Curve, Zenga’s Inequality Curve, Hazard Function, Survival Function.
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