Special Issue: Partially ordered sets digital
Applied Statistics is certainly devoted to extract information from any kind of data. Data which characterize objects of interest. Ranking, i.e. finding a complete order among objects, belongs to the tasks of Applied Statistics. Not anticipating a historical research, it seems, however, as if the task of ranking in terms of the theory of partially ordered sets does not play that role in statistics which it should do, taking into account the enormous multitude, diversity and popularity of ranking studies. The idea is simple, not to say trivial. Let objects x1, …, xn be characterized by m data, attributes, say qj(j = l, …, m), then xi1 < xi2 if and only if qj (xi1) = qj (xi2) for all j, and with at least one qj* with a strict inequality. It can be easily seen that this definition (being the basis of the ‘‘Hasse diagram technique’’ (HDT)) does not guarantee that every object is in a
A multi-criteria fuzzy approach for analyzing poverty structure digital
Poverty is a fuzzy and complex phenomenon which is intrinsically multidimensional. First attempts of tackling poverty with multidimensional measures trace back to the seventies with the conceptual writings on income poverty by Amartya Sen (1976). Since then much research has been devoted to answer questions of the type: (i) Who is poor? (ii) How poor is a poor? The measure of poverty and social exclusion is certainly a key point in poverty description. While much effort has been put in the last decades to the measurement of poverty, less attention has been paid to find relations among different poverty aspects. In this paper, we start from a classical definition of the population of the poor and we employ Fuzzy Multi-Criteria Analysis to provide an attempt to relate poverty aspects to one another, which we call a ‘structural representation of poverty’. Our focus is on the pattern of implications existing among different descriptors characterizing poverty aspects. We show how fuzzy relation theory and partially ordered set techniques are effective in representing complex relational structures and provide new insights into multidimensional poverty. As simple test cases the method is applied to data concerning two Italian regions based on EU-SILC database 2004. Keywords: Multidimensional Poverty, Multi-criteria Analysis, Poverty Structure, Ordinal Variables, Posets, Fuzzy Quasi-order Relations.
Risk assessment of chemicals in the river Main (Germany): application of selected partial order ranking tools digital
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.
Application of the PyHasse program features: Sensitivity,Similarity, and Separability for environmental health data digital
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.
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