A Study to Generate a Weak Order from a Partially Ordered Set, Taken. . .
77
4 Discussion
4.1 Lichen Biomonitoring/Bioaccumulation Matrices as
Multi-indicator Systems
Undoubtedly, any data pre-processing, as done here, are of high importance not
only in chemical risk assessment and management but also broader, in the decisionmaking process of environmental policy. However, here is not the place to discuss
in depth the pre-processing, defined by Nimis and Bargagli (1999), nevertheless, we
think that here some words may be helpful:
In biomonitoring techniques of air quality with native lichens, an approach to the
interpretation of data of native lichens is the so-called “naturality/alteration scales”
based on thresholds identifying classes of increasing element concentrations, and
obtained by the meta-analysis of a large set of bioaccumulation data. The method by
Nimis and Bargagli (1999) defines seven classes of element concentrations. These
classes are built up on hundreds of data points collected in Italy between the 1980s
and the 1990s. The seven class scale refer to (1) very high naturality, (2) high
naturality, (3) middle naturality, (4) low naturality/alteration, (5) middle alteration,
(6) high alteration and (7) very high alteration based on the percentile distributions
of element concentrations in lichens (Nimis et al. 2000).
Recently a paper was published, where the data pre-processing of data (is
examined under the methodological background of partial order theory, see Fattore
et al. (2019).
4.2 Applicability of the Proposed Method
The quantity epsav, Eq. 14 is an average value and is – as mentioned already above –
related to a single object. The domain of validity for Eq. 15 is given by 0.8 ≤
Dom(X 1 , X 2 ) ≤ 1.0.
If Dom(X 1 , X 2 ) → 0.8 the deviations Eps (Eq. 13) become quickly large as Figs.
1 and 2 (randomly generated data) show. Consequently in the following paragraph
we investigate reasons for large deviations of Eps.
4.3 Reasons for Large Deviations
First of all, a dissection of a poset (X, ≤) into two subposets (X 1 , ≤) and (X 2 ,
≤) leads to more symmetry in the resulting graphs of the subposets (as already
mentioned above). Hence, the degeneracy of Hav-values is increased. Even if the
enhanced degree of ties is accepted, there can be large deviations, which result from
structures like the one shown in Fig. 6.
77
4 Discussion
4.1 Lichen Biomonitoring/Bioaccumulation Matrices as
Multi-indicator Systems
Undoubtedly, any data pre-processing, as done here, are of high importance not
only in chemical risk assessment and management but also broader, in the decisionmaking process of environmental policy. However, here is not the place to discuss
in depth the pre-processing, defined by Nimis and Bargagli (1999), nevertheless, we
think that here some words may be helpful:
In biomonitoring techniques of air quality with native lichens, an approach to the
interpretation of data of native lichens is the so-called “naturality/alteration scales”
based on thresholds identifying classes of increasing element concentrations, and
obtained by the meta-analysis of a large set of bioaccumulation data. The method by
Nimis and Bargagli (1999) defines seven classes of element concentrations. These
classes are built up on hundreds of data points collected in Italy between the 1980s
and the 1990s. The seven class scale refer to (1) very high naturality, (2) high
naturality, (3) middle naturality, (4) low naturality/alteration, (5) middle alteration,
(6) high alteration and (7) very high alteration based on the percentile distributions
of element concentrations in lichens (Nimis et al. 2000).
Recently a paper was published, where the data pre-processing of data (is
examined under the methodological background of partial order theory, see Fattore
et al. (2019).
4.2 Applicability of the Proposed Method
The quantity epsav, Eq. 14 is an average value and is – as mentioned already above –
related to a single object. The domain of validity for Eq. 15 is given by 0.8 ≤
Dom(X 1 , X 2 ) ≤ 1.0.
If Dom(X 1 , X 2 ) → 0.8 the deviations Eps (Eq. 13) become quickly large as Figs.
1 and 2 (randomly generated data) show. Consequently in the following paragraph
we investigate reasons for large deviations of Eps.
4.3 Reasons for Large Deviations
First of all, a dissection of a poset (X, ≤) into two subposets (X 1 , ≤) and (X 2 ,
≤) leads to more symmetry in the resulting graphs of the subposets (as already
mentioned above). Hence, the degeneracy of Hav-values is increased. Even if the
enhanced degree of ties is accepted, there can be large deviations, which result from
structures like the one shown in Fig. 6.