Applying the concept of partially ordered sets on the ranking of near-shore sediments by a battery of tests

Ranking Factors of Infant Formula Milk Powder Using Improved Entropy Weight Based on HDT Method and Its Application of Food Safety

Food safety is about everyone’s health. Through risk assessment and early warning of food safety, food-related safety issues can be identified as early as possible and take timely precautions. However, the detection data of food safety are complex and non-linear, so it is necessary to find the relationship and hierarchical representation of factors affecting food safety. This paper presents an improved entropy weight based on Hasse diagram technology (HDT) method to analyze the influencing factors of food safety. The entropy weight method was used to calculate the weight of each factor index, and the relationship matrix was obtained. Then, the data of infant milk powder in China were analyzed hierarchically by the HDT method. Thus, we can obtain the multi-level structure that affects food safety. It provides an effective basis for early warning of food safety, can help government regulators to strengthen management, and urge enterprises to produce food safely.

Use of partial order in environmental pollution studies demonstrated by urban BTEX air pollution in 20 major cities worldwide

Urban air pollution with benzene, toluene, ethyl benzene and xylenes (BTEX) is a common phenomenon in major cities where the pollution mainly originates from traffic as well as from residential heating. An attempt to rank cities according to their BTEX air pollution is not necessarily straight forward as we are faced with several individual pollutants simultaneously. A typical procedure is based on aggregation of data for the single compounds, a process that not only hides important information but is also subject to compensation effects. The present study applies a series of partial ordering tools to circumvent the aggregation. Based on partial ordering, most important indicators are disclosed, and an average ranking of the cities included in the study is derived. Since air pollution measurements are often subject to significant uncertainties, special attention has been given to the possible effect of uncertainty and/or data noise. Finally, the effect of introducing weight regimes is studied. In a concluding section the gross national income per person (GNI) is brought into play, demonstrating a positive correlation between BTEX air pollution and GNI. The results are discussed in terms of the ability/willingness to combat air pollution in the cities studied. The present study focuses on Almaty, the largest city in Kazakhstan and compares the data from Almaty to another 19 major cities around the world. It is found that the benzene for Almaty appears peculiar high. Overall Almaty appears ranked as the 8th most BTEX polluted city among the 20 cities included in the study.

Hasse diagram as a green analytical metrics tool: ranking of methods for benzo[a]pyrene determination in sediments

This study presents an application of the Hasse diagram technique (HDT) as the assessment tool to select the most appropriate analytical procedures according to their greenness or the best analytical performance. The dataset consists of analytical procedures for benzo[a]pyrene determination in sediment samples, which were described by 11 variables concerning their greenness and analytical performance. Two analyses with the HDT were performed—the first one with metrological variables and the second one with “green” variables as input data. Both HDT analyses ranked different analytical procedures as the most valuable, suggesting that green analytical chemistry is not in accordance with metrology when benzo[a]pyrene in sediment samples is determined. The HDT can be used as a good decision support tool to choose the proper analytical procedure concerning green analytical chemistry principles and analytical performance merits.

Evaluation of analytical performance based on partial order methodology

Classical measurements of performances are typically based on linear scales. However, in analytical chemistry a simple scale may be not sufficient to analyze the analytical performance appropriately. Here partial order methodology can be helpful. Within the context described here, partial order analysis can be seen as an ordinal analysis of data matrices, especially to simplify the relative comparisons of objects due to their data profile (the ordered set of values an object have). Hence, partial order methodology offers a unique possibility to evaluate analytical performance. In the present data as, e.g., provided by the laboratories through interlaboratory comparisons or proficiency testings is used as an illustrative example. However, the presented scheme is likewise applicable for comparison of analytical methods or simply as a tool for optimization of an analytical method. The methodology can be applied without presumptions or pretreatment of the analytical data provided in order to evaluate the analytical performance taking into account all indicators simultaneously and thus elucidating a "distance" from the true value. In the present illustrative example it is assumed that the laboratories analyze a given sample several times and subsequently report the mean value, the standard deviation and the skewness, which simultaneously are used for the evaluation of the analytical performance. The analyses lead to information concerning (1) a partial ordering of the laboratories, subsequently, (2) a "distance" to the Reference laboratory and (3) a classification due to the concept of "peculiar points".

CombiSimilarity, an innovative method to compare environmental and health data sets with different attribute sizes example: eighteen Organochlorine Pesticides in soil and human breast milk samples

Human health and the health of the environment have entwined. In this paper we underpin this position by presenting a modeling approach named CombiSimilarity, which has been developed by the first author in the software tool PyHasse comprising a wide variety of partial ordering tools. A case study of 18 Organochlorine Pesticides (OCPs) detected in soil as well as in human breast milk samples in the Taurus Mountains in Turkey is carried out. Seven soil samples and 44 breast milk samples were measured. We seek to answer the question whether the contamination pattern in breast milk is associated with the contamination pattern in soil by studying the mutual quantitative relationships of the chemicals involved. We could demonstrate that there is a similarity with respect to the concentration profiles between the soil and breast milk pollution. Therefore the hypothesis may be formulated that the concentrations of chemicals in the milk samples are strongly related to the soil contamination. This supports the concept that soil could be a surrogate for human exposure at background locations.

Ranking of ecotoxisity tests for underground water assessment using the Hasse diagram technique

The present study deals with the novel application of the Hasse diagram technique (HDT) for the specific ranking of ecotoxicity tests capable of assessment of underground water quality. The area studied is a multi-municipal landfill in the northern Poland. The monitoring network of the landfill constitutes of 27 piezometers for underground water monitoring and two observation points at surface water courses. After sampling, chemical analysis of various water parameters was performed (pH, conductivity, temperature, turbidity (TURB), color, taste, smell and atmospheric conditions: temperature, precipitation and cloud cover, heavy metals content (Cu, Zn, Pb, Cd, Cr(6+), Hg), total organic carbon (TOC), sum of Polycyclic Aromatic Hydrocarbons (PAHs), Na, Mg, K, Ca, Mn, Fe, Ni, alkalinity (Alkal), general hardness, total suspended matter (SUSP), Biological Oxygen Demand (BOD), Chemical Oxygen Demand (COD), chlorides, fluorides, sulphides, sulphates, ammonium nitrogen, total nitrogen, nitrate and nitrite nitrogen, volatile phenols, ether extracts (ETHER), dry residues (DRY_RES), dissolved compounds). Parallel to the chemical parameters assessment six different ecotoxicity tests were applied (% root length(PG)/germination(PR) inhibition of Sorghum saccharatum (respectively PGSS/PRSS), Sinapis alba (respectively PGSA/PRSA), Lepidium sativum (respectively PGLS/PRLS), % bioluminescence inhibition of Vibrio fischeri (MT), % mortality of Daphnia magna (DM), % mortality of Thamnocephalus platyrus (TN)). In order to determine the applicability of the various ecotoxicity tests, a ranking of samples from different monitoring levels according to the test used (attributes) is done by using HDT. Further, the sensitivity of the biotests was determined and compared. From the sensitivity analysis of the both monitoring levels was evident that the choice of ecotoxicity tests could be optimized by the use of HDT strategy. Most reliable results could be expected by the application of root growth inhibition of Sorghum saccharatum (PGSS test). In order to clarify the relationship between the chemical parameters measured and each of the ecotoxicity tests a optimized similarity analysis between Hasse diagrams for the ecotoxicity tests for different levels of monitoring and Hasse diagrams obtained by the use of the chemical parameters was performed. Finally, it could be concluded that for reliable monitoring of underground waters passing a dump collector following chemical parameters are of significance: water hardness, dissolved matter, total nitrogen (ammonia and nitrate nitrogen), nickel, chlorides, alkalinity, total organic carbon and ether extract and the proper battery test could include PGSA, PGSS and PRSS.

Ranking COMMPS chemical substances by an improved POT/RLE approach

The combined monitoring-based and modeling-based priority setting (COMMPS) provides a procedure for the identification of priority hazardous substances outlined in the Working Document (ENV/191000/01 of January 16, 2001). This procedure is based on scoring a set of criteria which individually make substances more or less hazardous. The way scores are weighted and combined has been established by a panel of experts. Different authors outlined how such a procedure might be affected by subjectiveness of judgment, and alternative solutions based on partial order theory (POT) and random linear extensions (RLE) have been suggested. This method consists of generating a set of RLE and of averaging the rank given to each substance, so that a total order could be determined. Any POT/RLE approach must face the issue of covering as much as possible the space of linear extensions that, in the case of the 85 substances considered by COMMPS, becomes extremely large, and an exhaustive generation of linear extension is not feasible. Therefore, having a faster algorithm would help to consider a larger number of linear extensions in a given time frame. In this paper, we discuss this problem, and we outline a possible solution.

On the ranking of chemicals based on their PBT characteristics: comparison of different ranking methodologies using selected POPs as an illustrative example

Knowledge of the environmental behavior of chemicals is a fundamental part of the risk assessment process. The present paper discusses various methods of ranking of a series of persistent organic pollutants (POPs) according to the persistence, bioaccumulation and toxicity (PBT) characteristics. Traditionally ranking has been done as an absolute (total) ranking applying various multicriteria data analysis methods like simple additive ranking (SAR) or various utility functions (UFs) based rankings. An attractive alternative to these ranking methodologies appears to be partial order ranking (POR). The present paper compares different ranking methods like SAR, UF and POR. Significant discrepancies between the rankings are noted and it is concluded that partial order ranking, as a method without any pre-assumptions concerning possible relation between the single parameters, appears as the most attractive ranking methodology. In addition to the initial ranking partial order methodology offers a wide variety of analytical tools to elucidate the interplay between the objects to be ranked and the ranking parameters. In the present study is included an analysis of the relative importance of the single P, B and T parameters.

Multi-criteria decision analyses. Viewing MCDA in terms of both process and aggregation methods: some thoughts, motivated by the paper of Huang, Keisler and Linkov

The paper of Huang, Keisler and Linkov (HKL) (Huang et al., 2011) has motivated us to this note about the relation between ranking procedures and Multi-Criteria Decision Analysis (MCDA) tools. The key concept in the HKL-paper is in our eyes the 'trade-off'. A 'trade-off' seems necessary, when conflicting indicator values are present. HKL stress that the general application of MCDA is hampered by different terminology. We do not claim to have a solution for that problem. Nevertheless, we think that the discussion is worthwhile and this note presents some of our ideas, which basically imply the need of a broadening of the definition of MCDA.

Pretreatment of wastewater: optimal coagulant selection using Partial Order Scaling Analysis (POSA)

Jar-test is a well-known tool for chemical selection for physical-chemical wastewater treatment. Jar test 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. This makes the final selection of coagulants very dependent on the relative importance assigned to each measured parameter. In this paper, the use of Partial Order Scaling Analysis (POSA) and multi-criteria decision analysis is proposed to help the selection of the coagulant and its concentration in a sequencing batch reactor (SBR). Therefore, starting from the parameters fixed by the jar-test results, these techniques will allow to weight these parameters, according to the judgments of wastewater experts, and to establish priorities among coagulants. An evaluation of two commonly used coagulation/flocculation aids (Alum and Ferric Chloride) was conducted and based on jar tests and POSA model, Ferric Chloride (100 ppm) was the best choice. The results obtained show that POSA and multi-criteria techniques are useful tools to select the optimal chemicals for the physical-technical treatment.

Ranking using the Copeland score: a comparison with the Hasse diagram

This study concerns the problem of ranking objects (chemicals, projects, databases, etc.) when a number of indicators are available for these objects that convey different comparative information. There is no unique way to rank these objects while taking all indicators into account. Using the concept of partially ordered sets and the social choice theory, the Copeland score ranking methodology was applied outside of its usual political environment (voting) to rank objects in the sciences. This method avoids the disadvantages of the Hasse diagram and the linear extension usually used to resolve this issue. The ranking methodology was assessed using eight data sets, each with different numbers of objects and indicators. The results showed that the Copeland method appears to be an effective and stable tool for ranking objects, yielding results comparable to those of an evaluation by a Hasse diagram. Also, it has the advantage of facilitating the analysis of large partially ordered sets, which were practically impossible to handle using existing methods.

Influence of altitude concerning the contamination of humus soils in the German Alps: a data evaluation approach using PyHasse

BACKGROUND, AIM AND SCOPE

In an international project named MONARPOP (Monitoring Network in the Alpine Region for Persistent and other Organic Pollutants), selected chemicals in different environmental media were analysed in the years 2004 and 2005. Seventeen pesticides were chosen and analysed in humus and mineral soil in the German Alps. The samples were taken at different altitudes.

MATERIALS AND METHODS

In such a rather complex environmental datasets, it is often necessary to compare different sets of criteria and their influence on rankings. In the similarity analysis which is part of the theory of the Hasse diagram technique, we intend to calculate the similarity of different rankings. Furthermore, we perform a so-called dominance-dominance/dominance-separability method, followed by a sensitivity analysis, both subroutines in the newly developed PyHasse programme in order to find out if the concentration of the chemicals can be related to the altitudes at which the samples were taken.

RESULTS AND DISCUSSION

It can be demonstrated that the altitude has a considerable influence on the concentration of some organic chemicals in humus: The concentrations of some chemicals increase with the altitude. This increase shows certain irregularities for which several explication attempts including possible effects of atmospheric stratification phenomena in valleys have been made.

CONCLUSION

These results should be complemented in further studies with MONARPOP monitoring data from other Alpine countries, e.g. Austria, Switzerland, Italy and Slovenia.

A QSAR/QSTR study on the human health impact of the rocket fuel 1,1-dimethyl hydrazine and its transformation products Multicriteria hazard ranking based on partial order methodologies

The possible impact of the rocket fuel 1,1-dimethyl hydrazine (heptyl) (1) and its transformation products on human health has been studied using (Quantitative) Structure Activity/Toxicity ((Q)SAR/(Q)STR) modelling, including both ADME models and models for acute toxicity, organ specific adverse haematological effects, the cardiovascular and gastrointestinal systems, the kidneys, the liver and the lungs, as well as a model predicting the biological activity of the compounds. It was predicted that all compounds studied are readily bioavailable through oral intake and that significant amounts of the compounds will be freely available in the systemic circulation. In general, the compounds are not predicted to be acutely toxic apart from hydrogen cyanide, whereas several compounds are predicted to cause adverse organ specific human health effects. Further, several compounds are predicted to exhibit high probabilities for potential carcinogenicity, mutagenicity, teratogenicity and/or embryotoxicity. The compounds were ranked based on their predicted human health impact using partial order ranking methodologies that highlight which compounds on a cumulative basis should receive the major attention, i.e., N-nitroso dimethyl amine, 1,1,4,4-tetramethyl tetrazene, trimethyl, trimethyl hydrazine, acetaldehyde dimethyl hydrazone, 1, 1-formyl 2,2-dimethyl hydrazine and formaldehyde dimethyl hydrazone, respectively.

The interplay between QSAR/QSPR studies and partial order ranking and formal concept analyses

The often observed scarcity of physical-chemical and well as toxicological data hampers the assessment of potentially hazardous chemicals released to the environment. In such cases Quantitative Structure-Activity Relationships/Quantitative Structure-Property Relationships (QSAR/QSPR) constitute an obvious alternative for rapidly, effectively and inexpensively generatng missing experimental values. However, typically further treatment of the data appears necessary, e.g., to elucidate the possible relations between the single compounds as well as implications and associations between the various parameters used for the combined characterization of the compounds under investigation. In the present paper the application of QSAR/QSPR in combination with Partial Order Ranking (POR) methodologies will be reviewed and new aspects using Formal Concept Analysis (FCA) will be introduced. Where POR constitutes an attractive method for, e.g., prioritizing a series of chemical substances based on a simultaneous inclusion of a range of parameters, FCA gives important information on the implications associations between the parameters. The combined approach thus constitutes an attractive method to a preliminary assessment of the impact on environmental and human health by primary pollutants or possibly by a primary pollutant well as a possible suite of transformation subsequent products that may be both persistent in and bioaccumulating and toxic. The present review focus on the environmental – and human health impact by residuals of the rocket fuel 1,1-dimethylhydrazine (heptyl) and its transformation products as an illustrative example.

Hierarchical partial order ranking

Assessing the potential impact on environmental and human health from the production and use of chemicals or from polluted sites involves a multi-criteria evaluation scheme. A priori several parameters are to address, e.g., production tonnage, specific release scenarios, geographical and site-specific factors in addition to various substance dependent parameters. Further socio-economic factors may be taken into consideration. The number of parameters to be included may well appear to be prohibitive for developing a sensible model. The study introduces hierarchical partial order ranking (HPOR) that remedies this problem. By HPOR the original parameters are initially grouped based on their mutual connection and a set of meta-descriptors is derived representing the ranking corresponding to the single groups of descriptors, respectively. A second partial order ranking is carried out based on the meta-descriptors, the final ranking being disclosed though average ranks. An illustrative example on the prioritization of polluted sites is given.

Ecological scenarios analyzed and evaluated by a shallow lake model

We applied the complex ecosystem model EMMO, which was adopted to the shallow lake Müggelsee (Germany), in order to evaluate a large set of ecological scenarios. By means of EMMO, 33 scenarios and 17 indicators were defined to characterize their effects on the lake ecosystem. The indicators were based on model outputs of EMMO and can be separated into biological indicators, such as chlorophyll-a and cyanobacteria, and hydro-chemical indicators, such as phosphorus. The question to be solved was, what is the ranking of the scenarios based on their characterization by these 17 indicators? And how can we handle high quantities of complex data within evaluation procedures? The scenario evaluation was performed by partial order theory which, however, did not provide a clear result. By subsequently applying the hierarchical cluster analysis (complete linkage) it was possible to reduce the data matrix to indicator and scenario representatives. Even though this step implies losses of information, it simplifies the application of partial order theory and the post processing by METEOR. METEOR is derived from partial order theory and allows the stepwise aggregation of indicators, which subsequently leads to a distinct and clear decision. In the final evaluation result the best scenario was the one which defines a minimum nutrient input and no phosphorus release from the sediment while the worst scenario is characterized by a maximum nutrient input and extensive phosphorus release from the sediment. The reasonable and comprehensive results show that the combination of partial order, cluster analysis and METEOR can handle big amounts of data in a very clear and transparent way, and therefore is ideal in the context of complex ecosystem models, like that we applied.

The dualistic approach of FCA: a further insight into Ontario Lake sediments

The investigation of object-by-attribute matrices is very common in statistics and data analysis with the aim of uncovering every possible relationship among objects and/or attributes. Formal Concept Analysis (FCA) is a method, which stems directly from partial order and lattice theory, which provides an efficient tool to symmetrically uncover linkages among objects and attributes whenever a relation stands among the two sets. It provides efficacious graphical representation and computes association rules between attributes, thus helping in the detection of possible synergism or antagonism of attributes. In this paper, FCA potentialities are discussed and described by means of a case study already investigated by other partial order techniques: the case of Lake Ontario sediment samples. Data derive from a 'test battery' for a simultaneous analysis of degradation of Lake Ontario samples, which are basically of two typologies: hygienic and toxicity tests. A multi-valued approach is adopted to cope with the ordinal feature of data. Results highlight interesting interaction among hygienic compounds and a synergism between the two toxicity tests.

Three dissimilarity measures to contrast dendrograms

We discussed three dissimilarity measures between dendrograms defined over the same set, they are triples, partition, and cluster indices. All of them decompose the dendrograms into subsets. In the case of triples and partition indices, these subsets correspond to binary partitions containing some clusters, while in the cluster index, a novel dissimilarity method introduced in this paper, the subsets are exclusively clusters. In chemical applications, the dendrograms gather clusters that contain similarity information of the data set under study. Thereby, the cluster index is the most suitable dissimilarity measure between dendrograms resulting from chemical investigation. An application example of the three measures is shown to remark upon the advantages of the cluster index over the other two methods in similarity studies. Finally, the cluster index is used to measure the differences between five dendrograms obtained when applying five common hierarchical clustering algorithms on a database of 1000 molecules.

A combined QSAR and partial order ranking approach to risk assessment

QSAR generated data appear as an attractive alternative to experimental data as foreseen in the proposed new chemicals legislation REACH. A preliminary risk assessment for the aquatic environment can be based on few factors, i.e. the octanol-water partition coefficient (Kow), the vapour pressure (VP) and the potential biodegradability of the compound in combination with the predicted no-effect concentration (PNEC) and the actual tonnage in which the substance is produced. Application of partial order ranking, allowing simultaneous inclusion of several parameters leads to a mutual prioritisation of the investigated substances, the prioritisation possibly being further analysed through the concept of linear extensions and average ranks. The ranking uses endpoint values (log Kow and log VP) derived from strictly linear 'noise-deficient' QSAR models as input parameters. Biodegradation estimates were adopted from the BioWin module of the EPI Suite. The population growth impairment of Tetrahymena pyriformis was used as a surrogate for fish lethality.

Structure−Fate Relationships of Organic Chemicals Derived from the Software Packages E4CHEM and WHASSE

A risk assessment of chemicals is to be performed on the basis of the model EUSES, developed by the Commission of the European Union. The model package E4CHEM (Exposure Estimation for Potentially Ecotoxic Environmental Chemicals), developed in 1984-1992, is presented and applied in this paper as a model which allows a model-supported evaluation of chemicals. E4CHEM consequently does not have the wide applicability and technical comfort of the more recently developed model EUSES. The simulation models of E4CHEM characterize the chemical behavior in the environment by many aspects. Hence, there is a need to condense all of these aspects to get a clear impression of what will be the fate of the chemicals. Starting with the already published concept of exposure maps, we will discuss how partial orders may be helpful in establishing generalized structure-fate relationships. The software WHASSE is applied.

Giving molecules an identity. On the interplay between QSARs and partial order ranking

The interplay between 'noise-deficient' QSAR and Partial Order Ranking, including analysis of average linear ranks, constitutes an effective tool in giving substances which have not been investigated experimentally an identity by comparison with experimentally well-characterized, structurally similar compounds. It is disclosed that experimentally well-characterized compounds may serve as substitutes for highly toxic compounds in experimental studies without exhibiting the same extreme toxicity, while from an overall viewpoint they exhibit analogous environmental characteristics.

Aspects of decision support in water management--example Berlin and Potsdam (Germany) II--improvement of management strategies

Methods related to partial order theory such as the Hasse diagram technique (HDT) are increasingly used in the field of multi-criteria decision support. The HDT has the advantage of being a transparent evaluation tool, supported by several data analysis tools such as the concept of antagonistic indicators. However, the evaluation usually does not lead to a clear decision, because more than one possible solution is offered. In the example presented here, three of the nine water management strategies (scenarios) evaluated by HDT were identified as winners. However, these strategies were not comparable with each other because of the conflicting evaluation of at least two different indicators. Such antagonisms describe the advantage and disadvantage of each scenario. Based on this background information, a new innovative approach is demonstrated, enabling the stakeholders to design new, modified management strategies, with reduced negative effects. After improvement of the three potential solutions, one clear winner scenario could be identified.

Chemical databases evaluated by order theoretical tools

Data on environmental chemicals are urgently needed to comply with the future chemicals policy in the European Union. The availability of data on parameters and chemicals can be evaluated by chemometrical and environmetrical methods. Different mathematical and statistical methods are taken into account in this paper. The emphasis is set on a new, discrete mathematical method called METEOR (method of evaluation by order theory). Application of the Hasse diagram technique (HDT) of the complete data-matrix comprising 12 objects (databases) x 27 attributes (parameters + chemicals) reveals that ECOTOX (ECO), environmental fate database (EFD) and extoxnet (EXT)--also called multi-database databases--are best. Most single databases which are specialised are found in a minimal position in the Hasse diagram; these are biocatalysis/biodegradation database (BID), pesticide database (PES) and UmweltInfo (UMW). The aggregation of environmental parameters and chemicals (equal weight) leads to a slimmer data-matrix on the attribute side. However, no significant differences are found in the "best" and "worst" objects. The whole approach indicates a rather bad situation in terms of the availability of data on existing chemicals and hence an alarming signal concerning the new and existing chemicals policies of the EEC.

Ranking of chemical substances based on the Japanese Pollutant Release and Transfer Register using partial order theory and random linear extensions

In 1997 a Pollutant Release and Transfer Register (PRTR) pilot project was initiated in Japan. In 1998 the project was expanded and in 1999 a law concerning the establishment of a national PRTR was adopted. Data on the emissions of chemical substances are therefore now being reported on a continuous base. In relation to the PRTR project data on toxicity have been collected. In order to make efficient use of the collected information on emission and toxicity it is useful to group or rank the chemical substances according to the impact on human health and the environment. It has recently been argued that partial order theory (POT) in combination with the use of linear extensions (LE) may be the most objective way to create a linear rank. The methodology has been further expanded to handle larger data sets by the use of random linear extensions (RLE). In this paper the Japanese PRTR data are ranked using the POT/RLE methodology. An average rank is established for chemical substances in the 1998 and 1999 PRTR in Japan. The top 10 chemical substances in the 1998 PRTR are: dichlorvos, inorganic arsenic compounds, cobalt compounds, beryllium compounds, fenitrothion, disulfoton, parathion, diazinon, 4,4'-diamino-3,3'-dichlorodiphenylmethane and antimony compounds. The top 10 chemical substances from the 1999 PRTR are PCBs, lead compounds, fenitrothion, dichlorvos, disulfoton, inorganic arsenic compounds, chlorothalonil, thiobencarb, chromium and HCFC-141b. The descriptor having the highest influence on the ranking of the 1998 PRTR data is the production volume, which, however, is not given in the 1999 PRTR. Further, the disagreement between the ranking with the lack of toxicity data substituted with mean and maximum values, respectively, strongly indicates a general need for further toxicological investigations.

Aspects of decision support in water management--example Berlin and Potsdam (Germany) I--spatially differentiated evaluation

Decisions about sustainable development demand spatially differentiated evaluations. As an example, we demonstrate the evaluation of water management strategies in the cities of Berlin and Potsdam (Germany) with respect to their ecological effects in 14 sections of the surface water system. Two decision support systems were compared, namely PROMETHEE, which is designed to obtain a clear decision (linear ranking), and Hasse Diagram Technique (HDT), normally providing more than one favourable solution (partial order). By PROMETHEE, the spatial differentiation had unwanted effects on the result, negating the stakeholders determined weighting of indicators. Therefore, the stakeholder can barely benefit from the convenience of obtaining a clear decision (linear ranking). In contrast, the result obtained by HDT was not influenced by spatial differentiation. Furthermore, HDT provided helpful tools to analyse the evaluation result, such as the concept of antagonistic indicators to discover conflicts in the evaluation process.

Estimation of Averaged Ranks by a Local Partial Order Model

This paper continues the series of publications about applications of partial ordering. The focus of this publication is the derivation of approximate analytical expressions for the averaged rank and the ranking probabilities. To derive such combinatorial formulas a local partial order is suggested as an approximation. The performance of the approximation is rather high; we therefore conclude that three very simple descriptors of the local partial order seem to be sufficient to get a rough impression of the linear order, induced by the averaged ranks and the ranking probabilities of empirical partially ordered sets. Linear order derived from the partial order, ranking probabilities, and other characteristics are considered as parts of a so-called "General Ranking Model" (GRM). Following the local partial order, the averaged rank of an object x can be estimated applying the following simple formula: Rk(av) = (S+1)*(N+1)/(N+1-U). S is the number of successors of the object x, N is the total number of objects (of the quotient set), and U is the number of objects incomparable with x. More complex formulas for the ranking probabilities are given in the text. A list of abbreviations and symbols can be found in Tables 3 and 4.

Evaluation of the ranking probabilities for partial orders based on random linear extensions

Partial order theory and Hasse diagrams appears to be a promising tool for decision-making in environmental issues. Alternatives or objects are said to be partial ordered when it is impossible to find a mutual relationship (< or >) for all criteria. This is often the case in complicated real life situations. However, sometimes it is attractive to apply a total order, i.e. linear rank, and not just the partial order. Based on ranking probabilities and linear extensions it is possible to derive a total order. A linear extension is a projection of the partial order into a total order that comply with all the relations in the partial order. When all linear extensions are known the ranking probabilities can be found as the probability for an object to occupy a specific rank. However, the total number of linear extensions is proportional with the faculty of the number of objects in the partial order. Therefore it is practically impossible to identify all possible linear extensions for partial orders with more than around 20 objects. This study reviews and evaluates a method which estimates the ranking probability based on sampling of a minor random fraction of the linear extensions. Using standard statistics the necessary number of random linear extensions is described as a function of the ranking probability estimate and the restrictions on the confidence interval around the ranking probability. The analysis reveals a smaller systematic uncertainty, which occurs due to the random selection of ranking between two incomparable objects. The discrepancy appears to be dependent on the structure of the partial order. The method using random linear extensions thus appears as a valuable tool for analysing larger partially ordered sets, which are practically impossible to handle using the total set of linear extensions.

Order theoretical tools for the evaluation of complex regional pollution patterns

The mathematical and statistical evaluation of environmental data gains an increasing importance in environmental chemistry as the data sets become more complex. It is inarguable that different mathematical and statistical methods should be applied in order to compare results and to enhance the possible interpretation of the data. Very often several aspects have to be considered simultaneously, for example, several chemicals entailing a data matrix with objects (rows) and variables (columns). In this paper a data set is given concerning the pollution of 58 regions in the state of Baden-Württemberg, Germany, which are polluted with metals lead, cadmium, zinc, and with sulfur. For pragmatic reasons the evaluation is performed with the dichotomized data matrix. First this dichotomized 58 x 13 data matrix is evaluated by the Hasse diagram technique, a multicriteria evaluation method which has its scientific origin in Discrete Mathematics. Then the Partially Ordered Scalogram Analysis with Coordinates (POSAC) method is applied. It reduces the data matrix in plotting it in a two-dimensional space. A small given percentage of information is lost in this method. Important priority objects, like maximal and minimal objects (high and low polluted regions), can easily be detected by Hasse diagram technique and POSAC. Two variables attained exceptional importance by the data analysis shown here: TLS, Sulfur found in Tree Layer, is difficult to interpret and needs further investigations, whereas LRPB, Lead in Lumbricus Rubellus, seems to be a satisfying result because the earthworm is commonly discussed in the ecotoxicological literature as a specific and highly sensitive bioindicator.

Improved Estimation of the Ranking Probabilities in Partial Orders Using Random Linear Extensions by Approximation of the Mutual Ranking Probability

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.

QSARs for identifying and prioritizing substances with persistence and bioconcentration potential

From the 8511 chemicals with 1998 production volumes reported to the U.S. Environmental Protection Agency (U.S. EPA), the TSCA Interagency Testing Committee's (ITC's) Degradation Effects Bioconcentration Information Testing Strategies (DEBITS) was used to identify 56 chemicals. The DEBITS Quantitative Structure-Activity Relationships (QSARs) and the U.S. EPA's PBT profiler QSARs were used to predict the persistence and bioconcentration factors of these 56 chemicals. Partial order ranking was used to prioritise the chemicals based on persistence and bioconcentration potential.

Comparison of the combined monitoring-based and modelling-based priority setting scheme with partial order theory and random linear extensions for ranking of chemical substances

The combined monitoring-based and modelling-based priority setting scheme (COMMPS) used to establish a priority setting list within the EU Water Framework Directive plays a major role in the European environmental policy on chemical substances. The COMMPS procedure can be classified as a so-called scoring method. The applied functional relationship and weight factors are established based on expert judgement, which unfortunately appears to be vulnerable to subjective inputs. In this study an alternative priority setting methods based on partial order theory (POT) and random linear extensions (RLE) is suggested and compared to the COMMPS procedure. The POT/RLE is characterised as being based on fewer assumptions concerning functional relationships and does not apply weighting factors. Using the POT/RLE methodology a different ranking result occur than when using the COMMPS procedure. Eight of the top 20 substances from the COMMPS procedure are not ranked within the top 20 when using POT/RLE. From the viewpoint of environmental protection, especially the substances that have been given low priority in the COMMPS procedure, but a high rank in POT/RLE, are of interest in a regulatory context. These substances are naphthalene, trichloromethane, isoproturon, metolachlor, endosulfan, acenaphthene, alachlor and dichloromethane. An analysis of the ability of the descriptors to separate the single substance discloses that the most significant descriptor is the concentrations detected in the environment. Further, the frequency of detection is not applied as a descriptor in the COMMPS procedure. However, if this descriptor was to be applied the analysis revealed that it would have been the third most significant descriptor.

A comparison of partial order technique with three methods of multi-criteria analysis for ranking of chemical substances

An alternative to the often cumbersome and time-consuming risk assessments of chemical substances could be more reliable and advanced priority setting methods. An elaboration of the simple scoring methods is provided by Hasse Diagram Technique (HDT) and/or Multi-Criteria Analysis (MCA). The present study provides an in depth evaluation of HDT relative to three MCA techniques. The new and main methodological step in the comparison is the use of probability concepts based on mathematical tools such as linear extensions of partially ordered sets and Monte Carlo simulations. A data set consisting of 12 High Production Volume Chemicals (HPVCs) is used for illustration. It is a paradigm in this investigation to claim that the need of external input (often subjective weightings of criteria) should be minimized and that the transparency should be maximized in any multicriteria prioritisation. The study illustrates that the Hasse diagram technique (HDT) needs least external input, is most transparent and is least subjective. However, HDT has some weaknesses if there are criteria which exclude each other. Then weighting is needed. Multi-Criteria Analysis (i.e. Utility Function approach, PROMETHEE and concordance analysis) can deal with such mutual exclusions because their formalisms to quantify preferences allow participation e.g. weighting of criteria. Consequently MCA include more subjectivity and loose transparency. The recommendation which arises from this study is that the first step in decision making is to run HDT and as the second step possibly is to run one of the MCA algorithms.