1. Nationwide Sustainability Indicators and Their Integration, Evaluation, and Visualization Worldwide - UNEP Initiative - Sustainability Indicators Indicators of Human Environment Interface Human Environment Productive Harmony Indicators Nationwide Multidimentional Abstract Concept of Productive Harmony Worldwide

2. HIGHLIGHTS HIGHLIGHTS The law of human life, living, and human life cycle lies in supportive land, air, and water (LAW). Ancient scriptures express it very well: “…when the land is not livable, when the air is not breathable, when the water is not drinkable, man shall perish…” The worldwide human perception of the above comes through intuitive perspective of green land, blue sky, and clean water. Now that nationwide data have become available worldwide to help consider perceptive measures of greenness of land, blueness of sky, and cleanness of water, it is now possible to attempt to formulate and quantify a composite human environment index as a simple, elegant, and defensible societal instrument for national citizenry to discuss, debate and deal with human-environment interface in a public policy and planning arena. A most important purpose that such a human environment index is expected to serve is to help stimulate national and international dialogue leading to indepth policy discussion and debate essential for sustainable environment and development.

3. HIGHLIGHTS HIGHLIGHTS A major purpose of this study is to explore, investigate, and evaluate the proposed human environment index in light of any alternatives based on the concepts, methods, and tools available in the literature of individual indicators and integrated indicators. For human species and humanity, each of the environmental component land, air, and water is as important as another, and it is not possible to speak of one being more important than the other. This leads to the concept of equal importance of each component, and to the concept of equal weight to each component –a concept potentially useful in the construction of a composite indicator. The three basic individual component indicators are essentially uncorrelated and orthogonal in light of their largely uncorrelated columns. Therefore, their unweighted sum/average has no danger of allotting inadvertent importance to one over the other. Each basic individual component indicator is a bonafide fractional proportion between zero and one. It is dimensionless, being a ratio of a part to the whole in the same units. The unweighted sum/average does not involve adding apples and oranges. And this approach can be satisfactory as long as the parts and the wholes represent satisfactory entities for which commensurate data are available, nationwide and worldwide. Beauty lies in the eyes of the beholder. And that makes the difference. Indicators choice and their composites therefore become crucial when we view the environment in terms of landview, skyview, and waterview involving air, water, food, and shelter for the life support system for the humanity as we have known.

4. L AND, AIR, WATER INDICATORS for land - % of undomesticated land, i.e. total land area - domesticated (permanent crops and pastures, built up areas, roads, etc.) for air - % of renewable energy resources, i.e. hydro, solar, wind, geothermal for water - % of population with access to safe drinking water RANKCOUNTRYLANDAIRWATERHEI 1Sweden69.0135.241000.68 2Finland76.4619.05980.65 3Norway27.3863.981000.64 5Iceland1.7980.251000.61 13Austria40.5729.851000.57 22Switzerland30.1728.101000.53 39Spain32.637.741000.47 45France28.346.501000.45 47Germany32.562.101000.45 51Portugal34.6214.29820.44 52Italy23.356.891000.43 59Greece21.593.20980.41 61Belgium21.840.001000.41 64Netherlands19.431.071000.40 77Denmark9.835.041000.38 78United Kingdom12.641.131000.38 81Ireland9.251.991000.37

5. Figure 10. Absolute frequency distribution of trivariate data representation.

6. Figure 11. 3D Scatterplot for the LandAirWater dataset. Notice the tendency of records (countries).

15. Consider a situation in which one indicator column is the same as another indicator column, because the second indicator value is the same as the first indicator value. It is clear from the following figure that the second column does not add information/ discrimination to the first column. This is the situation when there is a strong underlying correlation between the two indicators. Recently, Landscape Ecology has discovered that some fifty landscape fragmentation pattern indicators amount to essentially five to ten indicators. MORE INDICATORS DO NOT NECESSARILY MEAN MORE INFORMATION AND MORE DISCRIMINATION

16. indicator two/ column two indicator one/column one

17. 17 Composite Indexes -- 1 I 1, I 2,..., I p indicators for ranking elements of some set G(I 1, I 2,..., I p ) = composite index Many possible choices for G: Only general requirement is that G must be increasing in each indicator separately

18. 18 Composite Indexes -- 2 Each choice of G determines a set of G-contours in indicator space and thereby determines a set of substitution or trade- off rules among the indicators Indicator 1 (x) Indicator 2 (y)  x x  x x  y y  y y Contour of constant G  x substitutes for  y

19. 19 Composite Indicator Approach –Requires choice of composite index G –Implicitly or explicitly, requires choice of substitution rules among different indicators (this is often like comparing apples and oranges) –Difficult to achieve a consensus on choice of G. Final decision is often made on basis of mathematical simplicity instead of scientific substance –Once G is chosen, future elements are easily incorporated into the ranking without changing relative ranks of earlier elements

20. 20 Figure. With two indicators, each object a divides indicator space into four quadrants. Objects in the second and fourth quadrants are ambiguous in making comparisons with a.

21. 21 Figure. Contour of index H passing through object a. A linear index is shown on the left and a non-linear index on the right.

22. 22 Figure. The top two diagrams depict valid contours while the bottom two diagrams depict invalid contours.

23. 23 Figure. The tradeoff or substitutability between height and weight in assessing the size of a person. The tradeoff is constant with a linear index (left) but varies across indicator space with a nonlinear index (right).

24. It lies in the ability for prioritization and ranking based on multiple indicator and stakeholder criteria without having to integrate indicators into an index, using Hasse diagrams,partial order sets, rank frequency distributions, stochastic orderings, markov chain monte carlo methods. It lies in the ability for prioritization and ranking based on multiple indicator and stakeholder criteria without having to integrate indicators into an index, using Hasse diagrams,partial order sets, rank frequency distributions, stochastic orderings, markov chain monte carlo methods. Ranking and Prioritization Innovation

25. We address the question of ranking a collection of objects when a suite of indicator values is available for each member of the collection. The objects can be represented as a cloud of points in indicator space, but the different indicators (coordinate axes) typically convey different comparative messages and there is no unique way to rank the objects. A conventional solution is to assign a composite numerical score to each object by combining the indicator information in some fashion. Consciously or otherwise, every such composite involves judgements (often arbitrary or controversial) about tradeoffs or substitutability between indicators. Environmental Indicators: Comparisons and Rankings without Integration---Some Statistical and Visual Tools

26. Rather than trying to impose a unique ranking, we take the view that the relative positions in indicator space determine only a partial ordering and that a given pair of objects may not be inherently comparable. Working with Hasse diagrams of the partial order, we study the collection of all rankings that are compatible with the partial order (admissible rankings). In this way, an interval of possible ranks is assigned to each object. The intervals can be very wide, however. Noting that ranks near the ends of each interval are infrequent under admissible rankings, a probability distribution is obtained over the interval of possible ranks. This distribution turns out to be unimodal (in fact, log-concave) and the original partial order is represented by stochastic ordering of probability distributions.

27. Our approach to ranking is in analogy with the crisp number to interval number to fuzzy number succession in fuzzy analysis. In fact, the crisp comparisons between comparable pairs of objects in the partial order can be extended to fuzzy comparisons between any pair of objects. By counting admissible rankings, we can assign a numerical degree or grade to the truth of the relation x < y for given objects x and y. The grade lies between 0 and 1, and equals 1 exactly when x < y is true in the original partial order.

28. HUMAN ENVIRONMENT INTERFACE LAND, AIR, WATER INDICATORS RANK COUNTRYLANDAIRWATER 1Sweden 2Finland 3Norway 5 Iceland 13 Austria 22 Switzerland 39 Spain 45 France 47 Germany 51 Portugal 52 Italy 59 Greece 61 Belgium 64 Netherlands 77 Denmark 78 United Kingdom 81 Ireland 69.01 76.46 27.38 1.79 40.57 30.17 32.63 28.34 32.56 34.62 23.35 21.59 21.84 19.43 9.83 12.64 9.25 35.24 19.05 63.98 80.25 29.85 28.10 7.74 6.50 2.10 14.29 6.89 3.20 0.00 1.07 5.04 1.13 1.99 100 98 100 82 100 98 100 for land - % of undomesticated land, i.e., total land area-domesticated (permanent crops and pastures, built up areas, roads, etc.) for air - % of renewable energy resources, i.e., hydro, solar, wind, geothermal for water - % of population with access to safe drinking water

29. Hasse Diagram (all countries)

30. Hasse Diagram (Western Europe)

31. Figure 5. Hasse diagrams for four different posets. Poset D has a disconnected Hasse diagram with two connected components {a, c, e} and {b, d}.

32. Figure 13: Hasse diagrams (right) of the two possible rankings for the poset on the left.

33. Figure 14. Rank-intervals for all 106 countries. The intervals (countries) are labeled by their midpoints as shown along the horizontal axis. For each interval, the lower endpoint and the upper endpoint are shown vertically. The length of each interval corresponds to the ambiguity inherent in attempting to rank that country among all 106 countries.

34. Figure 15. Rank-intervals for all 106 countries, plotted against their HEI rank. The HEI rank appears as the 45-degree line. The HEI tends to be optimistic (closer to the lower endpoint) for better-ranked countries and pessimistic (closer to the upper endpoint) for poorer-ranked countries.

35. Rank range run sequence. The bottom of each vertical line represents the minimum rank and the top of the line is the maximum rank for the indicators.

36. End-member Elimination. Maintenance and Enhancement Guidance.

37. Figure 16. A ranking of a poset determines a linear Hasse diagram. The numerical rank assigned to each element is that element’s depth in the Hasse diagram.

38. Figure 17. Hasse diagram of Poset B (left) and a decision tree enumerating all possible linear extensions of the poset (right). Every downward path through the decision tree determines a linear extension. Dashed links in the decision tree are not implied by the partial order and are called jumps. If one tried to trace the linear extension in the original Hasse diagram, a “jump” would be required at each dashed link. Note that there is a pure-jump linear extension (path a, b, c, d, e, f) in which every link is a jump.

39. Figure 18. Histograms of the rank-frequency distributions for Poset B.

40. Cumulative Rank Frequency Operator – 5 An Example of the Procedure In the example from the preceding slide, there are a total of 16 linear extensions, giving the following cumulative frequency table. Rank Element123456 a91416 b7121516 c041016 d0261216 e00141016 f00006 Each entry gives the number of linear extensions in which the element (row label) receives a rank equal to or better that the column heading

41. Cumulative Rank Frequency Operator – 6 An Example of the Procedure 16 The curves are stacked one above the other and the result is a linear ordering of the elements: a > b > c > d > e > f

42. Cumulative Rank Frequency Operator – 7 An example where F must be iterated Original Poset (Hasse Diagram) a f eb c g d h a f e b ad c h g a f e b ad c h g F F 2

43. Cumulative Rank Frequency Operator – 8 An example where F results in ties Original Poset (Hasse Diagram) a cb d a b, c (tied) d F Ties reflect symmetries among incomparable elements in the original Hasse diagram Elements that are comparable in the original Hasse diagram will not become tied after applying F operator

44. 44 Poset Cumulative Rank Frequency Approach –Entirely objective---no arbitrary choices involved –Computationally challenging (typically requires combinatorial MCMC) –Final ranking applies only to the given set of elements and reflects overall structure of entire Hasse diagram –If new elements are added to the collection to be ranked, all computations must be redone and relative rankings of earlier elements may change

45. RECONCILIATION Reconciliation between Partial Order and Composite Reconciliation between Partial Order and Composite Reconciliation between Ranks Reconciliation between Ranks Reconciliation between Weights Reconciliation between Weights Reconciliation between Stakeholder Group and Data Matrix/ Data Base and Indicators Construction Reconciliation between Stakeholder Group and Data Matrix/ Data Base and Indicators Construction

46. RECONCILIATION Stakeholder abstract concept, axis, ranking based on it.Stakeholder weights, composite index, rankings. Stakeholder abstract concept, axis, ranking based on it.Stakeholder weights, composite index, rankings. Data based abstract /latent concept, ranking based on it, data based weights, using POSAC. Data based abstract /latent concept, ranking based on it, data based weights, using POSAC. Representability approach for Reconciliation Representability approach for Reconciliation

47. 47 POSAC Method generally used to reduce the dimensionality of the indicators. Want to preserve as many of the comparabilities from the original data matrix as possible. A pair of objects a and b are comparable if a is better than b or if b is better than a for all indicators in the model. Similar to PCA, however POSAC preserves rank order rather than distance. POSAC plots the data on a two-dimensional plane, and thus produces two latent order variables (LOV1 and LOV2), which are the axes of the POSAC plot.

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49. 49 POSAC “loadings” We are interested in the strength of the influence of the original indicators on LOV1 and LOV2. Approximate loadings for each indicator can be computed in several ways We can discretize the LOV and the indicators into several levels, and measure the extent of match up variously.

50. 50 concordance method Compute the proportion of objects that the indicator and LOV gave the same scored value, which is then the approximate loading An alternate concordance method also gives some weight to objects where the indicator and LOV scored values differ by one. Using the concordance method, if object 1 has LOV value of 4 and indicator value 4, then give that object a 1.

51. 51 Differential Weights different methods for obtaining the differential weights for the indicators. The methods above may be characterized as investigative methods, in that the weights are computed from the data alone, and without input from the stakeholders about the indicator weights.

52. REPRESENTABILITY Patil, G. P. and Joshi S. W.(2012) Partial order ranking of objects with weights for indicators and its representability by a composite indicator. In Preparation. Patil, G. P. (2012) Comparative knowledge discovery using partial order and composite indicator. In Preparation. Invited inaugural address, 10 th International Workshop on Ranking and Prioritization with Partial Order, Berlin, Germany 52

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54. REPRESENTABILITY Patil, G. P. and Joshi S. W.(2012) Partial order ranking of objects with weights for indicators and its representability by a composite indicator. In Preparation. Patil, G. P. (2012) Comparative knowledge discovery using partial order and composite indicator. In Preparation. Invited inaugural address, 10 th International Workshop on Ranking and Prioritization with Partial Order, Berlin, Germany 54