Scandinavian SD The SAFE Way

Transcription

1 Sandinavian SD The SAFE Way Sari Haj Hussein Chalmers University of Tehnology Abstrat People of various interests talk about Sustainable Development (SD) and in their talks they understand SD very differently. A lexiographer for example may define SD aording to Oxford Advaned Learner's Ditionary as "the use of natural produts and energy in a way that does not harm the environment". While a passer-by may happily dub her soiety as sustainable if it is providing her with her life needs while onsidering the needs of generations to ome over a very long time. To take it to an extreme edge, the philosopher Lu Ferry [1] defines SD by saying: "I know that this term is obligatory, but I find it also absurd, or rather so vague that it says nothing!". In this paper we try to define and measure SD in Sandinavian ountries using a novel mathematial approah. We rely on a non-onrete model for this purpose; namely the SAFE model, whih is based on onepts derived from fuzzy logi. It is widely believed that the appliation of fuzzy logi brings powerful reasoning abilities in disiplines where onrete mathematial models do not exist; and SD is one suh disipline. In fat, fuzzy logi is an outstanding tool for mimiking human thinking and foresight. Based on the SAFE model, we give a areful assessments of sustainability in eah of the Sandinavian ountries. We also undergo a trend monitoring ombined with a sensitivity analysis in order to stand on the most important sustainability fators in eah of these ountries. 1. Introdution The environmental risis has beome obvious to almost everybody, therefore people are inreasingly talking about sustainability. In essene, a soiety is a highly omplex system, and when a problem arises in it, its solution depends on awareness, knowledge, values, will and perseverane. In days gone by, sustainability was not an issue beause human ations were not a hazard to the terrestrial, aquati or atmospheri eosystems the size of human population was small. At present, humans have already exeeded the Earth's apaity to supply food, absorb pollution and regenerate the human populations are engaged in an endless yle of onsumption of the eosystems to support their growth, often in an irreversible way. A question thus arises as a onsequene of the strain we are putting on the environment: How sustainable is our way of living? Suh a question gropes for definitions, methods and indiators for assessing sustainability. Mathematially speaking, sustainability is a omposition of funtions of several eo-variables. Deterministi evaluation of these funtions is not possible beause sustainability is inherently a blurred onept and annot be represented through traditional mathematis. Fuzzy evaluation, on the other hand, is appliable to sustainability beause it an model omplex systems whose struture is not known, or of whih the knowledge of dynamis is limited. The remainder of this paper is organized as follows: first, in Setion 2, we briefly disuss available sustainability indiators other than the SAFE and their downsides. Then, in Setion 3, we introdue a omprehensive desription of the mathematial foundations of the SAFE model. Thereafter, in Setion 4, we desribe the notion of sensitivity analysis. Last but not least, in Setion 5, we give and disuss our assessment results. 2. Sustainability Indiators Other Than The SAFE Sustainability Indiators (SIs) onsider ertain sustainability attributes quantitatively to provide an idea of the state of eah attribute. The onept behind SIs is illustrated in Figure 1 [2]. 1

2 Figure 1. The Conept Behind Sustainability Indiators (SIs) The Number Of Colleted Indiators Is Arbitrary In Figure 1, we see how seven apropos SIs (SI1 through SI7) are gathered from a given eosystem and alulated. The results of the alulation are then interpreted and used to draw sustainable ats. SIs an be grouped in disrepant ways. The simplest division is into five groups [2]: 1) Driving Fores SIs. These desribe eonomi and soial development and its impat on the lifestyles of individuals e.g. the population growth in a ountry. 2) Pressure SIs. These desribe development in use of natural resoures and release of physial and biologial agents e.g. the amount of land used for roads. 3) State SIs. These desribe the quality and quantity of physial, biologial or hemial phenomena in a ertain area e.g. the noise level in an airport neighborhood. 4) Impat SIs. These desribe the refletion of hanges in the state of the environment e.g. the frequeny of fish kills. 5) Response SIs. These desribe the responses of a soiety to alleviate hanges in the state of the environment e.g. the reyling rates of domesti waste. There is an amplitude of SIs; in the UN list [3], we an ount over 130. The larger the number of SIs we inlude in a study, the broader is the sope we are onsidering of sustainability. In the following setions, we eluidate some of the SIs before we elaborate on the SAFE model The Shannon-Wiener Index Of Biodiversity Shannon Wiener define the Index Of Biodiversity [2] as: = H = ( p i )(log 2 p i ), where s is the i= 1 number of speies in a sample taken from an eosystem, and p i denotes sample portion that belongs to speies i. The higher the value of H, the greater is the biodiversity of the sample. Shannon-Wiener Index Of Biodiversity has a number of downsides [2]. One of whih is that the number of speies in the eosystem sample must be known beforehand, although this number may not be available in pratie. Another downside is that the index measures biodiversity without respeting the differenes in the speies that ontribute to that diversity; this may lead to an extravagant loss of information Total Fator Produtivity (TFP) value of outputs froma farming system Lynam and Herdt (1989) define the TFP as [2]: TFP =. value of inputs into a farming system Lynam and Herdt (1989) suggest that an inrease in TFP means sustainability and vie versa. One disadvantage of TFP is that it does not aount for environmental and soial fators that may be entral to sustainability. It further annot handle omplex biologial proesses. As a result, a high TFP is not an eminent guarantor of sustainability. Other disadvantages inlude the diffiulty in linking TFP aross multiple periods [4], the diffiulty in measuring inputs, the omplexity of data obtained [5], the inability to deompose TFP into different effiieny types (e.g. tehnial and eonomi) [6] and the inability to onsider quality hanges [7]. As a matter of fat, Chen [8] pointed out that China's TFP growth rate is disappointing despite the high-speed eonomi growth in the ountry! i s 2

3 2.3. Maximum Sustainable Yield (MSY) The Maximum Sustainable Yield (MSY) [2] is the maximum number of individuals that an be harvested from an eosystem without attenuating the population. Note in Figure 2 that population hange in an eosystem is driven by four major fators; birth, immigration, deaths, and emigration. Figure 2. Population Change And The MSY The differene Harvesting = (Births + Immigration) (Deaths + Emigration) is the MSY. If harvesting over a year is at or below MSY, then harvesting is supposed to be safe and sustainable. The lassi story of the Peruvian anhovy fishery onfutes this laim. Anhovy fishery was at the MSY in the 1960's and the apture was about 10 million ton per year. Ten years later, the Peruvian anhovy fishery unexpetedly ollapsed. Thus, MSY did not truly reflet reality and did not ensure sustainability. The reason for this is that population hange is strongly dynami in nature and subjet to fators that annot be expressed algebraially. In the Peruvian story for example, the El Niño event in 1972 ould not be aounted for. El Niño started to bring warmer water into the fishery and this warmer water had a negative effet on the anhovy population, beause it enouraged an inreased number of anhovy predators. 3. The SAFE Model The SAFE model was introdued in 2001 by Phillis and Andriantiatsaholiniaina [9] to assess the suitability of nations or geographi regions. This model uses a olletion of indiators of eonomi effiieny and soial welfare as inputs and applies fuzzy inferene to output a sustainability measure. The overall sustainability (OSUS) in the SAFE model [10][11] is omposed of two omponents, eologial sustainability (ECOS) and human sustainability (HUMS). ECOS and HUMS are also known as the primary indiators (see Figure 3). Figure 3. Sustainability Components Of The SAFE Model ECOS is omposed of four seondary indiators; air quality (AIR), land integrity (LAND), water quality (WATER) and biodiversity (BIOD). In a similar way, HUMS is omposed of four seondary indiators; politial aspets (POLICY), eonomi welfare (WEALTH), health (HEALTH) and eduation (KNOW). The evaluation of eah seondary indiator is done using three more tertiary indiators; pressure (PR), state (ST) and response (RE). The evaluation of eah tertiary indiator is done using a bundle of basi indiators that an be adapted in ompliane with environmental, eonomi, and soial hanges. This makes the SAFE model very alimatizable to emerging and evolving onditions while measuring sustainability. 3

4 3.1. Model Configuration The onfiguration steps of the SAFE model are outlined below and illustrated in Figure 4. 1) We start with a series of values for eah basi indiator over a time period e.g. two series (Z,1, Z,2,, Z,n ) and (Z ',1, Z ',2,, Z ',n ) for two basi indiators and ' respetively. 2) Eah value in a series is normalized on the interval [0, 1] using linear interpolation between the most desirable and the least desirable values e.g. we get two normalized series (X,1, X,2,, X,n ) and (X ',1, X ',2,, X ',n ) from (Z,1, Z,2,, Z,n ) and (Z ',1, Z ',2,, Z ',n ) respetively. 3) We transform eah normalized series into a single value using exponential smoothing e.g. we get two values X and X ' from (X,1, X,2,, X,n ) and (X ',1, X ',2,, X ',n ) respetively. 4) For eah exponentially smoothed value, we ompute the membership grade to seleted fuzzy sets that form omplete ordered partition of the interval [0, 1]. This step is referred to as fuzzifiation. The output of this step is the fuzzy values of basi indiators. 5) We input the fuzzy values of basi indiators to a fuzzy inferene engine of the type Takagi- Sugeno-Kang (TSK) to get the fuzzy values of the tertiary indiators. 6) We repeat steps 4 and 5 inputting the fuzzy values of tertiary indiators to a seond TSK inferene engine to get the fuzzy values of the seondary indiators. 7) One more, we repeat steps 4 and 5 inputting the fuzzy values of the seondary indiators to a third TSK inferene engine to get the fuzzy values of the primary indiators. 8) Again, we repeat steps 4 and 5 inputting the fuzzy values of the primary indiators to a fourth TSK inferene engine to get the fuzzy value of OSUS. 9) We use defuzzifiation to obtain a single value of OSUS Basi Indiators Figure 4. Configuration Steps Of The SAFE Model In this setion, we define (some) of the basi indiators we used in our ountry-level sustainability assessment. Our definitions are taken from multiple soures of whih we mention the World Bank, the World Health Organization (WHO) and the Food and Agriultural Organization (FAO). ECOS Indiators AIR Indiators PR. Greenhouse Gas (GHG) emissions per apita: Emissions of total GHG (CO2, CH4, N2O, HFCs, PFCs and SF6) exluding land-use, land-use hange and forestry. ST. Mortality from respiratory diseases: These diseases redue lung funtion and are ommon in young hildren. RE. Renewable resoures prodution: The higher this indiator, the less a ountry is exhausting damaging energy soures suh as nulear energy. LAND Indiators 4

5 PR. Nulear waste: It omes from nulear power plants and it has negative reperussions on land sustainability. ST. Forest area: The land under natural or planted trees. Produtivity of trees is irrelevant. The higher this indiator, the greater is land sustainability. RE. Proteted area: The land dediated to the maintenane of biodiversity. Proteted area ensures land sustainability. WATER Indiators PR. Total water withdrawals: The amount of water withdrawal per amount of water resoures. Hyper-usage adulterates water sustainability. ST. Phosphorous onentration: It measures eutrophiation whih ripples aquati resoures. RE. Waste water treatment plants: Only publily held plants are ounted when estimating this indiator. BIOD Indiators PR. Threatened mammals: They inlude ritially endangered, endangered and vulnerable speies of mammals. ST. Forest area desribed above an also be used to evaluate the BIOD indiator. RE. Proteted area desribed above an also be used to evaluate the BIOD indiator. HUMS Indiators POLICY Indiators PR. Ratio of refugees from a ountry to the total population of that ountry. ST. Gini index: It measures the deviation of individuals' inome from perfetly uniform distribution. Perfet equality gives a Gini index of zero, while perfet inequality gives a Gini index of 100. RE. Tax revenue: Tax is any payment made to the government of a ountry for publi purposes. WEALTH Indiators PR. Unemployment: The portion of labor fore that is without a job. Unemployment ontradits with wealth. ST. Poverty rate: The perentage of population living below the national poverty line. RE. Exports: The value of goods exported by a ountry to the rest of the world. Exports inrease wealth. HEALTH Indiators PR. Infant mortality rate: The infants who die before reahing one year of age. ST. Life expetany: The number of years an infant would live if mortality patterns at its birth time were to remain the same throughout her life. RE. Publi health expenditure: The amount spent from apital budget on publi health. KNOW Indiators PR. Ratio of students to teahing staff in seondary eduation: Teahing staff do not inlude nonprofessionals who support the eduational proess. ST. Literay rate: The perentage of people aged 15 and above who an read and write a short statement on their daily life. RE. Internet users: The number of omputers diretly onneted to the Internet. Internet aess failitates learning and knowledge aquisition Linear Interpolation Basi indiators desribed in the previous setion are measured in a variety of ways, using a variety of units. In order to failitate the omparison of these indiators, it is essential to normalize their values on the interval [0, 1] using linear interpolation by assigning 0 to the least desirable value and 1 to the most desirable value. Let be a basi indiator and Z the value of for a given ountry. A normalized value X of Z is alulated as follows: 5

6 X 0 Z v τ v = 1 U Z U T 0 τ Z Z v v < Z T < Z < τ T < U Z U where v is the minimum value of Z for all ountries (or a set of ourtiers we are studying) and U its maximum. The range [τ, T ] is the range of equally desirable values of. Let us example with Norway and two basi indiators used to evaluate the AIR seondary indiator. The first indiator is the Consumption of Ozone Depleting Substanes (ODSs) and the seond one is the Greenhouse Gas (GHG) emissions per apita. Table 1 shows the target and least desirable values for eah indiator, the original values over a number of years and the orresponding normalized values. Beause the smaller the normalized value X, the better, we need to apply the formula U U Z T 1990 U 1 Z For example, X 1 = = = U T Table 1. Normalizing Two Basi Indiators For Norway Basi Indiator 1 = Consumption of Ozone Depleting Substanes (ODSs) 2 = Greenhouse Gas (GHG) emissions per apita Target Value T 1 = 0 T 2 = Least Desirable U 1 = U 2 = Value Year Original Value Z 1 Normalized Value X 1 Original Value Z 2 Normalized Value X Exponential Smoothing Obtaining aurate data on eah basi indiator is often arduous, therefore, we need to improve the quality of information we are using to assess sustainability. This is done through exponential smoothing by assigning weights to past and present values of basi indiators. Let be a basi indiator, X,1, X,2,, X,n the normalized values of in years t 1, t 2,, t n, and w 1, w 2,, w n their weights. The aggregate value of indiator an be gauged using the formula: X (n) = w 1 X,1 + w 2 X,2 + + w n X,n ; w 1 + w w n = 1 Logially, reent values of a basi indiator are more important than past ones, therefore, we should give reent values higher weights. We an ahieve this through single exponential smoothing for time series in whih the smoothed values are given by the formula: tk tk 1 tk t1 X, k + X, k 1β X,1β X ( k) = (*) tk tk 1 tk t1 1+ β β where β is a smoothing parameter taken from the range [0, 1]. If we used standard exponential smoothing, then the smoothed values beome: X (k) = (1 - β)x,k + β(1 β)x,k-1 + β k-1 (1 β)x,1 Note that the total sum of weights, in this type of smoothing, is not one; However, when n grows unboundedly, both types of smoothing give similar results. We define the smoothing error as the differene between the observations at time t k and at time t k-1 : e k = X,k X (k-1) 6

7 We set X (0) = 0 and X (1) = X,1, so e 1 = X,1 0 and e 2 = X,2 X,1. We also define the sum of squared errors (SSE) as: SSE = e e e n The best value of β is the one that minimizes SSE. To failitate omputations, we an put formula (*) reursively as follows: N( K) t 1 X ( k) = ; ( ) =, + ( 1) k tk t 1 N k X k N k β `, ( ) = 1+ ( 1) k tk D k D k β D( k) with N(1) = X,1 and D(1) = 1. Table 2 shows the exponential smoothing of indiator 1 (Consumption of Ozone Depleting Substanes) for Norway assuming β = Table 2. Exponential Smoothing Of Indiator 1 For Norway Assuming β = 0.29 k t k X 1,k t k t k-1 t k t k 1 N(k) D(k) X β ` 1 (k) e k = X 1,k X 1 (k-1) NA NA Finally we set X 1 equal to the most reent estimate X 1 (11) = Fuzzifiation As we saw in setion 3.1, we have to ompute the membership grade of eah exponentially smoothed value of basi indiators to seleted fuzzy sets that form omplete ordered partition of the interval [0, 1]. This step is referred to as fuzzifiation. For this purpose, we will define three fuzzy sets with three linguisti values "weak" (W), "medium" (M) and "strong" (S) as shown in Figure 5. Figure 5. Three Fuzzy Sets With Three Linguisti Values To Fuzzify Basi Indiators The linguisti value W is assigned to low exponentially smoothed basi indiator values. Normally, we assign three integer values 0, 1 and 2 to these three linguisti values suh that 0 orresponds to W, 1 orresponds to M and 2 orresponds to S. Let us illustrate omputing membership grades with an example. We found in setion 3.4 that the exponentially smoothed value of the basi indiator 1 for Norway is X 1 = Similar omputations reveal that the exponentially smoothed value of the basi indiator 2 for Norway is X 2 = The membership grades to fuzzy sets W, M and S are: µ W ( 1 ) = 0, µ M ( 1 ) = = , µ S ( 1 ) = = µ W ( 2 ) = 0, µ M ( 2 ) = = , µ S ( 2 ) = = To fuzzify omposite indiators, we need more fuzzy sets, therefore, we will define five more fuzzy sets with five linguisti values "very bad" (VB), "bad" (B), "average" (A), "good" (G), and "very 7

8 good" (VG). In the same way, we assign five integer values 0, 1,, 4 to these five linguisti values suh that 0 orresponds to VB, 1 orresponds to B and so on Rules Rules For OSUS The two major omponents of OSUS are ECOS and HUMS (see Figure 3), eah of whih has five linguisti values. This means that we have 5 2 = 25 possible ombinations for OSUS rules. Knowing that OSUS an be written as OSUS = ECOS + HUMS, we disover that the minimum value of OSUS is = 0, and the maximum value is = 8. Therefore, we will need nine fuzzy sets with nine linguisti values to desribe OSUS. The linguisti values are "extremely low" (EL), "very low" (VL), "low" (L), "fairly low" (FL), "intermediate" (I), "fairly high" (FH), "high" (H), "very high" (VH) and "extremely high" (EH). Now we an list the 25 different rules for OSUS in Table 3. Table 3. Rules For OSUS Ri ECOS HUMS OSUS Ri ECOS HUMS OSUS R1 VB VB EL R14 A G FH R2 VB B VL R15 A VG H R3 VB A L R16 G VB FL R4 VB G FL R17 G B I R5 VB VG I R18 G A FH R6 B VB VL R19 G G H R7 B B L R20 G VG VH R8 B A FL R21 VG VB I R9 B G I R22 VG B FH R10 B VG FH R23 VG A H R11 A VB L R24 VG G VH R12 A B FL R25 VG VG EH R13 A A I As an example, ontemplate rule R10, the integer value of ECOS is 1 and the integer value of HUMS is 4. Thus, the integer value of OSUS is = 5 whih orresponds to FH. Rules For ECOS And HUMS Eah of ECOS and HUMS has four inputs (see Figure 3), eah of whih has five linguisti values. This means that we have 5 4 = 625 possible ombinations for ECOS and HUMS rules. Knowing that ECOS an be written as ECOS = AIR + LAND + WATER + BIOD, we disover that the minimum value of ECOS is = 0, and the maximum value is = 16. Therefore, we will need 17 fuzzy sets with 17 linguisti values to desribe ECOS. This is inonvenient and would lead to an explosion in the number of linguisti values. To avoid that, we will keep on using the same five linguisti values for ECOS; however, we will map eah value to a range this time: VB 0 SUM 3 B SUM 4 7 ECOS = A 8 SUM 11 where SUM = AIR + LAND + WATER + BIOD G 12 SUM 15 VG SUM = 16 Same reasoning applies to HUMS whih an be written as HUMS = POLICY + WEALTH + HEALTH + KNOW. Rules For Seondary Indiators Following the same approah above, we an determine the linguisti value of eah seondary indiator using: VB 0 SUM 1 B SUM 2 4 Seondary Indiator = A 5 SUM 7 where SUM = PR+ ST+ RE G 8 SUM 10 VG 11 SUM 12 8

9 Rules For Tertiary Indiators Eah of the tertiary indiators has n basi indiators as inputs, eah of whih has three linguisti values. This means that we have 3 n possible ombinations for tertiary indiators. Knowing that eah tertiary indiator an be written as Tertiary Indiator = L1 + L2 + + Ln, we disover that the minimum value of a tertiary indiator is = 0, and the maximum value is = 2n. Suppose n = 2, then we have 3 2 = 9 rules listed in Table 4. Table 4. Rules For Tertiary Indiators With Two Basi Indiators Ri Basi Indiator 1 Basi Indiator 2 Tertiary Indiator R1 W W VB R2 W M B R3 W S A R4 M W B R5 M M A R6 M S G R7 S W A R8 S M G R9 S S VG Let us apply rule R5 to a numeri example. We found in setion 3.5 that the membership grades of the basi indiator 1 for Norway are: 0 to fuzzy set W, to fuzzy set M and to fuzzy set S. We further found that the membership grades of the basi indiator 2 for Norway are: 0 to fuzzy set W, to fuzzy set M and to fuzzy set S. Applying rule R5 gives the partial membership grade of the tertiary indiator (PR on AIR) to fuzzy set A: R5: 1 is M( ) and 2 is M( ) PR on AIR is A( * = ). To get the overall membership grade of the tertiary indiator (PR on AIR) to fuzzy set A, we have to apply rules R5 and R7, and then sum up partial membership grades we get. Of ourse, applying one rule (R1) is enough to ompute the membership grade to fuzzy set VB. 4. Sensitivity Analysis Sensitivity analysis [10] is a superior tool in deision making and formulating sustainable poliies. It entails monitoring the values of sustainability indiators as they hange over a period of time. This largely helps in determining the most important indiators that ontribute to sustainable development. To perform sensitivity analysis, we go through the following steps: 1) We gauge OSUS following the proedures we saw in setion 3. 2) We randomly hoose a basi indiator, perturb its normalized value X by an amount γ so that it beomes X + γ. We trunate the resulting value as neessary to make sure that it falls within the range [0, 1]. 3) We re-gauge overall sustainability OSUS(X + γ). 4) We ompute OSUS gradient using the formula = OSUS(X + γ) OSUS. 5) We repeat steps 2 and 3 with all basi indiators. 6) The maximum gradient we get orresponds to the most important basi indiator. 5. Assessment Results A giganti amount of alulations lists Sandinavian ountries in dereasing sustainability in Table 5. The data dates bak to 2005 and was aumulated from the soures mentioned in setion 3.2. Table 5. Sandinavian Countries Listed In Dereasing Sustainability Country ECOS HUMS OSUS Sweden Finland Denmark Norway

10 Applying sensitivity analysis showed that the most important basi indiators for Sandinavian ountries are those related to eology or environment e.g. renewable energy prodution, greenhouse gas emissions and forest hange. 6. Conlusions In this paper, we gave a fuzzy measurement of SD in Sandinavian ountries using the SAFE model. We started with a brief disussion of ommon sustainability indiators other than the SAFE, then we shed the light on the mathematial foundations of the SAFE model, eluidating its onfiguration and steps; starting with data olletion, moving to linear interpolation, exponential smoothing and multistage fuzzifiation, and ending with defuzzifiation. Thereafter, we demonstrated the notion of sensitivity analysis and how it an be ombined with the SAFE model in order to determine the most influential fators in sustainability. We ended by refleting on our assessment results. The environmental onsious in Sandinavia is quite awoke, although some experts argue that the Sandinavians first enrihed themselves by destroying enough of their environment and now they are using their wealth to protet the remaining. In either event and based on our study results, renewable energy prodution, greenhouse gas emissions and forest hange were found to be the major fators Sandinavians should onsider when artiulating future sustainable ats. 7. Aknowledgement I am deeply grateful for the proative and valuable partiipation of Ilona Heldal from the Department of Tehnology, Management and Eonomis at Chalmers University of Tehnology, for making useful suggestions that improved this paper. As well, I would like to extend my gratitude to Lisbeth-Mariann Ekman for her perpetual support. Referenes [1] «Protéger l'espèe humaine ontre elle-même», entretien ave Lu Ferry dans la Revue des Deux Mondes, otobre-novembre 2007, pp [2] Simon Bell and Stephen Morse, "Sustainability Indiators: Measuring the Immeasurable?", Seond Edition, Earthsan, UK, 2008, pp , 29, 39, 40, 69, 130. [3] UN list of sustainability indiators, on the web at: [4] Ram Ramakrishnan, "Notes 24", Cost Aounting Course, Aounting Department, University of Illinois at Chiago, Summer 1999, on the web at: [5] Alan Stainer, "Capital input and total produtivity management", "Management Deision", MCB University Press, 1997, pp [6] Total Fator Produtivity ("Index methods"), The International Benhmarking Network for Water and Sanitation Utilities, on the web at: Methodologies/PerformaneBenhmarking-TotalFatorProdutivity.php?L=6&S=2&ss=2. [7] R. Anthony Inman, PRODUCTIVITY CONCEPTS AND MEASURES, Enylopedia of Business, Seond Edition, on the web at: Measures.html. [8] Bing Xu and Berlin Wu, "On Nonparametri Estimation For The Growth Of Total Fator Produtivity: A Study On China And Its Four Eastern Provines", International Journal of Innovative Computing, Information and Control, Volume 3, Number 1, ICIC International, February [9] Yannis A. Phillis and Lu A. Andriantiatsaholiniaina, "Sustainability: an ill-defined onept and its assessment using fuzzy logi", The Journal of Eologial Eonomis, Volume 37, Issue 3, Pages , Elsevier, June [10] Yannis A. Phillis, Vassilis S. Kouikoglou and Lu A. Andriantiatsaholiniaina, "Sustainable development: a definition and assessment", Environmental Engineering and Management Journal, Volume 2, Number 4, Pages , Deember [11] Lu A. Andriantiatsaholiniaina, Vassilis S. Kouikoglou and Yannis A. Phillis, "Evaluating strategies for sustainable development: fuzzy logi reasoning and sensitivity analysis", The Journal of Eologial Eonomis, Volume 48, Issue 2, Pages , Elsevier, February