MODELLING THE URBAN SUSTAINABLE DEVELOPMENT BY USING FUZZY SETS

Abstract

The sustainable urban development is a subject of interest for regional policy makers and it needs appropriate assessment based on futile instruments for research, and for practical reasonsl (planning and decision making). Even if the sustainability's attainment is a research topic field for academia and urban planners and managers and, as well, an ambitious goal for any resource administrator, yet there is no precise way of defining and measuring it. The sustainability of the urban development policy implies multiple and diversified aspects from rational exploitation of the local resources and well-structured workforce to environmental issues, endowment of modern urban facilities and infrastructure elements. As the urban sustainability is measured using a multitude of basic indicators, needing proper information to make long term management decision and planning, the subject is treated with fuzzy setsseen as an appropriate manner to deal with ambiguity, subjectivity and imprecision in the human reasoning when processing large volumes of data, eventually unstructured and complex. The paper proposed a modeling approach based on fuzzy sets inspired by the SAFE (Sustainability Assessment by Fuzzy Evaluation), a model which provides a mechanism for measuring development sustainability. The papers intends presenting a quantitative methodology in assessing the potential sustainability of urban development (in terms of adequacy) by pointing the failures in pursuing trends that are associated to a robust growth in the urban areas. The advantages of such approach are derived from taking into account the multi-criteria and uncertainty facets of the phenomenon; also, having in mind that the sustainability remains a non-straight-cut concept, being vaguely defined it implies a non-deterministic character by using the fuzzy set logic. The proposed model is designed to assess the divergence from desired trajectories, the weak point in reaching indicators' target (as they are commonly regardedd as appropriate in what is understood as a good practices), it may then be addressed for policy makers in indicating some action measures in urban administration as they intendenly strive towards increasingly sustainable development on the long term. [PUBLICATION ABSTRACT]

Headnote

Abstract

The sustainable urban development is a subject of interest for regional policy makers and it needs appropriate assessment based on futile instruments for research, and for practical reasonsl (planning and decision making). Even if the sustainability's attainment is a research topic field for academia and urban planners and managers and, as well, an ambitious goal for any resource administrator, yet there is no precise way of defining and measuring it. The sustainability of the urban development policy implies multiple and diversified aspects from rational exploitation of the local resources and well-structured workforce to environmental issues, endowment of modern urban facilities and infrastructure elements. As the urban sustainability is measured using a multitude of basic indicators, needing proper information to make long term management decision and planning, the subject is treated with fuzzy setsseen as an appropriate manner to deal with ambiguity, subjectivity and imprecision in the human reasoning when processing large volumes of data, eventually unstructured and complex. The paper proposed a modeling approach based on fuzzy sets inspired by the SAFE (Sustainability Assessment by Fuzzy Evaluation), a model which provides a mechanism for measuring development sustainability. The papers intends presenting a quantitative methodology in assessing the potential sustainability of urban development (in terms of adequacy) by pointing the failures in pursuing trends that are associated to a robust growth in the urban areas. The advantages of such approach are derived from taking into account the multi-criteria and uncertainty facets of the phenomenon; also, having in mind that the sustainability remains a non-straight-cut concept, being vaguely defined it implies a non-deterministic character by using the fuzzy set logic. The proposed model is designed to assess the divergence from desired trajectories, the weak point in reaching indicators' target (as they are commonly regardedd as appropriate in what is understood as a good practices), it may then be addressed for policy makers in indicating some action measures in urban administration as they intendenly strive towards increasingly sustainable development on the long term.

Keywords: sustainability, urban management, indicators, fuzzy approach.

(ProQuest: ... denotes formula omitted.)

1. INTRODUCTION

Urban lifestyles are nowadays characterized by very different developing trajectories, based on high consumption levels, exuberant use of natural resources, excessive production of waste, a widening gap between rich and poor, and rapid growth of the global human population. More and more, scientists and various experts in the field of human health and nature preservation emphasize on subjects as high speed of urbanization, the pressure of human activities on the city green spaces, the noisy and more increased traffic, the burden of air pollution in urban areas. The points of interest are reflected by continuous preoccupation of various international organizations and agencies toward the subject - such as the United Nations Population Division, World Health Organization, International Road Federation, World Resources Institute etc. Related to the future of cities and urban areas, the sustainability become crucially important but it is an inherently vague concept whose scientific definition and measurement still lack widely common understanding.

There are number of initiatives working on indicators and frameworks for sustainable development (Singh, 2009, Hernández-Moreno and De Hoyos-Martínez, 2010). Indicators and composite indicators are increasingly recognized as a useful tool for policy making and public communication in conveying information on countries' performance in fields such as environment, economy, society, or technological development. Those interested could be experts and scientists, to policy makers and central/local authorities to the general public. For economists, the notion of sustainable development has meant a new major challenge, as they were forced to broaden existing analytical frameworks and a rising interest in research moves away from global sustainability analysis towards empirical policy-relevant research at the regional and urban level (Nijkamp, 2000). Assessing sustainability and vulnerability implies provision of information to evaluate the consequences of development strategies, policies and actions on development process. It is necessary to define a pragmatic framework, based on what is known from theories and what is learned in practice, that can be used as a model to guide, define and use appropriate indicators for the system (i.e. structure/ functions, scales/levels, viability/integrity, goods/services) and the steps for decision and policy making (i.e. conditions, diagnosis, forecasts, responses and evaluation). Devuyst (2001) introduces "sustainability assessment", a new concept that aims to help in steering societies in a more sustainable direction, and applies this concept to cities. It deals with practical ways to reach a more sustainable state in urban areas through such tools as strategic environmental assessment, sustainability assessment, direction analysis, baseline setting and progress measurement, sustainability targets, and ecological footprint analysis (Devuyst, 2001). More specific, Gagliardi (2007) treats the topic of evaluation of fuzzy logic trough the fuzzy logic instruments, describing procedures to assign weights to expert criteria used to estimate the sustainability of a city (Naples, Italy).

According to some authors (Braat, 1991), the sustainability indicators, either in a direct (predictive) or indirect manner (retrospective), should provide information about the future sustainability of social objectives such as material welfare, environmental quality and natural system amenity. In order to be able to assess with a reasonable level of accuracy, the sustainable urban development one needs information that should provide:

* current state of the urban management configuration (such as consumption and infrastructure and logistics)

* the reflection of time dimension as the urban system evolves

* the distance in time in reaching the previously stated policy objectives.

Statistical data for the basic indicators can be obtained from many sources, such as United Nations organizations, World Bank, World Resources Institute, international federations, governmental and nongovernmental organizations, etc. The indicators are selected from authorized and reliable sources - from the World Bank - World Development Report (WDI), UNDP - Human Development Report (HDR), United Nations Population Division, World Health Organization, International Road Federation, World Resources Institute, and other sources. There are various statistical databases that provide information on the urban and city development: an example is the World Bank (WB) indicators - a specific chapter of the collection of World Development Indicators (WDI) covering over 200 countries in over 420 different indicators, grouped in various sectors. As an example of the richness of information available, in the Table 1 is presented the set of indicators given by the World Development Report in the subject of Urban Development (source: http://data.worldbank.org/indicator).

2. THE FUZZY MODEL FOR ASSESSING URBAN SUSTAINABILITY

The urban sustainable development is difficult to define in pure quantitative terms, and during the past decades, the researchers recognize that it bears an imprecise and vague feature of being defined and tackled in many facets, with several ways of collecting data for indicators regarding the efficient and the effective usage of resources. Yet, there is an increasing need for using mathematical expressions on the sustainability issues as they are more appropriate to be related to the higher demand on software application in management (Hoffman, 2008). Under these circumstances, the fuzzy logic is well suited to handle such a vague, uncertain, and polymorphous concept (Lazim and Wahab, 2010, Colesca and Alpopi, 2010).

Fuzzy logic is justified because it is tolerant of imprecisely defined data, it can model non-linear functions of arbitrary complexity; and it is able to build on top of the experience of experts.

Sustainable development has also been described as fostering adaptive capabilities and creating opportunities (Winograd, 2007). The challenges for sustainable development are related to the improvement of resilience and adaptive capacities, take advantage of emerging opportunities and cope with the consequences of different processes of change. In this context, vulnerability (seen as function of risks and threats minus adaptive options and coping responses) is emerging as a critical component of any sustainable development strategy.

3. COLLECTION OF DATA

The SAFE model is used for the newly proposed model for assessing the urban sustainability and primarily it was introduced in Phillis and Andriantiatsaholiniaina (2001) and developed further (Andriantiatsaholiniaina and Kouikoglou, 2004) and (Phillis and Kouikoglou, 2011). SAFE is a hierarchical fuzzy inference system. It uses knowledge encoded into "if-then" rules and fuzzy logic to combine 75 inputs, called basic indicators, into more composite variables describing various environmental and societal aspects and, finally, provides an overall sustainability index in [0, 1].

Similar to the above mentioned SAFE methodology, the overall urban sustainability (OUS) of a certain urban area is appraised according to two major dimensions: the smooth dynamics (SD) and positive growth prospects (PG). These will be referred to as the crucial components of the overall urban sustainability. Both of them are regarded as depended on several dimensions of basic sustainability: current status (STA), evolving potential (POT), driven responses (coordinated interventions) (RES).

Figure 1 illustrates all the dependencies of urban sustainability components. To evaluate the secondary components, the newly proposed model follows the Pressure - State - Response approach [Organization for Economic Cooperation and Development (OECD), 1991], which was originally proposed to assess the general environmental component of sustainability.

STA describes the current overall state of an urban area; it is a function of a large number of indicators, acting as primitive determinants of the current living, economic and societal conditions of the urban areas; the STA variable is an aggregate measure of the basic indicators presented in the Table 2.

The POT variable, as well, is an aggregate measure of the changing forces human activities exert on the state of the corresponding secondary component; the subcomponent indicators used in calculating the POT value are given in the Table 3. And, the third primary variable - RES - summarizes the indicators related to the policy response to the environmental, economic, and social current conditions (Table 4); they measures the benefits of the envisaged actions, taken to bring lower pressure to the undesired levels of some indicators - it should indicate the efforts that might result in a better state (quality of life for the inhabitants and the operating business climate for the economic actors in the local urban area) and the potential triggers to bring more benefits in the urban area development.

Some representative indicators used in the sustainability model are given in 2-4 (yet, there are not describes in terms of power on influence, which is still an uncovered subject, posiible to be more explored conceptually).

Recently, fuzzy logic has been proposed as a systematic tool for the assessment of sustainability. Fuzzy logic is capable of representing uncertain data, emulating positive reasoning habits of skilled humans, and handling vague situations where traditional mathematics is ineffective. The fuzzy logic is addressed as a convenient way to treat the sustainability dimension as it allow considering the complexity and the scarce determination of the knowledge captured in the human experts reasoning on the subjects related to urban development. It may combine the imprecise pieces of information (often in linguistic variables) with objectives that are stated with ambiguous terms and expressions, difficult to be computed mathematically; still, under such circumstances, the fuzzy logic can give solid answers to problems posed in subjective or metaphorical formulations. In this way by using words and imprecise information in fuzzy logic mechanisms, the weaknesses of some traditional methods (such as the costbenefit analysis) that rely heavily of numerical data and quantification may be overpassed.

The fuzzy logic allows making correct and precise analysis of some linguistic formulations by involving the sequential process of fuzzyfication - making inferences - defuzzyfication. As a start, the real values are transformed into linguistic variables; these are processed according to some IF-THEN rules, resulting in the fuzzy output that allows decoding it in a crisp value. The proposed model is described in the Figure 2, by indicating the sequence of steps.

Normalization step: Data of each basic indicator are normalized on a scale between zero (lowest level of preference) and one (highest level of preference sustainability) to allow further arithmetical computations (aggregation) and to facilitate fuzzy computations. Instead of using the data for each indicator directly, they are normalized in order to allow summation and ignoring the specific units of measurement. To each basic indicator, v, some values are assigned: a target vt^sub i^, a minimum, v^sub min^, and a maximum value v^sub max^. The target can be a single value or, in general, any interval on the real line of the form [vt^sub min^, vt^sub max^] representing a range of desirable values for the indicator. The maximum and minimum values are taken over the set of available measurements of the indicator. It does this as it do not refer some well established or even, commonly agreed reference values for the involved statistical indicators, but rather uses the "best" values (in some particular views) or the average values as they are registered nowadays.

Let the v^sub i^ be the data value for the i indicator and the v^sub max^ and v^sub min^ the maximum and minimum values for all units in the sample, the vt^sub i^ is the target value for the same indicator, then the vn^sub i^ is computed according to the optimized direction corresponding to the indicator's description -Table 5.

The fyzzy model consists of: linguistic variables, the linguistic rules and the specification on the defuzzyfication method. Any linguistic variable is descried by: the name, by its linguistic values, by the membership values and the admissible domain for its values. The overall sustainability - the output variable - can be seen as a function of the subsystems' quality, devised by the fuzzy logic input variables. The function is the result of a set of dependence rules (treated as IF - THEN rules) derived from the experts reasoning.

Fuzzyfication step. The fuzzyfication module transforms the crisp, normalized value, vn^sub i^, of a indicator, into a linguistic variable in order to make it compatible with the rule base. A linguistic variable is a variable whose values are expresses as qualitative attributes - words or phrases. A linguistic value, LV, is represented by a fuzzy set using a membership function µ^sub LV^(vn). The membership function associates with each normalized indicator value, vni, a number, µ^sub LV^(vn^sub i^), in [0, 1] which represents the grade of membership of y^sub s^ in LV or, equivalently, the truth value of proposition "indicator v is LV".

In the model, the linguistic values of each basic indicator are weak (W), medium (M), and strong (S), each of them being expressed using a trapezoidal function of membership involved in the computation - Figure 3. The trapezoidal functions are chosen for the secondary and primary variables to represent an increased uncertainty; they are quite simple and the sustainability assessment results obtained from the model agree with widely held opinions. In representing the membership functions, the horizontal axis is composed by the normalized values for each variable (with values ranked from 0 to 1) and the vertical axis depict the membership degrees (with the domain of [0, 1]).

For the secondary composite indicators (such as SD or PG), five linguistic values are used: very poor (VP), poor (P), intermediate (I), satisfactory (S), and very satisfactory (VS) - figure 4 and 5. For the output indicator (OUS), five linguistic values are used: very bad (VB), poor (B), intermediate (I), good (G), and very good (VG) - figure 6.

The rules are represented in the Mamdani implication, so, the statement "if x=A then y=B" or " A[arrow right]B " results in a rule R such that: µ^sub r^(x, y) = min{µ^sub A^(x), µ^sub B^(y)}. In general, a rule base may contain several rules assigning subsets of the same linguistic value, LV^sub v^, to indicator s. For example, the rule base of the secondary component SD contains the following rules:

IF STA is medium AND POT is week AND RES is strong, THEN SD is intermediary.

IF STA is weak AND POT is strong AND RES is s trong, THEN SD is very satis factory .

The "IF - THEN" rules are expressions of the current and multidisciplinary understanding on the influence-impact mechanisms among a set of factors. Consider the secondary variable SD and its components STA, POT and RES. For simplicity, only three fuzzy sets are used: weak (W), medium (M), and strong (S), to represent the primary variables and five fuzzy sets for SD: very poor (VP), poor (P), intermediate (I), satisfactory (S), and very satisfactory (VS). Table 6 shows the corresponding rule base which consists of 33=27 rules.

Table 7 consists of set of rules describing the inference OUS=Function(SD, PG) - figure 7.

DEFUZZIFICATION STEP. DEFUZZYFICATION IS THE FINAL OPERATION ASSIGNING A NUMERICAL VALUE IN [0, 1] TO THE COMPOSITE INDICATOR S. AS DEFUZZYFICATION METHOD, THE CENTER-OF-GRAVITY FORMULA WILL BE USED; ... WHERE: Y^sub J^ IS THE VALUE FOR THE J INDICATOR IN THE OUTPUT FUZZY SET O^sub V^ WITH THE MEMBERSHIP FUNCTION OF µ^sub )v^ (y^sub j^).

In using numerical values, based on a selection of indicators for a sample of 40 countries from around the world (mainly, those of European Union, also, some additional ones representative on the international climate), the model was applied to calculate and assess the urban sustainability of the Romanian urban areas, in general terms - as opposed to other countries). As a minimum indicator to be normalized it was described the "Population density (people per sq. km of land area)" and as a maximum one -"GDP per capita, PPP (current international $)" - Table 8.

The selection of indicators (Table 9) in the normalized form (according to the formulas from Table 5, see TableS 10-12 for examples of applying the normalization stage in the case of two indicators) is fuzzyfied (according to the set of membership functions displayed in Figure 3).

Further they are aggregated (using equal weights) in computing the STA, POT and RES variables (also, in fuzzy form - Figure 4 and 5). Afterwards, the output of the model is a degree (%) of sustainability of the system under examination, meaning an urban area - using the corresponding set of linguistic varibles (figure 7). The three fuzzy variables are subject to inference rules (Table 6)so the new secondary variables SD and PG are computed (following the rules in Table 7), and, finally, the OUS crisp value (equal to 0,569) is generated (Figure 8).

The model is flexible in the sense that users can choose the set of indicators and adjust the rules of any knowledge base according to their needs and the characteristics of the socio-environmental system to be assessed. The model is open to new inputs as reality described by extended base of statistical indicators and it may include a temporal dimension for including the experience change - involving a sensitivity analysis.

4. CONCLUSIONS

Sustainable decision-making should have two simultaneous goals: achievement of human development to secure high standards of living and protection and improvement of the environment now and for the generations to come.

Policy makers need a tool based on scientific information to forecast the effects of future actions on sustainability and establish policies for sustainable development. In general, policy makers should be able to identify the factors that promote or impede progress towards sustainability and obtain quantitative information about them. Each sustainability variable is a function of a number of basic indicators. Decision makers have a multitude of considerations to make before they decide on a strategy such as availability of resources, money and people, political priorities, etc. A possible way to expand the analysis for urban sustainability management is to engage the sensitivity analysis which can emphasize the attention on those parameters that affect sustainability critically.

According to the results of sensitivity analysis and the target for each indicator, then, the interested parties may design policies to advance ecological, human, and overall sustainability by * proposing mechanisms and projects to improve promoting indicators or maintain them, if their values are optimal, taking precautionary measures to correct impeding indicators or maintain them, if their values are optimal, and adopting conservative actions for neutral indicators.

References

REFERENCES

Andriantiatsaholiniaina, L.A., Kouikoglou, V.S., Phillis, Y.A. (2004). Evaluating strategies for sustainable development: fuzzy logic reasoning and sensitivity analysis, Ecological Economics 48, pp. 149- 172

Braat, L. (1991). The predictive meaning of sustainability indicators, in Kuik, O. and Verbruggen, H (eds.), In Search of Indicators of Sustainable Development, Kluwer Academic Publishers, Dordrecht, pp. 57-70

Colesca S.E., Alpopi C. (2010). Quality of electronic government services. A fuzzy analysis, Quality - Access to Success, Vol. 7-8, pp. 88-95

Devuyst, D., Hens, L. and De Lannoy, W. (2001). How Green Is the City? Published by Columbia University Press

Gagliardi, F., Roscia, M. and Gheorghe Lazaroiu, G. (2007). Evaluation of sustainability of a city through fuzzy logic, Energy, Volume 32, Issue 5, May 2007, pp. 795-802.

Hernández-Moreno S. and De Hoyos-Martínez J. (2010). Indicators of urban sustainability in Mexico, Theoretical and Empirical Researches in Urban Management, 7(16), pp. 46-60

Hoffman, T. (2008). Vulnerability Assessments: Guidelines to Maximize Performance, The 9 hottest skills for '09, Computerworld

Lazim A. and Wahab N. (2010). A fuzzy decision making approach in evaluating ferry service quality Management Research and Practice, Vol. 2, Issue 1, pp. 94-107

Nijkamp, P. and Vreeker, R. (2000). Sustainability assessment of development scenarios: methodology and application to Thailand, Ecological Economics 33 (2000), pp. 7-27.

Phillis, Y.A. and Andriantiatsaholiniaina, L.A. (2001). Sustainability: an ill-defined concept and its assessment using fuzzy logic, Ecological Economics, Volume 37, Issue 3, June 2001, pp. 435-456.

Phillis, Y.A., Grigoroudisa. E. and Kouikoglou, V.S. (2011). Sustainability ranking and improvement of countries, Ecological Economics, Volume 70, Issue 3, 15 January 2011, pp. 542-553.

Singh, R.K., Murty, H.R., Gupta, S.K. and Dikshit, A.K. (2009). An overview of sustainability assessment methodologies, Ecological Indicators 9 (2009), pp. 189 - 212.

Winograd, M. (2007). Sustainability and vulnerability indicators for decision making: lessons learned from Honduras, International Journal of Sustainable Development, Vol. 10, Nos. 1-2