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An Approach for Environmental Impacts Assessment using Belief Theory H. Omrani, L. Ion-Boussier, P. Trigano

Abstract A novel methodology for decision-making under uncertainty in environmental assessment of urban mobility is proposed. The problem treated is complex with insufficient, fuzzy and uncertain data. Hence, we propose to use belief theory (Dempster-Shafer theory) in order to combine the opinions of experts to evaluate the environmental impact of an ameliorative action to be carried out in the sector of transportation. First, we present urban mobility and its environmental impact. Secondly, we propose an approach and an algorithm for decision making under uncertainty in order to assess projects related to transportation to improve urban mobility. Finally a study is used to validate the proposed approach. Index Terms Decision Making, Dempster-Shafer Theory, Environmental Impact Assessment, Evidence Theory, Fuzzy Logic, Urban Mobility, Uncertainty.

I. INTRODUCTION Impacts of the increase in the urban mobility required serious attention in the last few years because of the significant relationships between the characteristics of an urban traffic system and the quality of the urban environment. In response, the decision makers associated to traffic engineers and urban specialists elaborated various strategies for decreasing negative consequences of urban traffic (massive development of the public transport, introduction of fleets with clean vehicles, parking policy in the downtowns, etc. There are several approaches to evaluate the efficiency of these strategies: Life Cycle Analysis (LCA), Environmental Impact Assessment (EIA), Environmental Indicators (EI) (see [1] for a detailed review). No one proposes a methodology for a general evaluation of the financial, transport, socio-economic and pollution impacts of a measure in the transport field (strategy) to be carried out in the transport domain. It is the aim of our work which is included in SUCCESS project (Smaller Urban Communities in CIVITAS for Environmentally Sustainable Solutions) which was

submitted by the "Urban Community" of La Rochelle (France) supported by Preston (UK) and Ploiesti (Romania) This paper is organized as follow: firstly we propose a novel approach which seems to us in agreement with the established aims. Secondly, an algorithm will be developped to compute the efficiency of a measure and finally, this one will be tested for the park & ride implantation at La Rochelle in France. II. APPROACH TO EVALUATE THE IMPACTS OF A MEASURE IN THE URBAN TRAFFIC

The evaluation takes into account different categories (economy, energy, environment, society and transport), sub-categories and their corresponding impacts. Each potential impact is characterized by one or more indicators (e.g. vehicles/km to illustrate the congestion, NOx level for the quality of the air or degree of acceptance for safety, etc). The basic idea to evaluate the efficiency of a measure is to make a comparison between the pertinent indicators estimated before and after the measure implantation There are several problems to take into account: - the evaluation of a measure is based on several indicators which will have a different weight in the evaluation process and which may be illustrated by numerical values while others by linguistic variables. - several actors (experts) may give their evaluations; they can be political specialists, town planning decision makers, traffic engineers, citizens, etc. Each one has a degree of knowledge in a particular category, whose opinions are based on several sources having varying reliability. - the information sources of each expert may be different for the initial and ex-post evaluations. To evaluate the efficiency of a measure in the field of transport, the solution could be to couple or to adapt different approaches. A. Multi-criteria analysis

This work is funded by the conseil général (council general) of La Rochelle, in France. It is under the framework of SUCCESS project which is an European project funded by the European Commission under the CIVITAS program, under the reference (Contract no.: 513785). The SUCCESS project supported by three Europeans cities which are: La Rochelle-France, Ploiesti-Romania and Preston-UK. Hichem Omrani is at HEUDIASYC laboratory of the Université de Technologie de Compiègne (UTC, France) and at the Ecole d’Ingénieur en Génie des Systèmes Industriels (EIGSI) in La Rochelle, France (telephone: +33.05.46.45.80.47, e-mail: hichem.omrani@{utc.fr,eigsi.fr}. Luminita Ion-Boussier, Doctor in Physics, and she is with the Department of Physics, at the Ecole d’ingénieur en Génie des Systèmes Industriels, La Rochelle-France, (telephone: +33.05.46.45.80.41, e-mail: [email protected]). Philippe Trigano is a full Professor in computer science, with the department HEUDIASYC of the UTC. (e-mail: [email protected]).

Decision analysis looks at the paradigm in which an individual decision maker (or decision group) contemplates a choice of action in an uncertain environment. In multicriteria decision-making (MCDM) context, the selection is facilitated by evaluating each choice on the set of criteria. The criteria must be measurable; even if the measurement is performed only at the nominal scale (yes/no; present/absent) and their outcomes must be measured for every decision alternative. Criterion outcomes provide the basis for comparison of choices and consequently facilitate the selection of one, satisfactory choice. Criterion outcomes

of decision alternatives can be collected in a table (called decision matrix or decision table) comprised of a set of columns and rows. The table rows represent decision alternatives, with table columns representing criteria (Fig. 1). A value found at the intersection of row and column in the table represents a criterion outcome a measured or predicted performance of an alternative (Ap) on a criterion (Cq).

Fig. 1. Decision matrix according to MCDM (alternatives evaluated on multi-criteria)

For SUCCESS project, this approach must be adapted because the evaluation is conditioned by the aspects described above which make the decision-making complex. B. Multi-criteria and multi-experts analysis Since many experts exist and each one uses several sources of information during assessment, the new decision matrix is given according to the Fig. 2.

The proposed approach presents an hybrid methodology based on multi-criteria analysis and fusion multi sources and multi-experts under the framework of belief theory. This type of approach was already used in several applications [2], but it was not extensively applied to achieve an evaluation for environmental impact in transport field. On our knowledge, only one research team has recently published papers for environmental analysis which use the belief theory and multi-criteria analysis [3]-[5]. In their approach, the mass assignment corresponds only for singleton hypothesis and it has been introduced to aggregate multiple environmental factors without taking into account diverse sources of information. On the other hand, a new approach is proposed in this paper; taking into account different sources of information according to the nature of the environmental impacts valuation. Also, because of the uncertain character of our information to describe the impacts of a measure, we want to manipulate different subsets, singletons but also unions of hypothesis, so the decision is taken according the pignistic probability. In addition, the algorithm that we suggest will take into account the particularity of the evaluation of a measure linked to the urban mobility (information is not complete; sources are heterogeneous for different experts). It will be applied for the initial and post evaluation of the environmental, transport and socio-economic impacts. III. PROPOSED ALGORITHM

Fig. 2. Matrix of opinions (with several alternatives, multi-experts and multi-sources of information

The results will be a methodology and decision aid tools which will be by local authorities managers for comparing environmental friendly possible actions and their consequences (estimated value of the various environmental indicators), pointing out the relations between them (synergies or reverse between variables and parameters) and anticipating the benefits of each of them. The evaluation process of a measure is schematically presented in Fig. 3.

We present, in this part, a description of the proposed algorithm, for decision making under uncertainty, which is discussed briefly step by step. It is based into two steps: - Step 1: Define environment of the evaluation process and data collection - Step 2: Knowledge fusion and multi-criteria analysis Step 1: Define environment of the evaluation process and data collection o Define { At , t = 1, 2,… , m} as a set of existing measures; Ck for k = 1, 2,… , n , as a list of criteria considered relevant for environmental impact assessment of these measures. - Let ωk denote the importance related to the criteria Ck with 1 ≤ k ≤ n . - Let {S j , j = 1, 2,…, q} be a set of sources of information intervening

in

{Fj , j = 1, 2,… , q}

the

evaluation

process

with

be respectively their degree of

reliability and { Ei , i = 1, 2,… , p} is a set of experts. - Let Ω be the frame of discernment such as: Ω = { H1 , H 2 ,… , H r } . - Define r fuzzy functions (triangular or trapezoidal) related to the frame of discernment.

{ } be the matrix of assessment of an expert

t - Let At = aijk

Ei using several sources of information S j in order to

Fig. 3. Diagram of our Expert System for Environmental Improvement of Urban Mobility: steps of knowledge fusion and multi-criteria analysis

evaluate measure At according to criteria Ck , with: i = 1, 2,… , p ; j = 1, 2,… , q ; t = 1, 2,… , m and k = 1, 2,… , n .

- Compute a fuzzy number (under interval form) related to each evaluation given by a source of information (this points is more detailed before). - Assign masses to the frame of discernment from the opinions of experts in order to obtain a fuzzy n intervalbelief structure. - Define ( p × q × n) masses according the frame of t discernment Ω , such as mijk ; with: i = 1, 2,… , p ;

j = 1, 2,… , q and k = 1, 2,… , n , for each measure At with t = 1, 2,… , m . Step 2: Knowledge fusion (multi-source and multiexperts) and multi-criteria analysis - Combine the data given by each source of information for t be defined by: (fusion operator is each criterion. Let mik defined before) q

t t mikt = mijk = mit1k ⊕… ⊕ miqk j =1

(1)

- Combine knowledge from each expert by criterion according to the belief theory as follow: p

mkt = ⊗ mikt = m1tk ⊗… ⊗ mtpk i=1

(2)

- Multi-criteria analysis (evaluation by criteria and global assessment) - Compute the pignistic probability related to each hypothesis by criterion. - Determine the global utility (it can be crisp or fuzzy) related to each criterion by measure, where: u ( H1 ) ≤ u ( H 2 ) ≤ … ≤ u ( H m ) for positive impacts like safety and u ( H1 ) ≥ u ( H 2 ) ≥ … ≥ u ( H m ) for negative impacts like air pollution and noise. In this proposed approach based on evidential reasoning, the mass assignment and the computation of utility (related to each criterion or according to all criteria) are complex. So, we devote next section for describing in details the two steps.

A. Mass assignment 1. Transferable belief model: Theoretical tool The main underlying concepts of the belief theory were introduced, in 1968 by Dempster [6]. Then Shafer [7] showed the interest of beliefs functions for modeling uncertain knowledge. This theory is broken up into four distinct stages: the definition of a belief function, data fusion, discounting and finally the stage of decision. Definitions: The Transferable belief model represents quantified beliefs based on beliefs functions. Let Ω be a finite set of mutually exclusive and exhaustive hypotheses, called the frame of discernment. A Basic Belief Assignment (BBA) is a function called m from 2Ω to [0,1] verifying (3): m : 2Ω → [0,1] with ∑ m ( A) = 1 and m (∅) = 0 A∈2Ω

(3)

With A ⊂ Ω, m ( A) represents the belief that one is willing to commit exactly to A , given a certain piece of evidence. The subsets A of Ω such that m ( A) > 0 are

called the focal elements of m . Associated with m are a belief or credibility function bel and a plausibility function pl , defined, respectively for all A ⊆ Ω as [8] [9]: bel ( A) = ∑ m ( B ), pl ( A) = B⊆ A

∑ m ( B)

(4)

A∩ B≠∅

Data fusion: The greatest advantage of DS theory is the robustness of its way of combining information coming from various sources with the DS orthogonal rule. For example, let us denote two mass distributions m1 and m2 from two sources. Then, the DS combination can be represented by the following orthogonal rule: m1 ( B )⋅ m2 (C ) (5) ( m1 ⊗ m2 )( A) = ∑ B ,C ⊆Ω, B ∩C = A

Where ( m1 ⊗ m2 ) is the BBA representing the combined impact of the two pieces of evidence. Discounting: The technique of discounting allows to take in consideration the reliability of the information source that generates the BBA m . For α ∈ [0,1] , let α be the degree of confidence, assign to the source of information. If the source is not fully reliable, the BBA is discounted into a new less information BBA denoted by mα [10]: α    m ( A) = α ⋅ m ( A) for A ⊂ Ω (6)  α  Ω = − α + α ⋅ Ω m 1 m ( ) ( )    Decision making: After knowledge fusion, it remains to make a decision. The latter can be taken by several means. Among which there are the following rules: maximum of credibility, maximum of plausibility, maximum of pignistic probability, rules based on the confidence interval and decision per maximum of probability. We can find an exhaustive list of decision criterion in [12]. In the transferable belief model, when a decision must be taken, generally, beliefs are transformed into a probability measure denoted BetP [10]-[11]. The function building this probability is called the pignistic transformation and it is defined as: A∩ B m( B) ⋅ BetP ( A) = ∑ , ∀A ⊆ Ω (7) B 1− m (∅) A⊂B , B∈Ω Where B denotes the numbers of worlds in the set B .

2. Unit mass structure Initialization methods for the mass function in the DS theory are various and depend on the considered application framework. We present here, a mean for calculating unit mass structure. Let f be a fuzzy subset of a finite universe Ω such that the range of the membership function of f , µ f , is

{ y1, y2 ,…, yn } where yi > yi +1 > 0 . Then the mass assignment of f , denoted m f , is a probability distribution on 2Ω satisfying: [13] m f ( Fi ) = yi − yi+1 for i = 1,… , n −1   m f ( Fn ) = yn and m f (∅) = 1− y1 

(8)

{

Where Fi = x ∈ Ω µ f ( x ) ≥ yi

}

for i = 1,… , n and

{Fi ; i = 1,… , n} as referred to as the focal element of m f . Example: Let x be a variable (e.g. corresponding to the opinion of expert), into [0,10] with associated label set

f={Very Small(VS) ,Small (S) ,Medium( M) ,large ( L) , Very Large(VL)} Suppose that the appropriatess degrees for the five labels as follows: If each of the word fuzzy sets is a triangular, as in Fig. 4, then the corresponding mass functions, are given according to the Fig. 5.

Fig. 4. fuzzy sets corresponding to the meanings of the words related to the frame of discernment. Appropriatess degrees for, from left to right, very small, small, medium, large, very large.

We define a degree of uncertainty noted by ε = {ε1 , ε2 , ε3 , ε4 } witch degrees with the degree of reliability related to the source of information. This relationship can be given by the proposed heuristic function, as shown in Fig. 6. In a particular case, this function can be linear or with exponential form.

Fig. 6. Relation between degree of reliability and the degree of uncertainty, the function (1a) is linear, and the other functions (1a) (2a) (3a) (4a) and (2b) (3b) (4b) are exponential function.

So, if certain source ( S j ) gives us an evaluation ( n) from 0 to 1 with a degree of reliability ( r ) from 0 to 1, then we can compute a fuzzy number (interval of value) n , which is represented by: n =  n − ε, n + ε  where ε represents the degree of uncertainty computed taking in account the reliability of the source. From this fuzzy number, an interval-valued belief structure is computed as follow: IBSn =  min (0, mn − εi ), max (mn + εi ,1) , where

Fig. 5. Mass assignment for varying x

( )

( )

( )

( )

( )

mx {vs} ,m x {s} ,m x {m} ,mx {l} and m x {vl}

from left to right with solid line, mx (∅)

(

mx Hi , H j

are shown

mn is the mass assignment which is determinate above according to the Fig. 5.

)i≠ j; H H ⊂ f and i,

j

are shown as a dashed line.

2. Interval valued belief structure The traditional approach by using unit mass is well suited to numerical data but often what we are treating is either intervals (e.g., A means anything from 9 to 10) or fuzzy-type perceptions, words from the natural language like “small effect” or “large effect”. In practice the human experts find less difficulty to express their opinions in the form of interval and not only in the form of unit value. The “interval-valued belief structures” with interval-valued masses is a new formulation which extends the classical theory of belief functions by allowing imprecise assignment of belief masses to propositions. We propose a mean to define this structure by interval. In fact, from the definition of the mass assignment above, we can define an interval-valued belief structure instead of a singular mass. Hence, the expert gives their opinions according to a fuzzy number (like almost 2 : 2 ). Let F = { F1 , F2 , F3, F4 } be the degree of reliability of each source of information meaning respectively: {not reliable, less reliable, reliable, very reliable} and having respectively the set of values r = {r1 , r2 , r3, r4 } .

Fig. 7. Relation between degree of reliability ( r) and the degree of uncertainty (ε ) , linear (f1) and exponential (f 2 or f3 ) function.

At last, it is important to note that the degree of uncertainty is oppositely proportional to the degree of reliability of each source of information. In our study, we will take simple function like shown in Fig 7. The fusion multi-sources is done according these equations: Let I1 and I 2 two intervals defined by: I1 = a1 ± ε1 and

I 2 = a2 ± ε2 with ε1 and ε 2 are respectively their degrees of uncertainty. Their combination of can be written 1 2 1 2 as: I = a ± ε = ∑ a i ± ∑ ε i 2 i=1 2 i=1

B. Utility function After the fusion multi-sources, the combination multiexpert is done according belief theory. Then, we can

evaluate, rank and compare measures taking into account the preference given by decision making for the set of criteria considered pertinent for the evaluation process. Firstly, we can determine a global utility related to each criterion by measure, taking into account the utility of each evaluation grades belongs to the frame of discernment defined later and schematically represented by the Fig 8.

Fig. 8. Utility Functions (linear and exponential)

It is important to note, that the utility (noted by u ) given for the grades of assessment ( H ) can be not only crisp as shown in Fig. 8, but also fuzzy or expressed with interval. Secondly, comparison and selection of a measure is done thanks to a global assessment according to all criteria by computing a global utility taking in account the pertinence of each criterion. Finally, the selection of the best measure according to the objectives is given by maximizing the last global utility. The crisp utility and the utility with interval based on evidential reasoning ranking method are computed respectively as shown in next equations (9/10). m

uq = ∑ u ( H i )× BetP ( H i ) j

(9)

i=1

m

uq = ∑ u ( H i )×  BetP j



i=1

−

( H i ) , BetP + ( H i )

(10)

Where u ( H i ) represents the utility of an evaluation grades

H i , BetP− ( H i ) and BetP + ( H i ) represent the lower and upper

bounds

of

the

pignistic

probability.

u ( H i+1 ) ≥ u ( H i ) if H i +1 is preferred to H i which represented by ( H i +1

H i ) where the symbol "

" means

a crisp preference. The final step in the decision process consists in the comparison of the obtained expected utilities. A measure t

At1 is preferred to another measure A 2 on criteria Ck   written as follow:  At1 At2  , if and only if uqt1 ≥ uqt2 .  Ck  • Comparison and selection of a measure: - Determine a global assessment (it can be crisp or fuzzy) for a given measure At according to all criteria ( n criteria in all, Ck , k = 1, 2,… , n , having each one

respectively

as

crisp

pertinence

degree

ωk ,

k = 1, 2,… , n ) by computing: n

u t = ∑ ωk × uqt ; 1 ≤ t ≤ m

(11)

k =1

with uqt is a crisp utility given for a measure At on criteria

Ck . - Select the measure At that maximizes u t .

VI. APPLICATION In this study, the measure to evaluate is the implementation of a park & ride service in the city of La Rochelle, France. The experts in this study may be, town planning, the persons in charge of transport in generally a decision maker. On the other hand, the sources of information are e.g. advisers in environment, townsmen, survey, report of expertise, models of simulation intended for estimation of environmental impact.

A. Case Study The Data used for in this study are given as follow: • One measure: Park & Ride before and after realisation. • Indicators by Category: Category1: Environment (Air Quality (C1); Noise (C2)). Category2: Transport (Congestion Levels (C3)) Category3: Society (Safety (C4)) So, the Criteria set is given by: {C1, C2, C3, C4}={Air quality, Noise level, Congestion levels, Safety}, and the degree of pertinence related to indicators is given for example by: ω ({C1, C2, C3, C4})= (0.3,0.15,0.25,0.3) • Source of information: - Source1: Model (traffic, noise...) - Source2: Experimental Measures (collected, measurement) - Source3: Opinions citizens / Study - Source4: Expertise report / Advisers in environment • Reliability for the sources of information: Not Reliable (N.R), Less Reliable (L.R), Reliable (R), very Reliable (V.R) is equal respectively to the set (0.1, 0.2, 0.3, 0.4) • Evaluation: fuzzy number according to a scale of measurement from 0 to 10 (like 2 means, almost 2). The set of evaluation level is given by: Ω = {H1,H2,H3,H4, H5}={V.S,S,M,L,V.L}={Very Small, Small, Medium, Large, Very Large} and the vector of utility related to the level of evaluation is as follow: U={u(H1), u(H2), u(H3), u(H4), u(H5)}. such as: For a negative effect like the noise, the vector utility can be given as follow: U={u(H1),u(H2),u(H3),u(H4),u(H5)}={1,0.8,0.6,0.4,0.2}. For a positive effect like safety and user acceptance, the vector utility can be given, is this case, as follow: U={u(H1),u(H2),u(H3),u(H4),u(H5)}={0.2,0.4,0.6,0.8,1}. The relationship used to compute the degree of uncertainty taking into account the degree of reliability of a source is given by: ε = 0.4×(1− r ) as shown in Fig. 9, which is the simplest but it is considered enough adequate in this case study.

B. Results The "Park & Ride" measure is evaluated during the first stage (initial evaluation) according to Table I. The first stage is an initial evaluation before realisation and the second stage is after realisation. In addition, The evaluation takes into account two experts, four sources of information which are: model, experimental measures, study and adviser in environment and finally four indicators which are Air Quality, Noise level, Congestion level and safety related to environment, transport and society category. The results of data fusion with multi-sources are presented in Table II for the initial evaluation. Mass assignment matrix is presented according to the frame of discernment in Table III. The results of data fusion with

multi-experts are given in Table IV for the initial evaluation on all the criteria. In Table V, an evaluation by indicator is given according to the function of utility as shown in Fig. 8. TABLE I: MATRIX OF EVALUATION: INITIAL EVALUATION

the objectives, fixed at the beginning of the implementation for the measure, given by the decision maker. A similar presentation in Fig. 9 allows to interpret easily the evolution of each indicator before and after the measure implementation. VII. CONCLUSIONS

TABLE II: FUSION MULTI SOURCES: INITIAL EVALUATION

The prospect for this work consists in modeling opinions of experts with fuzzy approach in order to constitute the basic belief assignment, then to combine their knowledge according to belief theory. Finally, we would wish to develop a data-processing prototype allowing the visualization of knowledge resulting from the experts' opinions. The major advantage of this methodology is its capability to combine, in efficient way, several information from experts' opinions, even in the case of uncertain, fuzzy and incomplete data. It represents a reliable approach for knowledge fusion in order to evaluate environmental impact, economic and social impact of an action to be carried out by the persons in charge of transport. VIII. ACKNOWLEDGMENT

TABLE III: MASS ASSIGNMENT: INITIAL EVALUATION

TABLE IV: FUSION MULTI-EXPERT: INITIAL EVALUATION

TABLE V: ASSESSMENT: INITIAL EVALUATION

Fig. 9. Evaluation of each indicator before (solid line) and after (dashed line) measure implementation

At last a global evaluation is computed taking into account the pertinence of each indicator given according to

This work is funded by the conseil général (General Council) of La Rochelle, in France. It is carried out under the framework of SUCCESS project which is an European project funded by the European Commission under the CIVITAS program, under the reference (Contract no.: 513785). The authors are thankful to Hervé Le Berre and Tom Parker for valuable discussions and to anonymous referees for their valuable suggestions. REFERENCES [1]

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