4Th IQC May, 19 2010 351 Multicriteria Approach for Assessment Of
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4th International Quality Conference May 19th 2010 Center for Quality, Faculty of Mechanical Engineering, University of Kragujevac Multicriteria Approach for Assessment of Boris Agarski 1) Environmental Quality Igor Budak1) Abstract: Environment is important and inevitable element that has direct impact on life quality. Furthermore, Janko Hodolič1) environmental protection represents prerequisite for healthy and sustainable way of life. Environmental quality Đorđe Vukelić1) can be represented through specific indicators that can be identified, measured, analyzed, and assessed with adequate 1) Faculty of Technical methods for assessment of environmental quality. Problem Scinces, Novi Sad, Serbia of insight in total environmental quality, caused by different, mutually incomparable, indicators of environmental load and difficult expression of overall environment quality, can be solved with multicriterial assessment. This paper presents appliance of multicriterial methods for analysis of indicators that represent environmental quality for several sites. Keywords: multicriterial analysis, environment, indicators 1. INTRODUCTION multicriteria analysis, analytic hierarchy process (AHP) and TOPSIS method. The problem with the insight of Presented example gives application of overall quality of the environment that is multicriteria analysis in evaluating affected by many factors is primarily the environmental quality. Multicriteria nature of different factors and different analysis was conducted on six localities of measurement units in which they are the city of Novi Sad. For weighting of expressed. In these cases, the overall indicators of environmental impact AHP environmental quality can not be was used, and for determining of expressed by simple addition, it requires a environmental quality TOPSIS method complex method for evaluation of selected was used. elements of environmental quality. Multicriterial evaluation in environmental 2. ANALYTIC HIERARCHY protection is used in cases where there are PROCESS several alternatives, variations, locations or processes that have to be assessed by their Analytic hierarchy process (AHP) is total environmental load or quality. The used for decision making when a decision common result of multicriterial evaluation (choice of some of the available methods is dimensionless number that alternatives, or their ranking) is based on indicates the degree of environmental load several attributes that represent criteria. [4] of alternatives that are valued. In addition Solving complex decision problems using to indicators that represent the AHP method is based on their environmental impact it is possible to decomposition in a hierarchical structure include indicators that have economic, whose elements are goal (objective), social, and technological character. criteria (sub-criteria) and alternatives. An The paper describes two methods of important component of the AHP method 4th IQC May, 19 2010 351 is a mathematical model by which priorities of elements are calculated (weighted), for elements that are on the same level hierarchical structure. AHP was successfully used in environmental impact assessment for determining of weights for impact categories in paper [1]. In paper [3] AHP was used for verification of results gained by quantification of environmental aspects and impacts. Figure 1 – General hierarchical model in Application of AHP method can be AHP explained in four steps: (1) Setting a hierarchical model of Table 1 - Saaty evaluation scale [4] decision problems in order with Numerical Verbal scale Explanation goal on the top criteria and sub- values criteria at lower levels, and 1 Equal Two elements alternatives at the bottom of the importance are identical model (Figure 1). in significance (2) At each level of hierarchical compared to structure each elements of the objective structure are compared in pairs, whereby the decision makers 3 Week Experience or express their preferences with the dominance reasoning help of appropriate scale which slightly favor has 5 degrees and 4 sub-degrees one element of verbally described intensities over another and the corresponding numerical 5 Strong Experience or values for them in the range from dominance reasoning 1 to 9 (Table 1). significantly (3) Local priorities (weights) of favor one criteria, sub-criteria and element over alternatives at same hierarchical another structure level are calculated 7 Very strong Dominance of through appropriate mathematical dominance one element is model and afterwards they are confirmed in synthesized in total priorities of practice alternatives. 9 Absolute Highest (4) Implementation of the sensitivity dominance degree of analysis for final decisions. dominance In the second step weights (priorities) 2, 4, 6, 8 Intermediate Need for w are determined for n criteria (or values compromise alternatives) based on valuation of their or further division actions that are indicated with aij= wi/wj. If the matrix A is formed by measure of the relative importance of aij, for case of The matrix A has special features (all consistent estimations where aij = aikakj is of its rows are proportional to the first row, true, matrix A satisfies the equation: and they are all positive and aij = 1/aji is Aw=nw (1) true) and because of that only one of its 352 B. Agarski, I. Budak, J. Hodolič, Đ. Vukelić eigenvalue differs from 0 and is equal to n. ideal" solution which is composed of worst If the matrix A contains inconsistent values. The first condition is that the estimates (in practical examples almost selected alternative has the smallest always), weight vector w can be obtained Euclidean distance from the ideal solution by solving the equation (A−λmax I)w=0 in geometric term, and at the same time, with prerequisite that Σwi = 1, where λmax the other condition is that it has the is the largest eigenvalue in matrix A. greatest distance from the "anti-ideal Because of matrix A properties λmax ≥ n, solutions. Sometimes the chosen the difference λmax - n is used in measuring alternative, which has the minimum estimations consistency. With consistency Euclidean distance from the "ideal" index CI=(λmax − n)/(n−1) measure of solution, has a shortest distance to the consistency can be calculated: "anti-ideal solutions than other CR=CI/RI (2) alternatives. TOPSIS consists of 6 steps [2, 5]: Table 2: The average consistencies of 1. Normalization of the performance random matrices (RI values) matrix. The matrix of performance Matrix 1 2 3 4 5 ("payoff", "rating" or "decision matrix") Size has number values rij that in general have RI 0,0 0,0 0,58 0,9 1,12 different metrics. Each matrix row Matrix 6 7 8 9 10 corresponds to one alternative, and each Size column to a single criterion; element rij is RI 1,24 1,32 1,41 1,45 1,49 the rating (performance) of alternative Ai with respect to the criterion C . For m where RI is the random index (index of j criteria (C , C , ..., C ) and n alternatives consistency for the matrix with n randomly 1 2 m (A , A , ..., A ) performance matrix has the generated comparisons in pairs - table 2 1 2 n form R , and values (w ,w ,...,w ) with calculated values). (n,m) 1 2 m registered above matrix represent the If CR ≤ 0.10 is true for the matrix A, criteria weight defined by decision-maker, estimation of the relative importance of or some other way, the sum of criteria criteria (priority of alternatives) are weights is 1 Therefore, elements considered acceptable. Otherwise, normalization is performed by relation (3) investigation should be conducted for the to obtain normalized matrix X in which all reasons why assessment has unacceptably elements are dimensionless. high inconsistency. −1 ⎡ n ⎤ x = r r 2 ij ij ⎢ ∑ ij ⎥ ⎢ i=1 ⎥ 3. TOPSIS METHOD ⎣ ⎦ (3) TOPSIS method (Technique for Order 2. Normalized payoff matrix multiplied Preference by Similarity to Ideal Solution) with criteria weight. Weighted normalized is based on the concept that the chosen performance matrix V = (vij) has vij alternative should have the shortest elements where each vij represents product distance from the ideal solution and the of normalized performance of alternatives longest from the anti-ideal solution. [2, 4] X and the corresponding weighting criteria It is assumed that each criterion has coefficient. increase or decrease of monotonous 3. Determining the ideal solution. The tendency, so it is easy to find "ideal" - solution which is composed of all the best ideal solution A* and anti-ideal solution A criterion values that are reached, and "anti- are determined by relations (4) and (5) 4th IQC May, 19 2010 353 * 6. Ranking alternatives. Alternatives are A = {(maxν ij | jε G),(minν ij | jε G'),i = 1,...,n} • • ranked by descending values of Qi*. * * * = {ν1 ,ν 2 ,...,ν m} (4) − 4. EXAMPLE OF A = {(minν ij | jε G),(maxν ij | jε G'),i = 1,...,n} • • APPLICATION OF − − − = {ν1 ,ν 2 ,...,ν m} (5) MULTICRITERIAL METHODS AHP AND TOPSIS where: FOR ASSESSMENT OF G = {j = 1, 2,..., m │ j belongs to ENVIRONMENTAL QUALITY criteria that have to be maximized} 4.1 Defining the multicriterial problem G’ = {j = 1, 2,..., m │ j belongs to criteria that The aim of multicriteria analysis is the have to be minimized} assessment of environmental quality in the localities of the city of Novi Sad through The best alternatives that have the greatest indicators that indicate the load (potential vij for criteria that have to be maximized pollution) on the environment. Indicators and the minimum vij for the criteria that (criteria) for total environmental load has to be minimized. A* indicates the best evaluation have physical character and alternative - the ideal solution, and with quantitative values and they are related to - the same logic, A indicates the anti-ideal air quality, noise level and frequency of solution. passing vehicles in some parts of the city of Novi Sad. Air Quality is represented by 4. Determination of alternative distance the measured values of the total dust from the ideal solution. In this step, using (amount of suspended matter), the the relation (6) and (7) n-dimensional concentration of carbon monoxide CO and Euclidean distance for all alternatives from carbon dioxide CO2.