International Journal for Quality research UDK- 502.175 Original Scientific Paper (1.01) MULTICRITERIA APPROACH FOR ASSESSMENT OF ENVIRONMENTAL QUALITY Boris Agarski 1) Abstract: Environment is important and inevitable element that has Igor Budak1) direct impact on life quality. Furthermore, environmental Janko Hodolič1) protection represents prerequisite for healthy and sustainable way Đorđe Vukelić1) of life. Environmental quality can be represented through specific indicators that can be identified, measured, analyzed, and assessed 1) Faculty of Technical with adequate methods for assessment of environmental quality. Scinces, Novi Sad, Serbia Problem 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 several attributes that represent criteria. [4] Solving complex decision problems using AHP method is based The problem with the insight of overall quality of on their decomposition in a hierarchical structure whose the environment that is affected by many factors is elements are goal (objective), criteria (sub-criteria) and primarily the nature of different factors and different alternatives. An important component of the AHP measurement units in which they are expressed. In these method is a mathematical model by which priorities of cases, the overall environmental quality can not be elements are calculated (weighted), for elements that are expressed by simple addition, it requires a complex on the same level hierarchical structure. method for evaluation of selected elements of AHP was successfully used in environmental environmental quality. impact assessment for determining of weights for Multicriterial evaluation in environmental impact categories in paper [1]. In paper [3] AHP was protection is used in cases where there are several used for verification of results gained by quantification alternatives, variations, locations or processes that have of environmental aspects and impacts. to be assessed by their total environmental load or Application of AHP method can be explained in quality. The common result of multicriterial evaluation four steps: methods is dimensionless number that indicates the (1) Setting a hierarchical model of decision degree of environmental load of alternatives that are problems in order with goal on the top criteria valued. In addition to indicators that represent the and sub-criteria at lower levels, and environmental impact it is possible to include indicators alternatives at the bottom of the model (Figure that have economic, social, and technological character. 1). The paper describes two methods of multicriteria (2) At each level of hierarchical structure each analysis, analytic hierarchy process (AHP) and TOPSIS elements of the structure are compared in method. Presented example gives application of pairs, whereby the decision makers express multicriteria analysis in evaluating environmental their preferences with the help of appropriate quality. Multicriteria analysis was conducted on six scale which has 5 degrees and 4 sub-degrees localities of the city of Novi Sad. For weighting of of verbally described intensities and the indicators of environmental impact AHP was used, and corresponding numerical values for them in for determining of environmental quality TOPSIS the range from 1 to 9 (Table 1). method was used. (3) Local priorities (weights) of criteria, sub- criteria and alternatives at same hierarchical structure level are calculated through 2. ANALYTIC HIERARCHY PROCESS appropriate mathematical model and afterwards they are synthesized in total priorities of alternatives. Analytic hierarchy process (AHP) is used for (4) Implementation of the sensitivity analysis for decision making when a decision (choice of some of the final decisions. available alternatives, or their ranking) is based on Vol.4, No. 2, 2010 131 In the second step weights (priorities) w are prerequisite that Σwi = 1, where λmax is the largest determined for n criteria (or alternatives) based on eigenvalue in matrix A. Because of matrix A properties valuation of their actions that are indicated with aij= λmax ≥ n, the difference λmax - n is used in measuring wi/wj. If the matrix A is formed by measure of the estimations consistency. relative importance of aij, for case of consistent With consistency index CI=(λmax − n)/(n−1) measure of estimations where aij = aikakj is true, matrix A satisfies consistency can be calculated: the equation: CR=CI/RI (2) Aw=nw (1) Table 2: The average consistencies of random matrices (RI values) Matrix 1 2 3 4 5 Size RI 0,0 0,0 0,58 0,9 1,12 Matrix 6 7 8 9 10 Size RI 1,24 1,32 1,41 1,45 1,49 where RI is the random index (index of consistency for the matrix with n randomly generated comparisons in pairs - table 2 with calculated values). If CR ≤ 0.10 is true for the matrix A, estimation of the relative importance of criteria (priority of alternatives) are considered acceptable. Otherwise, Figure 1 – General hierarchical model in AHP investigation should be conducted for the reasons why assessment has unacceptably high inconsistency. Table 1 - Saaty evaluation scale [4] Numerical Verbal scale Explanation values 3. TOPSIS METHOD 1 Equal Two elements are TOPSIS method (Technique for Order Preference importance identical in significance by Similarity to Ideal Solution) is based on the concept compared to objective that the chosen alternative should have the shortest 3 Week Experience or reasoning distance from the ideal solution and the longest from the dominance slightly favor one anti-ideal solution. [2, 4] element over another It is assumed that each criterion has increase or 5 Strong Experience or reasoning decrease of monotonous tendency, so it is easy to find "ideal" solution which is composed of all the best dominance significantly favor one criterion values that are reached, and "anti-ideal" element over another solution which is composed of worst values. 7 Very strong Dominance of one The first condition is that the selected alternative dominance element is confirmed in has the smallest Euclidean distance from the ideal practice solution in geometric term, and at the same time, the 9 Absolute Highest degree of other condition is that it has the greatest distance from dominance dominance the "anti-ideal solutions. Sometimes the chosen alternative, which has the 2, 4, 6, 8 Intermediate Need for compromise or minimum Euclidean distance from the "ideal" solution, values further division has a shortest distance to the "anti-ideal solutions than other alternatives. The matrix A has special features (all of its rows TOPSIS consists of 6 steps [2, 5]: are proportional to the first row, and they are all positive 1. Normalization of the performance matrix. The and aij = 1/aji is true) and because of that only one of its matrix of performance ("payoff", "rating" or "decision eigenvalue differs from 0 and is equal to n. matrix") has number values rij that in general have If the matrix A contains inconsistent estimates (in different metrics. practical examples almost always), weight vector w can Each matrix row corresponds to one alternative, be obtained by solving the equation (A−λmax I)w=0 with and each column to a single criterion; element rij is the 132 B. Agarski, I. Budak, J. Hodolič, Đ. Vukelić rating (performance) of alternative Ai with respect to the where 0 ≤ Qi* ≤ 1 . Alternative Ai is closer to ideal criterion Cj. For m criteria (C1, C2, ..., Cm) and n solution if Qi* is closer to value 1, or at the same time, alternatives (A1, A2, ..., An) performance matrix has the if Si* is closer to 0. form R(n,m), and values (w1,w2,...,wm) registered above 6. Ranking alternatives. Alternatives are ranked by matrix represent the criteria weight defined by decision- descending values of Qi*. maker, or some other way, the sum of criteria weights is 1 Therefore, elements normalization is performed by relation (3) to obtain normalized matrix X in which all 4. EXAMPLE OF APPLICATION OF elements are dimensionless. MULTICRITERIAL METHODS AHP -1 n AND TOPSIS FOR ASSESSMENT OF é 2 ù xij = rij ê årij ú ENVIRONMENTAL QUALITY ê i=1 ú ë û (3) 2. Normalized payoff matrix multiplied with 4.1 Defining the multicriterial problem criteria weight. Weighted normalized performance matrix V = (vij) has The aim of multicriteria analysis is the assessment vij elements where each vij represents product of of environmental quality in the localities of the city of normalized performance of alternatives X and the Novi Sad through indicators that indicate the load corresponding weighting criteria coefficient. (potential pollution) on the environment. 3. Determining the ideal solution. The ideal Indicators (criteria) for total environmental load solution A* and anti-ideal solution A- are determined by evaluation have physical character and quantitative relations (4) and (5) values and they are related to air quality, noise level and * frequency of passing vehicles in some parts of the city A = {(max n ij | je G ), (min n ij | je G ' ), i = 1,..., n} · · of Novi Sad. * * * (4) = {n 1 ,n 2 ,..., n m } Air Quality is represented by the measured values - A = {(min n ij | j e G ), (max n ij | je G ' ), i = 1,..., n} of the total dust (amount of suspended matter), the · · concentration of carbon monoxide CO and carbon = {n - ,n - ,..., n - } (5) 1 2 m dioxide CO2. Frequency of passing vehicles provides where: information on the number of passing heavy (trucks), G = {j = 1, 2,..., m │ j belongs to criteria that light (passenger cars) vehicles and motorcycles on have to be maximized} traffic roads in the city of Novi Sad. G’ = {j = 1, 2,..., m │ j belongs to criteria that Measuring points for indicators are grouped in six have to be minimized} localities in the following way: 1.