ࡱ> UWT9 P5bjbj4P*l$t$7Dh|, , , , , , , JCLCLCLCLCLCLC$E G0pC, , , , , pC<+, , C<+<+<+, , , JC<+, JC<+<+,/~>|? , p *$4">?lD07D ?H**H?<+$$ change of decision making principles in Environmental ImpAct Assessment applied on screening matrices D. Rumenjak Ministry of Environmental protection, Zagreb, Croatia B. Salopek and D. Rajkovi Faculty of mining, geology and petroleum engineering, Zagreb, Croatia Abstract This work describes the transformation of decision making support system of utility kind in system based on equal evaluation of criteria (or: non-utility decision making support). The system based on fuzzy logic is proposed for transformation. The technics for transformation are shown, including method for developing consensus, by example of screening alternatives which latter enters the complex (full) impact assessment. 1.Introduction The methods for decision making support (or simply decision making) used in environmental impact assessment (EIA) are based on classical utility paradigm taken from the bussiness decision making. Because of differences of bussiness decision making compared to environmental protection the change of paradigm could be important. The reasons for this change are given (A. Portous, 2000, S.J. Armstrong and R.C. Botzler 1993) and are related to the critics of cost-benefit idea for decision making in environmental matters. The scope of this work is the transformation decision making support system of utility kind (Rapid Impact assessment Matrix or RIAM) to fuzzy logic system of non-utility kind. Transformation of DECISION MAKiNG Methods in ENVIRONMENTAL IMPACT ASSESSMENT The decision making principles The utility and non-utility paradigmas, when applied in systems for decision making support, are different in basic approaches. The basic approach for the utility kind is:  EMBED Equation.3 =max  EMBED Equation.3 f EMBED Equation.3 ,  EMBED Equation.3  or very often (D. Rumenjak 2000):  EMBED Equation.3  (1) where:  EMBED Equation.3 : utility value of chosen alternative f EMBED Equation.3 : utility function D : decision making model a: alternative A: set of alternatives u C: utility value(units or ordinal, interval or ratio scales) The non-utility decision making in logic terms could be performed through classical or fuzzy logic. In classical logic the value of the truth (or membership value) is:  = 1 or 0, in fuzzy logic  EMBED Equation.3  where: R: real number set. The basic approach for both logic is:  EMBED Equation.3  EMBED Equation.3  =  EMBED Equation.3  where:  EMBED Equation.3  EMBED Equation.3 : membership value of chosen alternative Cj = EMBED Equation.3 : set of criteria (objective, importance of criteria) Cj: membership value Table 1 Decision matrix for utility (u ij) and non  utility logic type (ij), respectively Alternative Criterion 1UtilityFuzzyalternative a1u1111alternative a2u2121 2.2. RIAM method RIAM is multiscale method for approximate reasoning used in environmental impact assessment (K.Jensen (ed.) 1998). The scales in the method, A1, A2, B1, B2 i B3 are defined as: A1: importance of condition (ordinal scale, range 0 to 4) A2:magnitude of change (ordinal scale, range - 3 to 3) B1: permanence of impacts (ordinal scale, range 1 to 3) B2 : reversibility (ordinal scale, range 1 to 3) B3: cumulativity (ordinal scale, range 1 to 3) The scale of products are defined by:  EMBED Equation.3  and the scale of results:  EMBED Equation.3  where: es: scale in the range 108 to 108 (the results are also designated by letters: - E, -D....D, E). According to these scales, concrete utility estimation unr= es is calculated by:  EMBED Equation.3  where: at,bt,es: individual values from scales, respectively. In RIAM method the criteria are used which could be also divided in subcriteria. Table 2 Some criteria and subcriteria from RIAM CriteriaSubcriteriaprotection of nature : Biota WildlifeNon-renewable resources: Soil WaterSpatial planning: Soil InfrastructureResidence quality:Noise level Air qualityadjusted to criteria used in EIA for mining projects in Croatia 2.3. Transformation of RIAM method to fuzzy logic based system For transformation RIAM method to fuzzy logic system, the mapping is proposed by which the results of collective (group) estimation is transfered to fuzzy arithmetics. By doing this, the advantages of Riam (K.Jensen (ed.) 1998) could also be preserved. For each ranking scale from RIAM (A1, A2, B1, B2 i B3) the mapping is defined:  EMBED Equation.3  (2) by which the fuzzy numbers  EMBED Equation.3 .... etc. (J.J. Buckley and E. Eslami, 2002) are obtained as:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , .... etc. The mapping function is defined:  EMBED Equation.3  (3) where:  EMBED Equation.3 :mapping function (membership value) for each member of scale N: the total number of choices for one scale mapping n: number of choices for respective value from the scale. Sums and products of fuzzy numbers, by analogy to sums and products of values from ranking scales in RIAM, are calculated by application of extension principle:  EMBED Equation.3   EMBED Equation.3  where: sup: supremum ( < max). Calculation of the output fuzzy number is also done by extension principle:  EMBED Equation.3  the disvadvantage of RIAM is a lack of clear way of collective decision making. Determination of consensus is condition for the application of system based on fuzzy logic. By consensus, the truth of proposition of fuzzy logic is evaluated by:  EMBED Equation.3  where: cons.: membership value of each consensus for the fuzzy numbers  EMBED Equation.3 .... etc. pred.: membership value of each predicate for the fuzzy numbers  EMBED Equation.3 .... etc. Approximate reasoning is performed in logic terms for determination the membership value of consequent which represents the (final) membership value from Table 1:  EMBED Equation.3  (4) where:  EMBED Equation.3 : fuzzy logic operator and  EMBED Equation.3 : membership values for predicates and consequent, respectively. 2.4. Results The search for improvement of EIA support decision making methodology is done by the support of Ministry of environment. In this context, comparision of RIAM and fuzzy logic system has been investigated. The hypotetic alternatives were used for investigation. The numerical values for the input were obtained by stohastic modelling. The criteria from table 2. were used. For evaluation of results of collective decision making in RIAM during the comparision the method of centroide (method of composite moments) was applied. for determination of consensus in non-utility (logic) system the method of weighing pairs (T.J.Ross 1995) was used. The process of developing the consensus is shown by the matrix (Fig 1). For membership values determination in consensus process the expression (3) was also used. Calculation of consequent membership values is done by (4). results of comparision is shown in table 4. Value of A1 :234102000.410.73100.70.90.940.60.300.80.8100.10.200.400.30.60.20.60Fig. 1 Consensus matrix in membership value for fuzzy number A1 (example) under criterion 1 (protection of nature) and alternative 1. The value A1= 3 is chosen Table 4 Results of modelling the choice of alternatives both by RIAM and fuzzy system AlternativeProtection of NatureResultsUtility:ESFuzzy: C1Utility: EMBED Equation.3 Fuzzy: min CjAlternative a1- 180.3- 68 (-D)0.17alternative a2-140.37- 60 (-D)0.26Results: alternative a2 is chosen according to both methods. As an example, the result in column 1 (criterion: protection of nature) is also shown The important question in approximate reasoning, used for decision making, is correct choice of criteria and subcriteria for evaluation of alternatives. In utility systems the simple calculation based on (1) is often done. In fuzzy systems the subcriteria are linked in a system by logic operators (T.J.Ross, 1995). 2.5. Future work By the future work it will have to develop the more complex decision making support system that comes after the phase of screening. The basic idea is to integrate the classical models from environmental engineering. The possible application of those type of models in fuzzy arithmetics is shown by example of the model for pollution of underground water in the case of multidimensional flow (K. Kovarik, 2000.):  EMBED Equation.3  (5) where:  EMBED Equation.3 dispersion coefficient t: time  EMBED Equation.3 length in i and j direction ij: velocity C: concentration of pollutant  EMBED Equation.3 :  cut for fuzzy functions: dispersion coefficient, concentration, derivatives of concentration, velocity. Solution of formula (5) in fuzzy arithmetics could be done by  cut method (J.J. Buckley and E. Eslami 2002). The approximate reasoning including such formulas could be basically the same as for mapped scales. CONCLUSION RIAM method, based on multiscale determination of utility, could be clearly transformed to the fuzzy logic method. By such transformation the change of decision making paradigm of utility kind is also achieved. The mapping is proposed by general formula (2), with possible change of formulas for (mapping function) determination. The transformation of RIAM method gives also rules for the collective decision using consensus process. In full EIA, that follows screening alternatives, transformation might include the models of impacts from environmental engineering. REFERENCES J.D. Portous (2000). Dictionary of environmental science and technology. Chichester: J. Wiley&Sons S.J. Armstrong and R.C. Botzler (1993), Environmental etichs: divergence and convergence. New York: Mc.Graw-Hill K.Jensen (ed.) (1998). Environmental impact assessment - using the rapid impact assessment matrix (RIAM). Fredensburg: Olsen&Olsen D. Rumenjak (2000), decision making in environmental Protection, VII th International Symposium Waste management. Zagreb: Gospodarstvo i okoli. p. 517 J.J. Buckley and E. Eslami (2002). An introduction to fuzzy logic and fuzzy sets. New York: Physica-Verlag T.J.Ross (1995). Fuzzy logic with engineering applications. New York: Mc.Graw-Hill Environmental Impact Assessment Study for sand Deposit tefanec. Zagreb: Cemtra d.o.o. K.Kovarik (2000). Numerical modelling of Groundwater pollution. Berlin: springer verlag.  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