### TABLE IV COSTS OF TRACE ANALYSIS FOR THE CONSTRAINTS (25) AND (26)

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### Table 6: Truth table for equations (25) and (26).

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"... In PAGE 18: ... The nal result is equation (20). Derivation of equations (25) { (26) : The truth table for determining vi?1 and ei?1 in the MHSSD scheme is shown in Table6 . Note that the \+ quot; and \? quot; symbols in the top row of the truth table denote algebraic addition and subtraction, respectively.... ..."

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### TABLE 1. TYPE #1 PROBABILITY FUNCTIONS USED (AS IN [25,26])

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### Table 1. Type #1 Probability functions used (as in [25,26])

"... In PAGE 5: ...* According to Eqs. 4.4, 4.6 and Table1 (4.1.... In PAGE 5: ...* According to Eqs. 4.4, 4.5 and Table1 (4.1.... ..."

### Table 11.1. FACS action units (AU). AUs with * indicate that the criteria have changed for this AU, that is, AU 25, 26, and 27 are now coded according to criteria of intensity (25A-E), and AU 41, 42, and 43 are now coded according to criteria of intensity.

### Table 3: Clustered selected solutions from multicriteria optimization. Solutions marked by A contain solutions # 22, 23, 25 and 26. Solutions marked by B contain solutions # 27 through 49, excluding solutions # 32, 40, 45 and 46.

"... In PAGE 30: ... A typical starting point is to choose criteria values at the utopia point as aspiration levels and values at the nadir point as reservation levels. The resulting quot;compromise quot; solution is shown in the Table3 as solution # 1. The compromise solution is obtained using automatically calculated trade-o s between the criteria based on the Utopia point and on the current approximation of the Nadir point.... In PAGE 30: ...g. solutions #18 and 19, see Table3 ) with similar costs, much better values of DO, and only slightly worse values of NH4. At this point an interactive multicriteria analysis may start.... In PAGE 32: ... Then we stabilized the values of INV and DO (by setting relatively narrow ranges between the respective aspiration and reservation levels) and began narrowing the range between aspiration and reservation levels for the other criteria. This is why we have obtained several sets of solutions which have rather similar values of criteria (those solutions are presented in Table3 ). However, we include in Appendix A all solutions in order to provide data for a more detailed analysis.... In PAGE 32: ... Selected and grouped solutions from two interactive sessions are presented in Table 3. The solutions presented in Table3 have been grouped in order to illustrate the main characteristics of the decision problem (discussed below). All solutions have been sorted according to increasing values of DO and are labeled by their sequence number (to be subsequently referred to as quot;solution # quot;).... In PAGE 32: ... In particular, one can observe ve outlying solutions (marked by shadowed circles) in Figure 2. Those solutions (# 1 and 6 in Table3 ) have DO levels similar to other solutions which have substantially higher TAC and INV values. This is because these solutions include capital-intensive technologies for the reduction of NH4.... In PAGE 36: ... This is illustrated by solutions #22-26, in which investments between 10.5 and 16 million USD result in practically the same ambient water quality (see Table3 and Figure 3). Obviously, OMR and therefore TAC costs are also di erent, but this is not so signi cant.... In PAGE 36: ... 5. Figure 6 illustrates TAC(DO) and INV(DO) relations for the cluster of solutions marked by B in Table3 and in Figure 2. These solutions also have a relatively small range in DO, BOD, NH4-N values used as water quality criteria.... In PAGE 36: ...3 Bene ts of multicriteria analysis Before presenting the bene ts from multicriteria analysis we present the following obser- vation that illustrates the necessity of a careful analysis of optimal solutions (regardless of whether they are obtained from SCDA or MCDA). Within a given cluster, the treatment con guration obtained (see Table3 ) shows certain variability. This appears primarily for smaller emissions, while the technologies for larger ones such as To or Ni remain rather robust.... In PAGE 36: ... This appears primarily for smaller emissions, while the technologies for larger ones such as To or Ni remain rather robust. If we consider the signi cantly di erent solutions of Table3 , the large number of potential policies is evident. However, a signi cant portion of them may not be feasible in practice for reasons external to the model.... In PAGE 36: ... For example, in practice it is crucial to introduce reliable and easily implementable strategies, notions of which play an impor- tant role in formulating legislation. As was shown in [SMPK94], quot;cheap quot; alternatives in Table3 may be too vulnerable (if in practice the assumed quot;design scenario quot; is not real- ized). Thus, a decision maker would most likely select a solution with DO about 5 mg/l, requiring INV=13-25 million USD.... ..."

### Table 6.1, were generated from experiments [25], [26].

### Table splitting. . . . . . . . . . . . . . . . . . . . . . . . . . . .34 TEAM software . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Thompson automaton . . . . . . . . . . . . . . 4, 25, 26

### Table 2.2 Comparison of PLBs [14], [15], [25], [26] PLB Atmel ORCA 2C Xilinx 4000

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