### Table 1: Rankings of Decision Making Methods

"... In PAGE 7: ... The DEA method delivers a more general classi#0Ccation of the sources. The rankings or classi#0Ccations produced by the individual methods are summarized in Table1 . In our example the #0Crst three methods all deliver the same ranking, whereas the DEA-method delivers a slightly di#0Berent clas- si#0Ccation, due to the lackofanyweighting of the criteria.... ..."

### Table 1: Rankings of Decision Making Methods

"... In PAGE 7: ... The DEA method delivers a more general classi cation of the sources. The rankings or classi cations produced by the individual methods are summarized in Table1 . In our example the rst three methods all deliver the same ranking, whereas the DEA-method delivers a slightly di erent clas- si cation, due to the lack of any weighting of the criteria.... ..."

### Table 1 The general decision

"... In PAGE 2: ... More details on target-based decision models as well as their potential applications and advantages could be referred to Abbas and Matheson (2005, 2004), Bordley (2002), Bordley and Kirkwood (2004), Castagnoli and LiCalzi (2006) and LiCalzi (1999). In this paper,1 we consider the problem of decision making in the face of uncertainty that can be most effectively described using the decision matrix shown in Table1 ; see, e.g.... In PAGE 4: ... 6. 2 Target-based model of the expected value Let us consider the decision problem as described in Table1 with assuming a proba- bility distribution PS over S. Here, we restrict ourselves to a bounded domain of the payoff variable that D =[cmin, cmax], i.... In PAGE 6: ... 3.1 State-independent targets Let us turn back to the problem of decision making in the face of uncertainty shown in Table1 . We now discuss this problem using fuzzy targets.... In PAGE 17: ...1 A target-based procedure for fuzzy decision making We now consider the problem of decision making under uncertainty where payoffs may be given imprecisely. Let us turn back to the general decision matrix shown in Table1 , where cij can be a crisp number, an interval value or a fuzzy quantity. Clearly in this case we have an inhomogeneous decision matrix and traditional methods can not be applied directly.... In PAGE 23: ... 8. Then we obtain the result corresponding to this target as shown in Table1 3, which yields the ranking order as A1 follows A4 follows A2 follows A3. In other words, with a more pessimistic attitude the DM is enough risk averse to refuse alternative A2 and select A1 for surely getting best profit.... ..."

### Table 1 Decision Problems in Finite Argument Systems Problem Instance Question

2007

"... In PAGE 5: ... While Fact 2 (a) ensures the existence of a preferred extension a property that is not guaranteed to be the case for stable extensions it is possible that the empty set of arguments (which is always admissible) is the unique such extension. Noting Table1 (c), whether a given argument system a80a73a74a81a12a24a23a25a13a27a77 has a non-empty preferred extension is unlikely to be ef ciently decidable in general. 3 The argument systems a80a133a132 and a134a135a132 and their properties A number of our subsequent hardness proofs regarding various graph-theoretic re- strictions are obtained by transforming argument systems used in earlier reductions... In PAGE 16: ...raphs, e.g. [30]. Planarity, however, does not help in the construction of ef cient decision procedures for the problems of Table1 . The reductions employed to prove this make use of a device which is of some independent interest: in terms of the formalism introduced in the preceding section this allows us to argue that planarity is a polynomially CA-universal property.... In PAGE 17: ...is NP complete with a80 restricted to planar graphs. For Q any of the decision problems of Table1 , we let QP denote the variant in which the argument system forming part of the instance is planar. Theorem 12 CAP is NP complete.... ..."

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### Table 2. Sample Weights on the Objectives in the KI Decision Problem

2006

"... In PAGE 15: ... By convention, weights are normalized to sum to 100%.6 Table2 displays an example with weights for each objective in the KI decision problem for a hypothetical local region using the swing weight method. For example, the subobjective of Maximize KI availability for children and pregnant women residents has the largest weight with 0.... ..."

### Table 1: Decision problems.

1999

"... In PAGE 3: ...ollowing examples. However, we show later that maxrankS(M) is the same for all in nite S. Clearly, both minrankS(M) minrankS0(M) and maxrankS(M) maxrankS0(M) when S S0. W = quot; x 1 1 2 # ; det W = 2x ? 1; minrankZ(W ) = 2 minrankQ(W ) = 1 (using x 7! 1 2) T = quot; x 1 2 x # ; det T = x2 ? 2; minrankQ(T ) = 2 minrankR(T ) = 1 (using x 7! p2) U = quot; x 1 ?1 x # ; det U = x2 + 1; minrankR(U) = 2 minrankC (U) = 1 (using x 7! i) V = quot; x x 1 x # ; det V = x2 ? x; maxrankGF(2)(V ) = 1 maxrankGF(4)(V ) = 2 (using x 7! a generator of GF (4)) 3 Summary of Results Most of our complexity results for the computation of minrank and maxrank are naturally phrased in terms of the decision problems given in Table1 . We have introduced two special problems, SING(ularity) and NONSING(ularity), which could possibly be easier than the more general minrank/maxrank problems.... ..."

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### Table 1: Decision problems.

"... In PAGE 3: ...ollowing examples. However, we show later that maxrankS(M) is the same for all in nite S. Clearly, both minrankS(M) minrankS0(M) and maxrankS(M) maxrankS0(M) when S S0. W = quot; x 1 1 2 # ; det W = 2x ? 1; minrankZ(W ) = 2 minrankQ(W ) = 1 (using x 7! 1 2) T = quot; x 1 2 x # ; det T = x2 ? 2; minrankQ(T ) = 2 minrankR(T ) = 1 (using x 7! p2) U = quot; x 1 ?1 x # ; det U = x2 + 1; minrankR(U) = 2 minrankC (U) = 1 (using x 7! i) V = quot; x x 1 x # ; det V = x2 ? x; maxrankGF(2)(V ) = 1 maxrankGF(4)(V ) = 2 (using x 7! a generator of GF (4)) 3 Summary of Results Most of our complexity results for the computation of minrank and maxrank are naturally phrased in terms of the decision problems given in Table1 . We have introduced two special problems, SING(ularity) and NONSING(ularity), which could possibly be easier than the more general minrank/maxrank problems.... ..."

### Table 2. Examples of IEM tools

in ISSUED BY

"... In PAGE 4: ... REFERENCES 11. GLOSSARY BOXES Box 1: Key definitions and understandings set the context for this document Box 2: Relevant definitions of sustainable development Box 3: Environmental rights of people in the South African Bill of Rights TABLES Table 1: Key features of environmental assessment and management tools from the 1970s to the present Table2 . Examples of IEM tools FIGURES Figure 1: Relationship between IEM tools, and complementary processes and supporting disciplines Figure 2: Commonly used tools in the IEM toolbox Figure 3: Example of a hierarchy of selected IEM tools in relationship to a typical development cycle 2 3 4 4 4 6 6 6 6 6 7 8 8 8 8 8 8 9 9 10 16 16 17 18 4 5 5 7 11 10 15... In PAGE 11: ... * The tools are supported by numerous specialist disciplines, which are in turn supported by technologies and methods for sourcing input data. Commonly used tools in support of integrated environmental management are listed and described in Table2 . References are provided to other documents in the DEAT Integrated Environmental Management Information Series, as well as websites or other useful sources of information on these tools.... ..."

### 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 1 OLS selection procedure for the simple scalar function modeling problem

2001

"... In PAGE 9: ... For this simple example, many sets of different noisy training data were generated, and the modeling results were consistent and similar to the results shown below, which were typical. It is informative to examine the selection process of the OLS algorithm, listed in Table1 . Notice that the normalized MSE continuously decreased as more terms were added.... In PAGE 10: ... This produced a 15-term model. The model weights had very large value, as can be seen in Table1 . This was a typical sign of over-fitting.... ..."

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