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7.1 Introduction

To be able to undertake informative MCA studies without requiring precise numerical data inputs is an attractive possibility. Some criteria do not naturally lend themselves to numerical measurement. Sometimes time or other resource constraints restrict the accuracy with which options’ performances can be measured.

In this manual, the recommended approach in such circumstances is either to undertake a limited assessment, based on the procedures set out in Chapter 4, or to use expert judgement to estimate subjectively performances on the relevant 0 – 100 scales for the criteria concerned, supplementing the overall evaluation with sensitivity testing.

An alternative approach, however, is to apply one of the MCA procedures specially designed to require no more than qualitative data inputs. Within this range of MCA methods, only one will be outlined here in any detail.

7.2 Qualitative outranking methods

Nijkamp and Van Delft101 and Voogd102 both suggest procedures for a

qualitative outranking analysis. Here, the version due to Nijkamp and Van Delft is explained. It is based on the assumption that performance on each criterion is categorised into one of four categories (●●●●, ●●●, ●● and ●) in descending order of quality. Similarly, criteria importance assessments

(weights) are qualitative and restricted to three categories (◆◆◆, ◆◆, ◆) in

decreasing order of importance.

First, pairwise comparisons are made for each criterion between all pairs from among the n options being considered, in a similar way to that set out in Appendix 6. Depending on the difference in assessed performance, each comparison might be:

at one extreme a major positive difference (●●●● against ●) coded as +++; at the other extreme, a major negative difference (● against ●●●●) coded as – – –; or any of the intermediate assessments ++, +, 0. – or – –.

For any one criterion, all the pairwise comparisons may be summarised by a ‘skew-symmetric’ matrix, with zeros down the leading diagonal.

101 _{Nijkamp, P. and Van Delft, A. (1977) Multi-criteria Analysis and Regional Decision Making, Martinus Nijhoff, Leiden.} 102 _{Voogd, H. (1983) Multi-criteria Evaluation for Urban and Regional Planning, Pion, London.}

Departing now from the procedure followed for ELECTRE I, three sets of concordance indices are calculated, one for each of the three criterion

importance categories (◆◆◆, ◆◆, ◆). These indices, c3(i,j), c2(i,j), and c1(i,j),

represent the frequency with which option i is better than option j, for

criteria with high (◆◆◆), medium (◆◆) and low (◆) importance. These outputs

may be summarised in three (n ⫻ n) concordance matrices, C3, C2and C1.

Separately for each of the concordance matrices into which these three sets of calculations have been set, it is now possible to compute three net total dominance indices. This is achieved by computing for each matrix the difference between the extent to which option i dominates all other options and the extent to which other options dominate option i (effectively the sum

of row i minus the sum of column i). These are denoted c3, c2and c1.

An (unweighted) discordance matrix is now calculated for each pair of plans in

a similar way. The discordance indices, d3(i,j), d2(i,j), and d1(i,j), are calculated

as the frequency with which the outcomes of option i are much worse (– – –), worse (– –) and slightly worse (–) than option j. This information feeds directly into three discordance matrices from which in turn three net discordance

dominance indices may be computed, d3, d2and d1in an analogous fashion to

the concordance dominance indices previously described.

Final selection is not based on any fully defined procedure, but revolves around an inspection of the net concordance and discordance indices at each of the three levels of criterion importance, seeking an option that exhibits high concordance and low discordance, especially with respect to the more important weight groups.

7.3 Other qualitative methods

A range of other qualitative methods are described in Nijkamp and Van

Delft and in Voogd. Additionally, the more recent Nijkamp et al.103 provides

other examples and a series of case studies. Within the range of qualitative methods, it is interesting that some begin to merge in terms of their general style and data requirements with the ranking-based approximations to the linear additive model described in Appendix 4.

For example, the Qualiflex method104 is essentially a permutation analysis,

aiming at deriving a rank order of options that is as far as possible consistent with ordinal information contained in the performance matrix and the weight

vector. The Regime Analysis method105 can be interpreted as an ordinal

generalisation of pairwise comparison methods such as concordance analysis.

Both these methods are set out and illustrated in Nijkamp et al.106

103 _{Nijkamp, P., Rietveld, T., and Voogd, H. (1990) Multi-criteria Evaluation in Physical Planning North Holland, Amsterdam.} 104 _{Paelinck, J.H. P. (1976) ‘Qualitative multiple criteria analysis, environmental protection and multiregional development,}

Papers of the Regional Science Association’, 36, pp.59–74; Paelinck, J.H. P. (1977) ‘Qualitative multiple criteria analysis:

an application to airport location’, Environment and Planning, 9, pp.883–95; and Van der Linden, J and Stijnen, H. (1995) Qualiflex version 2.3, Kluwer, 1995.

105 _{Hinloopen, E., Nijkamp, P. and Rietveld, P. (1983) The regime method: a new multi-criteria technique, in P. Hansen (ed.)}

Essays and Surveys on Multiple Criteria Decision Making, Springer Verlag, Berlin.

Appendix 8 Fuzzy MCA

Fuzzy MCA methods are at the moment largely confined to the academic literature or to experimental applications, although ideas about MCA based on fuzzy sets have been discussed for more than twenty years. Fuzzy sets, conceptualised by Zadeh in the 1960s, are broadly equivalent to the sets found in conventional mathematics and probability theory with one important exception. The exception is that, instead of membership of a set being crisp (that is, an element is either definitely a member of a given set or it is not), set membership is graduated, or fuzzy or imprecise.

Set membership is defined by a membership function, µ(x), taking values between zero and one. Thus a particular issue might be regarded as a

member of the set of major social concerns with a membership value of 0.8. A membership function value of 0 conveys definitely not a member of the set, while µ = 1 conveys definitely a member of the set. µ = 0.8 suggests quite a strong degree of belief that the problem is a major one, but not complete certainty.

Proponents of fuzzy MCA would argue that one of the strengths of the fuzzy approach is that it recognises the reality that many of the concepts involved in decision making are far from clear or precise to those involved. Fuzzy sets provide an explicit way of representing that vagueness in the decision maker’s mind in an explicit way. Developing this line of argument has led to many suggestions for fuzzy extensions to conventional MCA methods,

such as fuzzy outranking methods and fuzzy utility theory.107 Nonetheless,

it remains that, overall in the MCA community, enthusiasm for fuzzy MCA remains muted. Reasons for this include:

• a lack of convincing arguments that the imprecision captured through fuzzy sets and the mathematical operations that can be carried out on them actually match the real fuzziness of perceptions that humans

typically exhibit in relation to the components of decision problems;108

• doubts as to whether prescriptively trying to model imprecision, which is in some sense a descriptive reflection of the failings of unaided human decision processing, is the right way to provide support to deliver better decisions;

• failure to establish ways of calibrating membership functions and

manipulating fuzzy values that have a transparent rationale from the point of view of non-specialists.

In combination, issues such as these continue to throw substantial doubt on the practical value of fuzzy MCA as a practical tool for supporting the main body of public decisions.

107 _{Examples can be found, e.g., in Chen, S.J. and Hwang, C.L. (1992) Fuzzy Multiple Attribute Decision Making: Methods and} Applications, Springer Verlag, Berlin.