Discordance index

To build the outranking relationship, the decision maker has to define concordance and discordance thresholds. An alternative a outranks b if the concordance index is greater than or equal to the concordance threshold and the discordance index is less than the discordance threshold. The decision maker may have to vary these thresholds in order to obtain an informative outranking relation. The result is a set of preferred alternatives such that any alternative not in the set is outranked by at least one alternative in the set and all alternatives in the set are incomparable. 

Keywords Net flow method, rough set method, thresholds, concordance index, discordance index, preference and non-preference rules, ranking, gluconic acid production. 

A discordance index [/, j is then calculated for each criterion k using the preference and veto thresholds ... 

Fig. 7.2 (a) Individual concordance index, and (b) discordance index calculations used in NFM algorithm to determine ranking scores for the Pareto domain solutions. 

Solution Using a pair-wise comparison, the difference 7], the individual concordance index q [i, j], and the discordance index are calculated using Eqs. (7.4), (7.5), and (7.7), respectively. The values... 

The total concordance index Ca and the total discordance index Da of the alternative A are (Formula 6 and ) ... 

The CDA consists of comparison of variants of pair selection. It measures the degree by which the variants of selection and the weights of factors prove or disprove the ratio between the variants. The differences in the weights of criteria and in the evaluations of criteria are analysed by means of the procedures of concordance and discordance separately. The index of concordance between the variant A and the variant B is defined as a proportion of the sum of weights of those criteria, for which the standardized evaluation A (baj) is greater than or equal to the standardized evaluation B (gfiy), and the sum of weights of aU criteria. Then the concordance index Cab and the discordance index Dab are (Formula 4 and 5) ... 

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