Rating RelationsRules for Ascribing Advantage

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2.2 Theoretical Background

ORDIT ranking method uses multi-indicators in the ranking process, where its theoretical concepts are discussed in the following sub sections based on Myers and Patil 2010.

2.2.1 Rating RelationsRules for Ascribing Advantage

This section describes the protocols for comparing cases or collectives of cases via ratings, rules and relations that ascribe advantage to some cases over some others or fail to do so for particular pairs. There are 3 possibilities in comparing a pair of cases, where one case is denoted by and the other by . “Г aa ” wherein Г has ascribed advantage over . Г has subordinate status to “Г ss ” which implies “ aa Г”. “Г ii ” whereby these are indefinite instances without ascribed advantage and without subordinate status, which impli es “ ii Г”. Thus the protocol either designates one member of a pair as having ascribed advantage and the other subordinate status, or that pairing as being indefinite. ff aa is the frequency of number of occurrences for the ascribed advantage. ffss is the frequency of number of occurrences for the subordinate status. ffii is the frequency of number of occurrences for being indefinite. Each of the N cases can be compared on this basis to all others in the deleted domain DD=N –1 of competing cases with the percent occurrence of these relations being tabulated as follows, AA = 100 × ffaaDD, SS = 100 × ffssDD, II = 100 × ffiiDD. Clearly, AA + SS + II = 100; and for later use let CCC = 100 – AA as the complement of case condition relative to ascribed advantage AA Wayne and Patil 2010. Figure 6 gives is a Hasse Diagram of entities at Table 1. This simple X- shaped Hasse diagram is used to illustrate wherein entity A has ascribed advantage over B, D, and E while being indefinite with regard to C. Entity B has subordinate status to A and C with ascribed advantage over D and E. The deleted domain DD is four, since an entity is not paired with itself for present purposes. 18 Table 1 Entities with 3 indicators Entity Ranking Indicator1 Indicator2 Indicator3 A 1.5 2 3 B 3 5 4 C 1.5 3 2 D 8 6 7 E 7 8 6 Figure 6 X-shaped Hasse diagram of five entities labeled as A, B, C, D and E

2.2.2 Subordination Schematic and ORDIT