A new method similar (or close) to TOPSIS

Mais, peu à peu, on a ajouté des nouvelles choses: new règles de fusion (les PCR5, les BCRs, les règles unformes ou partially uniformes, etc.), la DSmPe, etc. La PCR6, meme designée par Arnaud, fait maintenant partie de la DSmT. Ensuite l’on a inclu le complement/négation, après des longs insistances - quand meme Arnaud est intervenu. So, l'on a elargi au maximum l'espace de fusion - il peut etre different d'une algebre booléenne quand les elements n'ont pas des frontières precises. Ensuite, l'intersection inconnu (A∧B = indeterminate, qui peut arriver dans la pratique) que personne n'a fait dans la fusion. Nous avons besoin aussi de decision-making, different de

AHP (Saaty), qui soit mieux et plus générale. Nous devons peut-être aborder l'espace continu (pas seulement celui discret) de la fusion. Donc de plus en plus l'on se distingue beaucoup de la DST et l'on est plus général que la DST.

A new method similar (or close) to TOPSIS

C1 C2 C3

12/16 7/16 1/16 A1 7 9 9 A2 8 7 8 A3 9 6 8 A4 6 7 8

Scilogs, V: joining the dots

One multiplies on columns with the weights 12/16, 7/16, and 1/16 respectively, and one gets:

C1 C2 C3 A1 84/16 27/16 9/16 A2 96/16 21/16 8/16 A3 108/16 18/16 8/16 A4 72/16 21/16 8/16 With bold we have the largest numbers for each column, and underlined are the smallest numbers on each column. We compute the sums for each line, by subtracting each number from the largest one: S1+ = |84/16-108/16| + |27/16-27/16| + |9/16-9/16| = 1.5000 S2+ = |96/16-108/16| + |21/16-27/16| + |8/16-9/16| = 1.1875 S3+ = |108/16-108/16| + |18/16-27/16| + |8/16-9/16| = 0.6250 S4+ = |72/16-108/16| + |21/16-27/16| + |8/16-9/16| = 2.6875 Classifying these sums we get them on places: S3+, S2+, S1+, S4+ in the order of which one is closer to the maximum. Then: S1- = |84/16-72/16| + |27/16-18/16| + |9/16-8/16| = 1.3750 S2- = |96/16-72/16| + |21/16-18/16| + |8/16-8/16| = 1.6875 S3- = |108/16-72/16| + |18/16-18/16| + |8/16-8/16| = 2.2500 S4- = |72/16-72/16| + |21/16-18/16| + |8/16-8/16| = 0.1875 Classifying these sums we get them on places: S3-, S2-, S1-, S4in the order of which one is further from the minimum.

If we compute Ti, we get the same ordering:

T1 = (S1-) / [(S1-) + (S1+)] = 0.478261

T2 = (S2-) / [(S2-) + (S2+)] = 0.586957

T3 = (S3-) / [(S3-) + (S3+)] = 0.782609

T4 = (S4-) / [(S4-) + (S4+)] = 0.065217 hence the order is the same: T3, T2, T1, T4. *

Belton and Gear [1983] firstly considered the example below:

A B C A 1 1/9 11 B 9 1 9 C 1 1/9 1 and the result using AHP is: A = 1/11, B = 9/11, C = 1/11 (with alpha-D one gets the same result). Then they say they repeated line of B: A B C B A 1 1/9 1 1/9 B 9 1 9 1 C 1 1/9 1 1/9 B 9 1 9 1 They constructed the above matrix. Then, using the AHP one gets rank reversal. *