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- Title
An Analytical Solution to Dujmovic's Iterative OWA.
- Authors
Troiano, Luigi; Díaz, Irene
- Abstract
Iterative OWA (ItOWA) as proposed by Dujmovic, is a two-stage procedure for computing the weighting vector by a double nested iteration: (i) weights at step h are computed as limit to infinity of a matrix power, (ii) the result is used to start the computation at step h + 1, until the OWA operator arity n is reached. Thereafter Dujmovic suggested a computational solution based on the conjecture that the limit exists, and numerical simulations have being supported the hypothesis that the conjecture is correct. In this paper, we prove that the limit actually exists and we provide an analytical solution to the procedure, so the weighting vector can be computed directly instead of an iterative time-consuming procedure. This theoretical result enables a faster computation of the weighting vector and characterization in terms of weights values, attitudinal character and entropy.
- Subjects
ITERATIVE methods (Mathematics); AVERAGING method (Differential equations); STATISTICAL weighting; OPERATOR theory; COMPUTER simulation
- Publication
International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 2016, Vol 24, p165
- ISSN
0218-4885
- Publication type
Article
- DOI
10.1142/S0218488516400158