Convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi-criteria decision making problems

In this paper, we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices, in the context of multi-criteria decision making. We first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts. We consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons, such as the uncertainty level, alternative preference scales and different weight estimation methods. We also consider the case where the comparisons are carried out in a fuzzy manner. It is shown that in most circumstances, augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal. We next address the issue of how this probability can be estimated in practice, from information gathered simply from the comparison matrices of a single expert group. We propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions. The framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome.     

q-Random Walks on Zd,d = 1, 2, 3

Methodology and Computing in Applied Probability - In this work, we consider nearest neighbour q-random walks on Zd for d = 1,2,3, with transition probabilities q-varying by the number of...     

A framework of incorporating confidence levels to deal with uncertainty in pairwise comparisons

Central European Journal of Operations Research - Pairwise comparison is a key ingredient in multi-criteria decision analysis. The method is based on a set of comparisons conducted by a group of...     

Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method

The performance of high-powered wavelength-division multiplexed (WDM) optical networks can be severely degraded by four-wave-mixing- (FWM-) induced distortion. The multicanonical Monte Carlo method (MCMC) is used to calculate the probability-density function (PDF) of the decision variable of a receiver, limited by FWM noise. Compared with the conventional Monte Carlo method previously used to estimate this PDF, the MCMC method is much faster and can accurately estimate smaller error probabilities. The method takes into account the correlation between the components of the FWM noise, unlike the Gaussian model, which is shown not to provide accurate results.     

Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling

Free-space optics (FSO) can provide cost-effective, high-bandwidth, wireless connections. However, atmospheric turbulence may degrade the performance of FSO links by causing intensity and power scintillations at the receiver. Multicanonical Monte Carlo sampling is used in conjunction with the phase screen method to calculate the statistics, and particularly the probability density function (PDF), of the power fluctuations at an FSO receiver. This allows the efficient calculation of the PDF even for very small values with a limited number of iterations. The obtained PDF can be used to characterize the performance of the system in terms of the error probability.