A mixed-data evaluation in group TOPSIS with differentiated decision power

[[abstract]]This main objective of this paper is to provide decision support for mixed data in group Technique for Order Preference by Similarity to Idea Solution (TOPSIS) with differentiated decision power. We use a signum function to compare the ordinal performance of alternatives on any qualitative criterion, or the partial information provided by decision makers. The proposed process for ordinal information is uniformly coherent with the traditional TOPSIS steps, preserving the characteristic of distance-based utilities. Ordinal weights are also considered herein, and the decision power of the group members is formulated by their weights under an agreement in the group. Two examples demonstrate that the proposed approach has some benefits and achieves robustness with two types of sensitivity analyses. Some discussions and their limitations to the approach are also provided.[[notice]]補正完

The rank reversal problem in multi-criteria decision making : a literature review

Despite the importance of multicriteria decision-making (MCDM) techniques for constructing effective decision models, there are many criticisms due to the occurrence of a problem called rank reversal. Nevertheless, there is a lack of a systematic literature review on this important subject which involves different methods. This study reviews the pertinent literature on rank reversal, based on 130 related articles published from 1980 to 2015 in international journals, which were gathered and analyzed according to the following perspectives: multicriteria technique, year and journal in which the papers were published, co-authorship network, rank reversal types, and research goal. Thus our survey provides recommendations for future research, besides useful information and knowledge regarding rank reversal in the MCDM field

Rank Reversal in the AHP with Consistent Judgements: A Numerical Study in Single and Group Decision Making

In this paper we study, by means of numerical simulations, the influence of some relevant factors on the Rank Reversal phenomenon in the Analytic Hierarchy Process, AHP.We consider both the case of a single decision maker and the case of group decision making. The idea is to focus on a condition which preserves Rank Reversal, RR in the following, and progressively relax it. First, we study how the estimated probability of RR depends on the distribution of the criteria weights and, more precisely, on the entropy of this distribution. In fact, it is known that RR does’nt occur if all the weights are concentrated in a single criterion, i.e. the zero entropy case. We derive an interesting increasing behavior of the RR estimated probability as a function of weights entropy. Second, we focus on the aggregation method of the local weight vectors. Barzilay and Golany proved that the weighted geometric mean preserves from RR. By using the usual weighted arithmetic mean suggested in AHP, on the contrary, RR may occur. Therefore, we use the more general aggregation rule based on the weighted power mean, where the weighted geometric mean and the weighted arithmetic mean are particular cases obtained for the values p → 0 and p = 1 of the power parameter p respectively. By studying the RR probability as a function of parameter p, we again obtain a monotonic behavior. Finally, we repeat our study in the case of a group decision making problem and we observe that the estimated probability of RR decreases by aggregating the DMs’ preferences. This fact suggests an inverse relationship between consensus and rank reversal. Note that we assume that all judgements are totally consistent, so that the effect of inconsistency is avoided

Bayesian Markov Chain Monte Carlo-based copulas: factoring the role of large-scale climate indices in monthly flood prediction

Floods are caused by heavy rainfall associated with variation of large-scale climate index, El Niño–Southern Oscillation (ENSO). The chapter applies an advanced statistical copula approach to model lag relationships between monthly Southern Oscillation Index (SOI), an ENSO indicator, and monthly Flood Index (FI) that can be used for flood prediction. Copula parameters were numerically derived from under a hybrid-evolution Markov chain Monte Carlo (MCMC) approach within a Bayesian framework. The empirical findings showed that monthly SOI data from Aug to Dec have a significant correlation with monthly FI that can be predicted at least four months ahead using SOI information. These advanced flood prediction models, presented in this chapter, are indeed imperative tools for civil protection and important to early warning and risk reduction systems