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Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

In this paper, we propose a new method for solving multiple criteria decision-making/aiding (MCDM/A) sorting problems in the context of multi-attribute value theory (MAVT), based on a flexible and interactive elicitation process. It uses partial information to require less information from the decision maker (DM), which is given in the form of preference statements. The proposed method keeps the axiomatic structure of the traditional tradeoff elicitation procedure, without requiring exact values of indifference to be set, which can be a difficult task for the DM to perform. The use of linear programming, combined with the decision rules, allows an alternative to be assigned into a class without the need to provide complete information. By being flexible and interactive, the proposed method allows the DM to monitor the range of possible classes for each alternative at any level of information available during the process, which can save time and effort. The applicability of the method is shown by solving a project management problem on sorting activities.

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.

The Cox proportional hazards model is commonly used to examine the covariate-adjusted association between a predictor of interest and the risk of mortality for censored survival data. However, it assumes a parametric relationship between covariates and mortality risk though a linear predictor. Generalized additive models (GAMs) provide a flexible extension of the usual linear model and are capable of capturing nonlinear effects of predictors while retaining additivity between the predictor effects. In this paper, we provide a review of GAMs and incorporate bivariate additive modeling into the Cox model for censored survival data with applications to estimating geolocation effects on survival in spatial epidemiologic studies.

The Cox proportional hazards model is commonly used to examine the covariate-adjusted association between a predictor of interest and the risk of mortality for censored survival data. However, it assumes a parametric relationship between covariates and mortality risk though a linear predictor. Generalized additive models (GAMs) provide a flexible extension of the usual linear model and are capable of capturing nonlinear effects of predictors while retaining additivity between the predictor effects. In this paper, we provide a review of GAMs and incorporate bivariate additive modeling into the Cox model for censored survival data with applications to estimating geolocation effects on survival in spatial epidemiologic studies.