Different from conventional decision-making environments, decision makers (DMs) in a community setting usually exhibit the complex social preferences and intricate social interactions, which may lead to high-decision costs for group consensus reaching. To address this challenge, we design a minimum cost consensus-based social network group decision making (SNGDM) approach considering altruism-fairness preferences and ordered trust propagation. First, a trust propagation method with order effect and path length is proposed to estimate the completed trust relationships among DMs in order to determine the weights of DMs. Then, inspired by the interaction of altruism and fairness preferences, we define the individual altruism-fairness preference utility function and utility level for cost consensus, and explore some properties. Afterwards, a new minimum cost consensus-based SNGDM with individual altruism-fairness preference utility is constructed. Finally, the validity of the proposed consensus framework is confirmed through the carbon reduction consensus problem of China’s aviation enterprises. Moreover, the sensitivity studies and comparative analysis are conducted to further demonstrate the merits of our proposal.

This article investigates the optimal ordering policies of spare parts for preventive replacement of a single component deteriorating system in this article. The operational system suffers from a deterioration process and is also subject to random shocks during its service, where discrete shocks are categorized into fatal ones and nonfatal ones. To preventing the catastrophic losses resulting from degraded failures or shock incurred failures, a spare unit for replacement is ordered at some time between the system’s initial operation and its undesirable failure. The average cost rate with lower-limit constrained availability is minimized to seek the optimal spare unit ordering time, in which the Kuhn–Tucker necessary condition is satisfied. As a comparison strategy, the expected cost effectiveness defined as the ratio of system availability to average cost rate is maximized to dynamically adjust the optimum ordering time of the spare unit. Numerical experiments are designed to validate the existence and uniqueness of the joint optimal spare unit ordering and preventive replacement policies, as well sensitivity analysis of critical parameters are conducted.

Methods based on Bayesian decision tree ensembles have proven valuable in constructing high-quality predictions, and are particularly attractive in certain settings because they encourage low-order interaction effects. Despite adapting to the presence of low-order interactions for prediction purpose, we show that Bayesian decision tree ensembles are generally anti-conservative for the purpose of conducting interaction detection. We address this problem by introducing Dirichlet process forests (DP-Forests), which leverage the presence of low-order interactions by clustering the trees so that trees within the same cluster focus on detecting a specific interaction. We show on both simulated and benchmark data that DP-Forests perform well relative to existing interaction detection techniques for detecting low-order interactions, attaining very low false-positive and false-negative rates while maintaining the same performance for prediction using a comparable computational budget.

We consider the problem of nonparametric regression in the high-dimensional setting in which $P \gg N$. We study the use of overlapping group structures to improve prediction and variable selection. These structures arise commonly when analyzing DNA microarray data, where genes can naturally be grouped according to genetic pathways. We incorporate overlapping group structure into a Bayesian additive regression trees model using a prior constructed so that, if a variable from some group is used to construct a split, this increases the probability that subsequent splits will use predictors from the same group. We refer to our model as an overlapping group Bayesian additive regression trees (OG-BART) model, and our prior on the splits an overlapping group Dirichlet (OG-Dirichlet) prior. Like the sparse group lasso, our prior encourages sparsity both within and between groups. We study the correlation structure of the prior, illustrate the proposed methodology on simulated data, and apply the methodology to gene expression data to learn which genetic pathways are predictive of breast cancer tumor metastasis.