The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state and the observation noises. Recursive algorithms for the optimal local linear filter at each sensor as well as both centralized and distributed linear fusion estimators are derived using an innovation approach. The Tk-properness assumption implies a reduction in the dimension of the augmented system, which yields computational savings in the previously mentioned algorithms compared to their counterparts, which are derived from real or widely linear processing. A numerical simulation example illustrates the obtained theoretical results and allows us to visualize, among other aspects, the insignificant difference in the accuracy of both fusion filters, which means that the distributed filter, although suboptimal, is preferable in practice as it implies a lower computational cost.

Fuzzy Linear Programming Models for a Green Logistics Center Location and Allocation Problem under Mixed Uncertainties Based on Different Carbon Dioxide Emission Reduction Methods

This study explores a foundational logistics center location and allocation problem in a three-stage logistics network that consists of suppliers, logistics centers, and customers. In this study, the environmental sustainability of the logistics network is improved by optimizing the carbon dioxide emissions of the logistics network based on multi-objective optimization and carbon tax regulation. Mixed uncertainties in the planning stage, including the supply capacities of suppliers, operation capacities of logistics centers, and demands of customers, are modeled using triangular fuzzy numbers based on the fuzzy set theory to order to enhance the reliability of the logistics center location and allocation planning. To solve the green logistics center location and allocation problem under mixed uncertainties, we establish two fuzzy mixed integer linear programming models. The fuzzy credibilistic chance-constrained programming is then adopted to obtain the crisp and linear reformulations of the fuzzy programming models. A numerical case is given to verify the feasibility of the proposed methods, in which the performance of carbon tax regulation in reducing carbon dioxide emissions is then tested based on the benchmark provided by the multi-objective optimization. Lastly, sensitivity analysis and fuzzy simulation are utilized to reveal the effect of the mixed uncertainties on the logistics location and allocation planning and further determine the best confidence level in the fuzzy chance constraints to provide decision makers with a crisp plan.