A PROMETHEE II-BELIEFapproach for multi-criteria decision-making problems with incomplete information

Multi-criteria decision aid methods consider decision problems in which many alternatives are evaluated on several criteria. These methods are used to deal with perfect information. However, in practice, it is obvious that this information requirement is too strict. In fact, the imperfect data provided by more or less reliable decision makers usually affect decision results, since any decision is closely linked to the quality and availability of information. In this paper, a PROMETHEE II-BELIEF approach is proposed to help multi-criteria decisions based on incomplete information. This approach solves problems with incomplete decision matrix and unknown weights within PROMETHEE II method. On the basis of belief function theory, our approach first determines the distributions of belief masses based on PROMETHEE II’s net flows, and then calculates weights. Subsequently, it aggregates the distribution masses associated with each criterion using Murphy’s modified combination rule in order to infer a global belief structure. The final alternative ranking is obtained via pignistic probability transformation. A case study of a real-world application concerning the location of a treatment center of waste from healthcare activities with infectious risk in the center of Tunisia is studied to illustrate the detailed process of the PROMETHEE II-BELIEF approach. Keywords: multiple criteria aid, incomplete information, PROMETHEE II method, belief function theory.

Multi-Target Joint Detection; Tracking and Classification Based on Marginal GLMB Filter and Belief Function Theory

This paper proposes a new solution to multi-target joint detection, tracking and classification based on labeled random finite set (RFS) and belief function theory. A class dependent multi-model marginal generalized labeled multi-Bernoulli (MGLMB) filter is developed to analytically calculate the multi-target number, state estimates and model probabilities. In addition, a two-level classifier based on continuous transferable belief model (cTBM) is designed for target classification. To make full use of the kinematic characteristics for classification, both the dynamic modes and states are considered in the classifier, the model dependent class beliefs are computed on the continuous state feature subspace corresponding to different dynamic modes and then fused. As a result that the uncertainty about the classes is well described for decision, the classification results are more reasonable and robust. Moreover, as the estimation and classification problems are jointly solved, the tracking and classification performance are both improved. In the simulation, a scenario contains multi-target with miss detection and dense clutter is used. The performance of multi-target detection, tracking and classification is better than traditional methods based on Bayesian classifier or single model. Simulation results are illustrated to demonstrate the effectiveness and superiority of the proposed algorithm.

Multi-Objective Redundancy Allocation for Multi-State System Design Under Epistemic Uncertainty of Component States

Multi-state is a typical characteristic of engineered systems. Most existing studies of redundancy allocation problems (RAPs) for multi-state system (MSS) design assume that the state probabilities of redundant components are precisely known. However, due to lack of knowledge and/or ambiguous judgements from engineers/experts, the epistemic uncertainty associated with component states cannot be completely avoided and it is befitting to be represented as belief quantities. In this paper, a multi-objective RAP is developed for MSS design under the belief function theory. To address the epistemic uncertainty propagation from components to system reliability evaluation, an evidential network (EN) model is introduced to evaluate the reliability bounds of an MSS. The resulting multi-objective design optimization problem is resolved via a modified non-dominated sorting genetic algorithm II (NSGA-II), in which a set of new Pareto dominance criteria is put forth to compare any pair of feasible solutions under the belief function theory. A numerical case along with a SCADA system design is exemplified to demonstrate the efficiency of the EN model and the modified NSGA-II. As observed in our study, the EN model can properly handle the uncertainty propagation and achieve narrower reliability bounds than that of the existing methods. More importantly, the original nested design optimization formulation can be simplified into a one-stage optimization model by the proposed method.