Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

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The weapon-target assignment (WTA) problem is a key issue in Command & Control (C2). Asset-based multiobjective static WTA (MOSWTA) problem is known as one of the notable issues of WTA. Since this is an NP-complete problem, multiobjective evolutionary algorithms (MOEAs) can be used to solve it effectively. The multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a practical and promising multiobjective optimization technique. However, MOEA/D is originally designed for continuous multiobjective optimization which loses its efficiency to discrete contexts. In this study, an improved MOEA/D is proposed to solve the asset-based MOSWTA problem. The defining characteristics of this problem are summarized and analyzed. According to these characteristics, an improved MOEA/D framework is introduced. A novel decomposition mechanism is designed. The mating restriction and selection operation are reformulated. Furthermore, a problem-specific population initialization method is presented to improve the efficiency of the proposed algorithm, and a novel nondominated solution-selection method is put forward to handle the constraints of Pareto front. Appropriate extensions of four MOEA variants are developed in comparison with the proposed algorithm on some generated scenarios. Extensive experiments demonstrate that the proposed method is effective and promising.

The weapon-target assignment (WTA) problem is a crucial decision issue in the process of cooperative aerial warfare (CAW). The decision strategy of fighter teams involved in the CAW is susceptible to the influence of the enemy fire attack and electronic interference, which will lead to both the antagonism and uncertainty of the decision making. In this paper, a novel antagonistic game WTA (AGWTA) model with uncertainty is introduced. The antagonism is described by a non-cooperative zero-sum game model conducted by two fighter teams. Then, a modified sensor data fusion method using belief entropy and similarity of sensor data is presented to manage the uncertainty of AGWTA. According to the characteristics of the AGWTA model, a decomposition co-evolution algorithm (DCEA-AGWTA) is proposed to obtain the non-cooperative Nash equilibrium (NCNE) strategy. The experimental results show that the modified sensor data fusion method contributes to higher reliability of target type identification and the AGWTA model is meaningful in the antagonistic and uncertain situation of CAW. In addition, the DCEA-AGWTA is effective and has a promising ability in finding the closest strategy to the NCNE strategy compared with the other three intelligent evolution-based algorithms.INDEX TERMS Antagonistic game WTA model with uncertainty, decomposition co-evolution algorithm, non-cooperative Nash equilibrium strategy, sensor data fusion.