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摘要:
冲突证据决策方法研究是证据理论重要研究课题。鉴于现有的证据理论改进方法在冲突证据决策过程中存在计算量较大,归一化过程不合理,证据组合效果不理想等一系列问题,提出基于二次组合的冲突证据决策方法。首先,提出新的基于二次组合的冲突证据决策方法的流程图;然后,提出新的乘性归一化规则,并对新的乘性归一化规则进行算例分析,验证其合理性;最后,分析现有冲突度量函数的不足,并提出新的冲突度量函数,并分析冲突度量函数的合理性。通过算例分析,并与现有证据组合规则的比较表明,所提方法不仅计算量得以改善,组合结果也得到提升。
Abstract:Research on conflict evidence decision methods is an important research topic of evidence theory. In view of the existing problems in the evidence theory improvement process, such as large computational complexity, unreasonable normalization process and unsatisfactory evidence combination, this paper proposes a method based on quadratic combination for conflict evidence decision-making. Firstly, the paper proposes a new flowchart of conflict evidence decision method based on quadratic combination. Secondly, a new multiplicative normalization rule is proposed, and a new multiplicative normalization rule is analyzed by example to verify its rationality. Finally, the shortcomings of the existing conflict measurement function are analyzed, a new conflict measurement function is proposed, and the rationality of the conflict measurement function is analyzed. Through the analysis of examples and the comparison with the existing evidence combination rules, it is shown that the proposed method not only improves the calculation amount, but also improves the combination results.
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表 1 加性与乘性归一化折扣证据组合结果
Table 1. Additive and multiplicative normalized discount evidence combination results
组合规则 mi(A) mi(B) mi(AB) mi(C) mi(AC) mi(BC) mi(ABC) PCR6 0.5436 0.0939 0.0403 0.2544 0.0224 0.0454 0 PCR6+ 0.5386 0.0938 0.0314 0.0588 0.0095 0.0205 0.2475 PCR6× 0.6379 0.0751 0.0622 0.0523 0.0641 0.1083 0 表 2 证据组BPAs
Table 2. Evidence group BPAs
mi(·) BPA A B AB C AC BC ABC m1 0.7 0.1 0.1 0.1 0 0 0 m2 0.6 0.2 0 0.1 0 0 0.1 m3 0.6 0.05 0 0.05 0 0 0.3 m4 0.4 0.3 0 0.2 0.1 0 0 m5 0.1 0.7 0 0.1 0 0 0.1 m6 0.9 0.05 0 0.05 0 0 0 表 3 折扣证据组BPAs
Table 3. Discounted evidence group BPAs
mi′(·) BPA A B AB C AC BC ABC m′1 0.74 0.11 0.04 0.11 0 0 0 m′2 0.64 0.21 0 0.11 0 0 0.05 m′3 0.72 0.06 0 0.06 0 0 0.16 m′4 0.40 0.30 0 0.20 0.10 0 0 m′5 0.03 0.21 0 0.03 0 0 0.73 m′6 0.90 0.05 0 0.05 0 0 0 表 4 算例不同组合规则计算结果
Table 4. Calculation results of different combination rules of example
组合规则 mi(A) mi(B) mi(AB) mi(C) mi(AC) mi(BC) mi(ABC) PCR1 0.57 0.22 0.02 0.10 0.02 0 0.08 PCR2 0.57 0.22 0.02 0.10 0.02 0 0.08 PCR3 0.67 0.24 0 0.06 0 0 0.04 PCR5 0.46 0.35 0.01 0.07 0.01 0 0.10 PCR6 0.72 0.21 0 0.03 0 0 0.04 本文方法 0.77 0.07 0 0.02 0 0 0.14 -
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