不确定性处理：概率与模糊逻辑

# 不确定性处理：概率与模糊逻辑 ## 1. 确定性理论 ### 1.1 证据组合算法 在规则中，证据之间的关系通过“and”和“or”明确表示。若不同证据要独立地对单个假设做出贡献，则需放在不同规则中。证据组合算法借鉴了Zadeh的可能性理论，涵盖了合取（and）、析取（or）和否定（not）三种情况： - **合取**：对于形如“if <证据E1> and <证据E2> then <假设> with certainty factor <CF>”的规则，组合证据的确定性为 \(C(E_1 \text{ and } E_2) = \min[C(E_1), C(E_2)]\)。 - **析取**：对于形如“if <证据E1> or <证据E2> then <假设> with certainty factor <CF>”的规则，组合证据的确定性为 \(C(E_1 \text{ or } E_2) = \max[C(E_1), C(E_2)]\)。 - **否定**：对于形如“if not <证据E> then <假设> with certainty factor <CF>”的规则，否定证据的确定性为 \(C(\sim E) = 1 - C(E)\)。 ### 1.2 确定性理论示例 为说明确定性理论的应用，以电站锅炉安全阀是否需要清洗为例。有四条规则，每条规则都有规则编写者估计的确定性因子： ```plaintext uncertainty_rule r3_1c if release_valve is stuck then task becomes clean_release_valve with certainty factor 1.0 . uncertainty_rule r3_2c if warning_light is on then release_valve becomes stuck with certainty factor 0.2 . uncertainty_rule r3_3c if pressure is high then release_valve becomes stuck with certainty factor 0.9 . uncertainty_rule r3_4c if temperature is high and water_level is not low then pressure becomes high with certainty factor 0.5 . ``` 输入数据为： - water_level is not low. - warning_light is on. - temperature is high. 假设规则按 \(r3_4c \to r3_3c \to r3_2c \to r3_1c\) 的顺序触发，规则跟踪结果如下： ```plaintext uncertainty_rule r3_4c; CF = 0.5 H = pressure is high; C(H) = 0 E1 = temperature is high; C(E1) = 1 E2 = water_level is low; C(E2) = -1, C(~E2) = 1 C(E1&~E2) = min[C(E1),C(~E2)] = 1 CF' = CF × C(E1&~E2) = CF C(H|(E1&~E2)) = CF' = 0.5 /* Updated certainty of "pressure is high" is 0.5 */ uncertainty_rule r3_3c; CF = 0.9 H = release_valve is stuck; C(H) = 0 E = pressure is high; C(E) = 0.5 CF' = CF × C(E) = 0.45 C(H|(E)) = CF' = 0.45 /* Updated certainty of "release_valve is stuck" is 0.45 */ uncertainty_rule r3_2c; CF = 0.2 H = release_valve is stuck; C(H) = 0.45 E = warning_light is on; C(E) = 1 CF' = CF × C(E) = CF C(H|(E)) = C(H) + [CF' × (1-C(H))] = 0.56 /* Updated certainty of "release_valve is stuck" is 0.56 */ uncertainty_rule r3_1c; CF = 1 H = task is clean_release_valve; C(H) = 0 E = release_valve is stuck; C(E) = 0.56 CF' = CF × C(E) = 0.56 C(H|(E)) = CF' = 0.56 /* Updated certainty of "task is clean_release_valve" is 0.56 */ ``` ### 1.3 示例讨论 给定上述确定性因子，该示例得出安全阀需要清洗的结果，其置信度与贝叶斯更新示例相似。在贝叶斯更新中，规则 \(r3_2b\) 和 \(r3_3b\) 可合并为一条规则而不改变效果；但在确定性理论中，若将规则 \(r3_2c\) 和 \(r3_3c\) 合并，需选择一个单一的确定性因子。合并后的规则可能如下： ```plaintext uncertainty_rule r3_5c if warning_light is on and pressure is hig ```