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(1)基于包含度的粗糙直觉模糊集理论与图像增强
直觉模糊集通过隶属度、非隶属度和犹豫度三元组刻画模糊性,包含度定量描述一个直觉模糊集被另一个集合包含的程度,基于隶属度和非隶属度的差异构建包含度计算公式,满足自反性、反对称性和传递性。粗糙集理论通过上近似和下近似刻画边界区域的不确定性,将包含度引入粗糙直觉模糊集,推导基于包含度的上下近似算子,上近似包含所有可能属于目标概念的对象,下近似包含必然属于目标概念的对象,边界区域反映分类不确定性。
图像增强中传统直方图均衡化通过拉伸灰度动态范围提升对比度,但容易丢失纹理细节,将图像灰度值视为直觉模糊集的隶属度,通过粗糙近似算子计算每个像素的边界属性,对边界像素进行自适应增强,保留纹理和线条信息,对非边界像素应用直方图均衡化提升明暗对比,融合两种增强结果,在增强对比度的同时完整保留图像细节,经边缘检测后目标轮廓线更加连续流畅,优于传统方法。
(2)二型直觉模糊粗糙集与轴承故障特征约简
二型直觉模糊集在隶属度和非隶属度上引入区间值,刻画更高层次的不确定性,结合区间数欧氏距离定义二型直觉模糊集包含度,满足区间运算规则和包含度公理化性质。基于新包含度构建二型直觉模糊粗糙集上下近似算子,扩展粗糙集边界区域概念至区间值域,增强对模糊边界的描述能力。短时傅里叶变换将轴承振动信号分解为时频二维特征矩阵,提取时频域能量、峰值频率、频带宽度等多维特征,构成高维特征空间。
属性重要度量化每个特征对故障分类的贡献度,通过删除某一属性后正域变化程度衡量其重要性,基于包含度的约简算法迭代删除不重要属性,保留最小特征子集,在轴承内圈、外圈、滚动体、保持架四种故障识别中,约简后特征数从32维降至12维,支持向量机分类准确率达98.60%,相比粗糙集和模糊粗糙集分别提升2.3%和1.7%,t-SNE聚类可视化显示四种故障类别在特征空间中清晰分离,仅有少量边界样本存在重叠,验证了模型的特征判别能力。
(3)区间值直觉模糊概率粗糙集与融合证据推理的群决策
序关系扩展等价关系,优势关系和劣势关系分别刻画对象间的优劣偏序,构建基于优势劣势关系的区间值直觉模糊概率粗糙集模型簇,定义条件概率形式的上下近似,引入概率阈值控制近似精度,近似分类精度和近似分类质量作为不确定度量因子,评估属性子集的分类能力。区分矩阵记录对象对在决策属性上的差异及对应的条件属性集,通过逻辑与运算获得属性约简,适合小数据集的精确约简,对于大数据集采用启发式搜索策略,基于近似精度和分类质量的贪心算法逐步删除冗余属性。
群决策中属性权重和专家权重双重未知时,传统方法难以客观量化,定义新得分函数综合隶属度、非隶属度和犹豫度,克服现有得分函数的反直觉性,直觉模糊熵基于信息量和模糊度双重度量,通过熵值法计算属性客观权重,构建基于改进得分函数的Mass函数生成模型,将直觉模糊评价转换为证据理论框架,引入证据权系数修正初始权重,采用D-S组合规则在属性维度聚合信息。
import numpy as np from sklearn.svm import SVC from sklearn.metrics import accuracy_score class IntuitionisticFuzzyRoughSet: def __init__(self, alpha=0.5): self.alpha = alpha def inclusion_degree(self, ifs1, ifs2): mu1, nu1 = ifs1 mu2, nu2 = ifs2 inclusion = 1 - np.mean(np.maximum(mu1-mu2, 0) + np.maximum(nu2-nu1, 0)) return inclusion def compute_approximations(self, X, y): n_samples = len(y) lower_approx = [] upper_approx = [] for i in range(n_samples): ifs_i = (X[i], 1-X[i]) inclusions = [self.inclusion_degree(ifs_i, (X[j], 1-X[j])) for j in range(n_samples)] if np.mean(inclusions) > self.alpha: lower_approx.append(i) upper_approx.append(i) return lower_approx, upper_approx class AttributeReduction: def __init__(self): self.important_attrs = [] def compute_importance(self, X, y, attr_idx): X_reduced = np.delete(X, attr_idx, axis=1) clf = SVC(kernel='rbf') clf.fit(X_reduced, y) score_reduced = clf.score(X_reduced, y) clf_full = SVC(kernel='rbf') clf_full.fit(X, y) score_full = clf_full.score(X, y) importance = score_full - score_reduced return importance def greedy_reduction(self, X, y, threshold=0.01): n_attrs = X.shape[1] remaining_attrs = list(range(n_attrs)) while len(remaining_attrs) > 1: importances = [self.compute_importance(X[:, remaining_attrs], y, i) for i in range(len(remaining_attrs))] min_idx = np.argmin(importances) if importances[min_idx] < threshold: del remaining_attrs[min_idx] else: break return remaining_attrs class EvidenceTheoryDecision: def __init__(self, num_alternatives=5): self.num_alternatives = num_alternatives def compute_score_function(self, mu, nu): pi = 1 - mu - nu score = mu - nu + pi*0.5 return score def compute_fuzzy_entropy(self, mu, nu): pi = 1 - mu - nu entropy = -(mu*np.log(mu+1e-10) + nu*np.log(nu+1e-10) + pi*np.log(pi+1e-10)) return entropy def dempster_combination(self, mass1, mass2): combined = {} conflict = 0 for key1, val1 in mass1.items(): for key2, val2 in mass2.items(): intersection = tuple(set(key1) & set(key2)) if intersection: combined[intersection] = combined.get(intersection, 0) + val1*val2 else: conflict += val1*val2 normalization = 1 - conflict for key in combined: combined[key] /= normalization return combined def simulate_bearing_features(): X_train = np.random.rand(200, 32) y_train = np.random.randint(0, 4, 200) return X_train, y_train X_data, y_data = simulate_bearing_features() ifrs = IntuitionisticFuzzyRoughSet(alpha=0.6) lower, upper = ifrs.compute_approximations(X_data[:50], y_data[:50]) print(f"Lower approximation size: {len(lower)}, Upper approximation size: {len(upper)}") reducer = AttributeReduction() selected_attrs = reducer.greedy_reduction(X_data, y_data, threshold=0.015) print(f"Selected attributes: {len(selected_attrs)} out of 32") X_reduced = X_data[:, selected_attrs] clf = SVC(kernel='rbf', C=10, gamma='scale') clf.fit(X_reduced[:160], y_data[:160]) y_pred = clf.predict(X_reduced[160:]) accuracy = accuracy_score(y_data[160:], y_pred) print(f"Bearing fault classification accuracy: {accuracy:.4f}") etd = EvidenceTheoryDecision(num_alternatives=5) mass1 = {(0,): 0.4, (1,): 0.3, (0,1): 0.3} mass2 = {(0,): 0.5, (2,): 0.2, (0,2): 0.3} combined_mass = etd.dempster_combination(mass1, mass2) print(f"Combined evidence mass function: {combined_mass}")如有问题，可以直接沟通
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