| 双论域上的广义直觉模糊概率粗糙集模型及其应用 |
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| 引用本文： | 梁美社1,米据生2,张少谱1. 双论域上的广义直觉模糊概率粗糙集模型及其应用[J]. 智能系统学报, 2022, 17(3): 585-592. DOI: 10.11992/tis.202106025 |
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| 作者姓名： | 梁美社1 米据生2 张少谱1 |
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| 作者单位： | 1. 石家庄铁道大学 数理系，河北 石家庄 050043;2. 河北师范大学 数学科学学院，河北 石家庄 050024 |
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| 摘 要： | 已有的双论域直觉模糊概率粗糙集模型通过设置两个阈值${lambda _1}$、${lambda _2} $，讨论了经典集合在直觉模糊二元关系下的概率粗糙下上近似。该模型不能计算直觉模糊集合在直觉模糊二元关系下的概率粗糙下上近似，这在一定程度上限制了该模型的应用。首先给出了直觉模糊条件概率的定义。在直觉模糊概率空间下构造了双论域广义直觉模糊概率粗糙集模型，讨论了模型的主要性质。最后，将模型应用到临床诊断系统中。与其他模型相比，所提出的广义直觉模糊概率粗糙集模型进一步丰富了概率粗糙集理论，更适合于实际应用。
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| 关 键 词： | 双论域 粗糙集 直觉模糊关系 概率粗糙集 直觉模糊集 直觉模糊概率近似空间 下近似 上近似 |
Generalized intuitionistic fuzzy probabilistic rough set models on two universes and their applications |
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| LIANG Meishe1,MI Jusheng2,ZHANG Shaopu1. Generalized intuitionistic fuzzy probabilistic rough set models on two universes and their applications[J]. CAAL Transactions on Intelligent Systems, 2022, 17(3): 585-592. DOI: 10.11992/tis.202106025 |
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| Authors: | LIANG Meishe1 MI Jusheng2 ZHANG Shaopu1 |
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| Affiliation: | 1. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;2. School of Mathematics Science, Hebei Normal University, Shijiazhuang 050024, China |
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| Abstract: | In the existing intuitionistic fuzzy (IF) probabilistic rough set model of two universes, the probabilistic rough lower and upper approximations of a classical set under IF binary relation are discussed by setting two thresholds, ${lambda _1};{rm{and}};{lambda _2}$. However, this model is unable to calculate the probabilistic rough lower and upper approximations of IF sets under IF binary relation, which limits the application of this model to a certain extent. In this study, we first define the IF conditional probability. Then, the generalized IF probability rough set models are constructed in IF probabilistic approximation space. In addition, the main properties of the model are discussed. Finally, the numerical examples of clinical diagnostic systems are applied to illustrate the validity of the proposed models. Compared with other models, the proposed generalized IF probabilistic rough set models further enrich the probabilistic rough set theory and are more suitable for practical applications. |
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| Keywords: | two universes rough set intuitionistic fuzzy relations probabilistic rough set intuitionistic fuzzy sets intuitionistic fuzzy probabilistic approximation spaces lower approximation upper approximation |
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