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Soft Computing
Published in Vivek Kale, Digital Transformation of Enterprise Architecture, 2019
The purpose of rough sets is to discover knowledge in the form of business rules from imprecise and uncertain data sources. Rough set theory is based on the notion of indiscernibility and the inability to distinguish between objects, and provides an approximation of sets or concepts by means of binary relations, typically constructed from empirical data. As an approach to handling imperfect data, rough set analysis complements other more traditional theories such as probability theory, evidence theory, and fuzzy set theory. The intuition behind the rough set approach is the fact that in real life, when dealing with sets, we often have no means of precisely distinguishing individual set elements from each other due to limited resolution (lack of complete and detailed knowledge) and uncertainty associated with their measurable characteristics.
ROUGH SET
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
Rough set philosophy is based on the concept that with every object of the universe of discourse some information (data and knowledge) is associated. For instance, if objects ate patients suffering from a certain disease, symptoms of the disease form information about patients. Objects characterized by the same information are indiscernible (similar) in view of the available information about them. Thus, the indiscernibility relation is generated, which is the essence of rough set theory. Any set of all indiscernible (similar) objects is called an elementary set, which forms a basic granule (atom) of knowledge about the universe. Any union of some elementary sets is referred to as a crisp (precise) set, otherwise the set is rough (vague). Each rough set has boundary-line cases, that is, objects, which cannot be with certainty classified, by employing the available knowledge, as members of the set or its complement. Obviously, rough sets, in contrast to precise sets, cannot be characterized in terms of information about their elements. With any rough set a pair of precise sets, called the lower and the upper approximation of the rough set, is associated. The lower approximation consists of all objects, which surely belong to the set and the upper approximation contains all objects, which possibly belong to the set. The difference between the upper and lower approximation constitutes the boundary region of the rough set. Approximations are fundamental concepts of rough set theory [213, 214, 215].
Applying rough set theory to analyze the antecedents of customer satisfaction for homestay service quality in Kinmen
Published in Artde Donald Kin-Tak Lam, Stephen D. Prior, Siu-Tsen Shen, Sheng-Joue Young, Liang-Wen Ji, Innovation in Design, Communication and Engineering, 2020
Chien-Hua Wang*, Song-Bo Wang, Jich-Yan Tsai, Sheng-Hsing Liu
The rough set theory, proposed by Pawlak in 1982, can serve as a new mathematical tool for dealing with data-classification problems. It adopts the concept of equivalence classes to partition training instances according to some criteria. Two kinds of partitions are formed in the mining process: lower approximations and upper approximations, from which both certain and possible rules can easily be derived. It is widely used in knowledge extraction, information system analysis, and AI, and can also be applied to the correlation between multi-dimensional attribute data.
Missing data imputation for traffic flow based on combination of fuzzy neural network and rough set theory
Published in Journal of Intelligent Transportation Systems, 2021
Jinjun Tang, Xinshao Zhang, Weiqi Yin, Yajie Zou, Yinhai Wang
Rough set theory is a widely used tool for dealing with uncertainty. In the rough set theory, the information system is expressed as (X, A), where X is a limited set of data instance and A is a set of non-empty finite attributes. For BA, the indistinguishable relation of B is: where, RB is the equivalence relation. This particular information system contains decision attributes that contain classes for each data instance. If AX, then the upper and lower approximations of set A are defined as:
A weighted complement-entropy system based on tri-level granular structures
Published in International Journal of General Systems, 2020
Lingyu Tang, Xianyong Zhang, Zhiwen Mo
Rough set theory serves as a fundamental methodology of data analysis, and it can effectively identify decision rules and dependencies from data tables for information processing. Nowadays, it has been extensively applied in data mining, pattern recognition, machine learning, artificial intelligence, etc. (Raza and Qamar 2017; Saha, Sarkar, and Maulik 2019; Słowiński, Greco, and Matarazzo 2002; Xu and Guo 2016; Yuan, Zhang, and Feng 2018). Note that rough set theory has a basic data background, the decision table (Calvanese et al. 2018; Ge et al. 2017; Liu, Hua, and Zou 2018; Miao et al. 2009), and the relevant formal framework leads to the central theme of attribute reduction, which depends on optimization and generalization to gain in-depth insights (Boixader and Recasens 2018; Cornejo, Medina, and Ramirez-Poussa 2017; Fan, Liau, and Liu 2011; Honko 2016, 2018; Konecny 2017; Ma et al. 2014). In particular, Zhang and Miao (2017) fundamentally endow the decision table with a sort of tri-level granular structure, as is shown by later Figure 3, and thus, with attribute reduction, there are two basic hierarchical types, which are the prevailing classification-based reduction (Pawlak 1991) and the novel class-specific reduction (Ma and Yao 2018; Yao and Zhang 2017; Zhang, Yang, and Tang 2020; Zhang et al. 2020).
Affective design using machine learning: a survey and its prospect of conjoining big data
Published in International Journal of Computer Integrated Manufacturing, 2020
Kit Yan Chan, C.K. Kwong, Pornpit Wongthongtham, Huimin Jiang, Chris K.Y. Fung, Bilal Abu-Salih, Zhixin Liu, T.C. Wong, Pratima Jain
To address ambiguity in affective design evaluation, Nagamachi (2010) adopted rough set theory to address uncertainty in ambiguous data. The lower and upper approximations of affective customer needs are bounded in the rough set, where the lower approximations are certainly classified in the target classes and the upper approximations are vaguely covered in the target classes. When the lower and upper approximations are different, the approximations in the boundary region cannot be certainly classified into a class. Rough sets can be used to indicate uncertainties of approximations. The basic concept of rough set theory is to formulate an approximation of a crisp set from vague or imprecise information. Hence rough set theory can be applied in affective design evaluation which is ambiguous or subjective.