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The purpose of this paper is to present research methods in processing uncertain information.

Vague set and rough set are both‐wings‐mode for expressing uncertainty systems, and based on the both‐wings‐mode of expressing uncertainty systems, the connections of vague set and rough set are discussed.

This paper presents the relationships between vague set and rough set.

Based on these connections between vague set and rough set, theoretical and means of vague set can be used for rough set; also theoretical and means of rough set can be used for vague set.

The paper contributes to the discussion on the research of vague set and rough set. The conclusions are useful in information processing.

The rough set concept is a new mathematical approach to imprecision, vagueness and uncertainty. This paper introduces the emergent computational paradigm and discusses its applicability and potential in rough set theory.

A conceptual discussion and approach are taken.

For accepting a system is displaying an emergent behavior, the system should be constructed by describing local elementary interactions between components in different ways of describing global behavior and properties of the running system over a period of time. The proposals of an emergent computation structure for implementing basic rough sets theory operators are also given in this paper.

The results will have an important impact on the development of new methods for knowledge discovery in databases, in particular for development of algorithmic methods for pattern extraction from data.

The purpose of this paper is to present a measure method of the uncertainty for rough fuzzy set based on general binary relation.

Rough set and fuzzy set are two different but complementary theories for expressing uncertainty information, and based on the combination of these two uncertainty theories of expressing and handling uncertainty information, the rough fuzzy set model and uncertainty measure based on general relation are discussed.

This paper reveals the intrinsic of the uncertainty for rough fuzzy set based on general relation and presents a new measure method by introducing the Shannon entropy to generalized approximation space.

The paper contributes to the discussion on the research of rough set and fuzzy set. The conclusions are useful in information processing with uncertainty.

The purpose of this paper is to propose an innovative integration method based on decision-theoretic rough set and the extended VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) methods to address the resilient-sustainable supplier selection and order allocation (SS/OA) problem.

Specifically, a two-stage approach is designed in this paper. First, the decision-theoretic rough set is employed to calculate the rough number for coping with the subjective uncertainty of data and assigning the weights for a resilient-sustainable evaluation criterion. On this basis, the supplier resilient-sustainable performance is ranked in combination with the extended VIKOR method. Second, a novel multi-objective optimization model is proposed that applies an improved genetic algorithm to select the resilient-sustainable supplier and allocate the corresponding order quantity under a multi-tier supplier network.

The results reveal that joint consideration of resilience and sustainability is essential in the SS/OA process. The method proposed in this study based on decision-theoretic rough sets and the extended VIKOR method can handle imprecise information flexibly, reduce information loss and obtain acceptable solutions for decision-makers. Numerical cases validate that this integrated approach can combine resilience and sustainability for effective and efficient SS/OA.

This paper provides industry managers with a new perspective on SS/OA from a resilience and sustainability perspective as a basis for best practices for industry resilience and sustainability. The proposed method helps to evaluate the resilient-sustainable performance of potential suppliers, which is applicable to solving real-world SS/OA problems and has important practical implications for the resilient-sustainable development of supply chains.

The two interrelated priorities of resilience and sustainability have emerged as key strategic challenges in SS/OA issues. This paper is the first study of this issue that uses the proposed integrated approach.

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

This paper aims to utilize machine learning and soft computing to propose a new method of rough sets using deep learning architecture for many real-world applications.

The objective of this work is to propose a model for deep rough set theory that uses more than decision table and approximating these tables to a classification system, i.e. the paper propose a novel framework of deep learning based on multi-decision tables.

The paper tries to coordinate the local properties of individual decision table to provide an appropriate global decision from the system.

The rough set learning assumes the existence of a single decision table, whereas real-world decision problem implies several decisions with several different decision tables. The new proposed model can handle multi-decision tables.

The proposed classification model is implemented on social networks with preferred features which are freely distribute as social entities with accuracy around 91 per cent.

The deep learning using rough sets theory simulate the way of brain thinking and can solve the problem of existence of different information about same problem in different decision systems

This paper utilizes machine learning and soft computing to propose a new method of rough sets using deep learning architecture for many real-world applications.

This paper aims to introduce relatively novel multi‐supply chain activity overview rough set theoretic applications to aid management decision making with an especial focus on green and sustainable supply chain management.

The methodology is a review of recent literature with extensions around rough set or neighborhood rough set methodologies for supply chain management. An overview of how the techniques can be applied to various stages of green supply chain management, selection, evaluation, development is presented in various sections.

The paper finds that rough set methodology is flexible enough to be applied as a selection tool, performance measurement evaluation tool, and a development program evaluation tool. Its application to green supply chain management topics is warranted and valuable.

Limitations of the approach provide additional avenues for further research. One major limitation of the research is that a real‐world application to validate the approaches is necessary. Extensions and integration with other tools can also provide avenues for improvement.

A three‐staged ecological green supplier management process may help to get a broader corporate social responsibility and general sustainability perspective on the supply chain. Management can use these tools for planning, decision making, and maintenance of green supply chain activities.

The application of sustainability and environmental issues for supply chain management has significant social impact.

Methodologically, this is the first time that neighborhood rough set has been comprehensively evaluated as a tool for managing green suppliers. A comprehensive overview of the green supplier management process considering the sustainability factors helps researchers to identify many opportunities for further investigation.

The purpose of this paper is to introduce a methodology to identify sustainable supply chain key performance indicators (KPI) that can then be used for sustainability performance evaluation for suppliers.

Initially the complexity of sustainable supply chain performance measurement is discussed. Then, a two-stage method utilizing neighborhood rough set theory to identify KPI and data envelopment analysis (DEA) to benchmark and evaluate relative performance using the KPI is completed. Additional analysis is performed to determine the sensitivity of the KPI set formation and performance results.

The results show that KPI can be determined using neighborhood rough set, and DEA performance results provide insight into relative performance of suppliers. The supply chain sustainability performance results from both the neighborhood rough set and DEA can be quite sensitive parameters selected and sustainability KPI sets that were determined.

The data utilized in this study are illustrative and simulated. Only one model for the neighborhood rough set and DEA was utilized. Additional investigations using a variation of rough set and DEA models can be completed.

This tool set is valuable for managers to help identify sustainable supply chain KPI (from among hundreds of potential measures) and evaluate sustainability performance of various units within supply chains, including supply chain partners, departments, projects and programs.

Sustainability incorporates many business, economic and social implications. The methods introduced in this paper can help organizations and their supply chains become more strategically and operationally sustainable.

Few tools and techniques exist in the sustainable supply chain literature to help develop KPIs and evaluate sustainability performance of suppliers and the supply chain. This paper is one of the first that integrates neighborhood rough set and DEA to address this important sustainable supply chain performance measurement issue.

Text mining has been used for various knowledge discovery based applications, and thus, a lot of research has been contributed towards it. Latest trending research in the text mining is adopting the incremental learning data, as it is economical while dealing with large volume of information.

The primary intention of this research is to design and develop a technique for incremental text categorization using optimized Support Vector Neural Network (SVNN). The proposed technique involves four major steps, such as pre-processing, feature selection, classification and feature extraction. Initially, the data is pre-processed based on stop word removal and stemming. Then, the feature extraction is done by extracting semantic word-based features and Term Frequency and Inverse Document Frequency (TF-IDF). From the extracted features, the important features are selected using Bhattacharya distance measure and the features are subjected as the input to the proposed classifier. The proposed classifier performs incremental learning using SVNN, wherein the weights are bounded in a limit using rough set theory. Moreover, for the optimal selection of weights in SVNN, Moth Search (MS) algorithm is used. Thus, the proposed classifier, named Rough set MS-SVNN, performs the text categorization for the incremental data, given as the input.

For the experimentation, the 20 News group dataset, and the Reuters dataset are used. Simulation results indicate that the proposed Rough set based MS-SVNN has achieved 0.7743, 0.7774 and 0.7745 for the precision, recall and F-measure, respectively.

In this paper, an online incremental learner is developed for the text categorization. The text categorization is done by developing the Rough set MS-SVNN classifier, which classifies the incoming texts based on the boundary condition evaluated by the Rough set theory, and the optimal weights from the MS. The proposed online text categorization scheme has the basic steps, like pre-processing, feature extraction, feature selection and classification. The pre-processing is carried out to identify the unique words from the dataset, and the features like semantic word-based features and TF-IDF are obtained from the keyword set. Feature selection is done by setting a minimum Bhattacharya distance measure, and the selected features are provided to the proposed Rough set MS-SVNN for the classification.

The purpose of this paper is to advance a novel grey variable dual precision rough set model for grey concept.

To obtain the approximation of a grey object, the authors first define the concepts of grey rough membership degree and grey degree of approximation on the basic thinking logic of variable precision rough set. Based on grey rough membership degree and grey degree of approximation, the authors proposed a grey variable dual precision rough set model. It uses a clear knowledge concept to approximate a grey concept, and the output result is also a clear concept.

The result demonstrates that the proposed model may be closer to the actual decision-making situation, can effectively improve the rationality and scientificity of the approximation and reduce the risk of decision-making. It can effectively achieve the whitenization of grey objects. The model can be degenerated to traditional variable precision rough fuzzy set model, variable precision rough set model and classic Pawlak rough set, when some specific conditions are met.

The method exposed in the paper can be used to solve multi-criteria decision problems with grey decision objects and provide a decision rule. It can also help us better realize knowledge discovery and attribute reduction. It can effectively achieve the whitenization of grey object.

This method proposed in this paper implements a rough approximation of grey decision object and obtains low-risk probabilistic decision rule. It can effectively achieve a certain degree of whitenization of some grey objects.