Rough Set Research Articles

A Method to Handle the Missing Values in Multi-Criteria Sorting Problems Based on Dominance Rough Sets

The handling of missing attribute values remains a challenging and problematic issue in data analysis. Imputation techniques are key procedures used to deal with missing attribute values. However, although these methods are widely used, they cause data bias. Rough set theory, a unique mathematical tool for decision making under uncertainty, overcomes this problem by properly adjusting the relationships. Rough sets are often preferred in both classification and sorting problems. The aim of sorting problems is to sort the objects in the decision table (DT) from best to worst and/or to select the best one. For this purpose, it is necessary to obtain a pairwise comparison table (PCT) from the DT. However, in the presence of missing values, the transformation from DT to PCT is not feasible because there are no ranking methods in the literature for sorting problems based on rough sets. To address this limitation, this paper presents a way to transform from DT to PCT and introduces a generalization of the relation belonging to the “do not care” type of missing values in the dominance-based rough set approach (DRSA) to the decision support tool jRank. We also adapted the DomLem algorithm to enable it to work in PCT with missing values. We applied our method step by step to a decision table with 11 objects and investigated the effect of missing values. The experimental results showed that our proposed approach captures the semantics of `do not care’ type missing values.

Intuitionistic Fuzzy Sequential Three-Way Decision Model in Incomplete Information Systems

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods.

New Insights into Rough Set Theory: Transitive Neighborhoods and Approximations

Rough set theory is a methodology that defines the definite or probable membership of an element for exploring data with uncertainty and incompleteness. It classifies data sets using lower and upper approximations to model uncertainty and missing information. To contribute to this goal, this study presents a newer approach to the concept of rough sets by introducing a new type of neighborhood called j-transitive neighborhood or j-TN. Some of the basic properties of j-transitive neighborhoods are studied. Also, approximations are obtained through j-TN, and the relationships between them are investigated. It is proven that these approaches provide almost all the properties provided by the approaches given by Pawlak. This study also defines the concepts of lower and upper approximations from the topological view and compares them with some existing topological structures in the literature. In addition, the applicability of the j-TN framework is demonstrated in a medical scenario. The approach proposed here represents a new view in the design of rough set theory and its practical applications to develop the appropriate strategy to handle uncertainty while performing data analysis.

Rough and T-Rough Sets Arising from Intuitionistic Fuzzy Ideals in BCK-Algebras

Rough and T-Rough Sets Arising from Intuitionistic Fuzzy Ideals in BCK-Algebras

Evaluation of geomorphological classification uncertainty using rough set theory: A case study of Shaanxi Province, China

AbstractGeomorphological classification is affected by classification principles, indicators, methods, and data resolution, which can lead to uncertainty in the results. Such uncertainty directly affects the quality and subsequent applications of geomorphological classification. To quantify and control the uncertainty, it is important to select an appropriate and effective method for evaluating the uncertainty of geomorphological classification. This study evaluated the uncertainty of geomorphological classification of Shaanxi Province at the ground‐feature class and image scales, which derived from rough set theory: rough entropy, approximate classification quality, and approximate classification accuracy. The three indicators helped effectively assess the uncertainty of geomorphological classification at multi‐scale and measured the degree to which different factors affected the uncertainty of geomorphological classification. The relative impacts of three factors on the uncertainty of classification decreased in the order of classification methods, data resolution, and classification indicators. This finding is helpful to objectively evaluate and control the uncertainty generated in the process and results of geomorphological classification, and can provide targeted reference and guidance for future geomorphological classification work, which is more conducive to decision‐making and application. At the same time, this study is also a beneficial supplement to the geomorphological research based on digital terrain analysis.

Emergent Model Based On Hybrid Rough Sets Systems

The development of many knowledge discovery methods provided us with a good foundation for building hybrid systems based on rough set theory for knowledge discovery in a database. The need for more effective methods of generating and maintaining global nonfunctional properties suggests an approach analogous to those of natural processes in generating emergent properties. An emergent model allows the constraints of the task to be represented more naturally and permits only pertinent task-specific knowledge to emerge in the course of solving the problem. This paper describes some basics of emergent phenomena and its implementation in the hybrid system of rough sets combined with other methods. Further, demonstrations and guidelines are presented on how to exploit emergent intelligence and extend the problem-solving capabilities of these hybrid systems.

Rough set theory-based multi-class decision-making framework for cost-effective treatment

Rough set theory-based multi-class decision-making framework for cost-effective treatment

Photovoltaic Power Prediction Based on NRS-PCC Feature Selection and Multi-Scale CNN-LSTM Network

To improve the quality of photovoltaic (PV) data and power prediction accuracy, a PV power prediction method based on neighborhood rough set and Pearson correlation coefficient (NRS-PCC) feature selection and multi-scale convolutional neural networks and long short-term memory (CNN-LSTM) network is proposed. We first calculate the correlation between different PV features based on PCC and select strongly correlated features to cross-multiply to get the fusion features to enrich the data source. Then, dimensionality reduction of the fusion features by NRS. Finally, correlation analysis based on PCC on the dimensionality reduction of the fusion features to screen out the effective features. Furthermore, a multi-scale CNN-LSTM is designed to predict PV power. The output vectors of different convolutional layers are first fused to extract multi-scale features, then the features of different scales are spliced as the input of the LSTM network, and finally, the LSTM network performs regression prediction. The effectiveness of the proposed method is verified on a real PV power dataset.

Gaussian estimates vs. elliptic regularity on open sets

AbstractGiven an elliptic operator $$L= - {{\,\textrm{div}\,}}(A \nabla \cdot )$$ L = - div ( A ∇ · ) subject to mixed boundary conditions on an open subset of $$\mathbb {R}^d$$ R d , we study the relation between Gaussian pointwise estimates for the kernel of the associated heat semigroup, Hölder continuity of L-harmonic functions and the growth of the Dirichlet energy. To this end, we generalize an equivalence theorem of Auscher and Tchamitchian to the case of mixed boundary conditions and to open sets far beyond Lipschitz domains. Yet, we prove the consistency of our abstract result by encompassing operators with real-valued coefficients and their small complex perturbations into one of the aforementioned equivalent properties. The resulting kernel bounds open the door for developing a harmonic analysis for the associated semigroups on rough open sets.

Dominance-Based Rough Set Model in Hesitant Fuzzy Information Systems

Hesitant fuzzy information systems have been widely applied in decision-making due to their ability to handle uncertain information. In addition, dominance relationships are often taken into account in many practical decision-making problems. Therefore, it is of great significance to conduct research on hesitant fuzzy information systems involved with dominance relations. In this study, we introduce dominance relations in a hesitant fuzzy information system to make it a dominance-based hesitant fuzzy information system, which can provide a solid new idea for comparing hesitant fuzzy elements. Furthermore, a hesitant fuzzy dominance-based rough set model is constructed, and an attribute reduction method is designed to simplify the dominance-based hesitant fuzzy information system. Further, we propose lower and upper approximation discernibility matrices in the dominance-based hesitant fuzzy decision information system to extract decision rules. In addition, two numerical examples are given to demonstrate the effectiveness of the proposed attribute reduction methods.

Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed.

Rapid and optimized parallel attribute reduction based on neighborhood rough sets and MapReduce

Attribute reduction is a crucial step in data pre-processing and feature engineering. It is the selection of a subset of relevant data attributes to reduce the computational complexity of machine learning models and improve their performance. Neighborhood rough set (NRS) theory provides a valuable framework for attribute reduction. It leverages neighborhood information to identify non-redundant and informative attributes for data analysis and machine learning tasks. Attribute subsets based on NRS theory are highly qualitative, producing effective prediction accuracies in Euclidean space. However, existing NRS-based solutions are resource-intensive because of the large search space required for finding neighborhoods and redundant computations. To overcome these limitations, we propose the rapid and optimized attribute reduction (ROAR) algorithm that optimizes the current state-of-the-art attribute-reduction method in NRS theory. The strength of ROAR lies in its ability to accelerate computations by rapidly determining the neighborhood consistency of data samples and consequently expediting the identification of both positive and boundary regions. This efficiency significantly enhances the overall processing time for the data analysis tasks. Experimental results on 12 standard datasets demonstrate that the ROAR algorithm exhibits high efficiency by obtaining accurate reduction results with rapid response times. To ensure that the ROAR algorithm is suitable for high-dimensional datasets, we provide a parallel implementation, namely, the P-ROAR algorithm. The P-ROAR algorithm is the first parallel attribute-reduction algorithm in the classical NRS theory. Computational speeds and scalability metrics establish that P-ROAR is much faster and more scalable for datasets with an enormous attribute space. These algorithms provide a tool for handling feature reduction in data engineering without compromising accuracy and performance.

New covering techniques and applications utilizing multigranulation fuzzy rough sets

In order to conduct an in-depth study of Zhan’s methodology pertaining to the covering of multigranulation fuzzy rough sets (CMG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {C}_{{MG}}$$\\end{document}FRSs), we build two families: the family of fuzzy β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-minimum descriptions and the family of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-maximum descriptions. Subsequently, utilizing these notions, we proceed to develop two variations of covering via optimistic (pessimistic) multigranuation rough set samples (CO(P)MG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CO(P)}_{{MG}}$$\\end{document}FRS). The axiomatic properties are examined. In this study, we examine four models of covering using variable precision multigranulation fuzzy rough sets (CVPMG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CVP}_{{MG}}$$\\end{document}FRSs). We proceed with analyzing the features of these models. Interconnections between these planned plans are also elucidated. This study explores algorithms that aim to identify innovative strategies for addressing multiattribute group decision-making problems (MAGDM) and multicriteria group decision-making problems (MCGDM). The test examples have been elucidated to provide an inclusive grasp of the efficacy of the offered samples. Ultimately, the distinctions between our methodologies and the preexisting research have been demonstrated.

Human–computer interaction using artificial intelligence-based expert prioritization and neuro quantum fuzzy picture rough sets for identity management choices of non-fungible tokens in the Metaverse

Necessary improvements should be made to increase the effectiveness of non-fungible tokens on the Metaverse platform without having extra costs. For the purpose of handing this process more efficiently, there is a need to determine the most important factors for a more successful integration of non-fungible tokens into this platform. Accordingly, this study aims to determine the appropriate the identity management choices of non-fungible tokens in the Metaverse. There are three different stages in the proposed novel fuzzy decision-making model. The first stage includes prioritizing the expert choices with artificial intelligence-based decision-making methodology. Secondly, the criteria sets for managing non-fungible tokens are weighted by using Quantum picture fuzzy rough sets-based M-SWARA methodology. Finally, the identity management choices regarding non-fungible tokens in the Metaverse are ranked with Quantum picture fuzzy rough sets oriented VIKOR. The main contribution of this study is that artificial intelligence methodology is integrated to the fuzzy decision-making modelling to differentiate the experts. With the help of this situation, it can be possible to create clusters for the experts. Hence, the opinions of experts outside this group may be excluded from the scope. It has been determined that security must be ensured first to increase the use of non-fungible tokens on the Metaverse platform. Similarly, technological infrastructure must also be sufficient to achieve this objective. Moreover, biometrics for unique identification has the best ranking performance among the alternatives. Privacy with authentication plays also critical role for the effectiveness of this process.

Exploring Climate Interactions: A Fuzzy Rough Set Theory Approach

Analysing climate change is challenging due to climate data’s intricate and dynamic nature. The primary issue is starting with high dimensionality. High dimensionality impacts the model’s performance, computation time, cost, and accuracy. Feature selection can be employed as a strategy to address the issue of dimensionality reduction, resulting in more precise insights and the identification of more explicit patterns. Various techniques are used for feature selection. Still, there is scope for progress in this field. This study uses fuzzy rough set theory (FRST) to perform feature selection in the analysis of climatic data. The dataset in the present study, obtained from Kaggle, is an authentic climate change dataset in the real world. FRST effectively addresses uncertainty and vagueness in climate data by identifying the most relevant temperature parameters and treating them as the deciding attribute. We identified 25 reducts from the original dataset using FRST. Compared to the original dataset, the best reducts had good classification accuracy. It indicates that FRST reducts preserve the essential features of the original climate data, assuring the reduced dataset’s integrity and relevance. FRST was more accurate than usual climate data analysis methods, proving its efficacy.

Artificial intelligence-based expert weighted quantum picture fuzzy rough sets and recommendation system for metaverse investment decision-making priorities

There should be some improvements to increase the performance of Metaverse investments. However, businesses need to focus on the most important actions to provide cost effectiveness in this process. In summary, a new study is needed in which a priority analysis is made for the performance indicators of Metaverse investments. Accordingly, this study aims to evaluate the main determinants of the performance of the metaverse investments. Within this context, a novel model is created that has four different stages. The first stage is related to the prioritizing the experts with artificial intelligence-based decision-making method. Secondly, missing evaluations are estimated by expert recommendation system. Thirdly, the criteria are weighted with Quantum picture fuzzy rough sets-based (QPFR) M-Step-wise Weight Assessment Ratio Analysis (SWARA). Finally, investment decision-making priorities are ranked by QPFR VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje). The main contribution of this study is the integration of the artificial intelligence methodology to the fuzzy decision-making approach for the purpose of computing the weights of the decision makers. Owing to this condition, the evaluations of these people are examined according to their qualifications. This situation has a positive contribution to make more effective evaluations. Organizational effectiveness is found to be the most important factor in improving the performance of metaverse investments. Similarly, it is also identified that it is important for businesses to ensure technological improvements in the development of Metaverse investments. On the other side, the ranking results indicate that regulatory framework is the most critical alternative in this regard.

Selection of AI Architecture for Autonomous Vehicles Using Complex Intuitionistic Fuzzy Rough Decision Making

The advancement of artificial intelligence (AI) has become a crucial element in autonomous cars. A well-designed AI architecture will be necessary to attain the full potential of autonomous vehicles and will significantly accelerate the development and deployment of autonomous cars in the transportation sector. Promising autonomous cars for innovating modern transportation systems are anticipated to address many long-standing transporting challenges related to congestion, safety, parking, and energy conservation. Choosing the optimal AI architecture for autonomous vehicles is a multi-attribute decision-making (MADM) dilemma, as it requires making a complicated decision while considering a number of attributes, and these attributes can have two-dimensional uncertainty as well as indiscernibility. Thus, in this framework, we developed a novel mathematical framework “complex intuitionistic fuzzy rough set” for tackling both two-dimensional uncertainties and indiscernibility. We also developed the elementary operations of the deduced complex intuitionistic fuzzy rough set. Moreover, we developed complex intuitionistic fuzzy rough (weighted averaging, ordered weighted averaging, weighted geometric, and ordered weighted geometric) aggregation operators. Afterward, we developed a method of MADM by employing the devised operators and investigated the case study “Selection of optimal AI architecture for autonomous vehicles” to reveal the practicability of the devised method of MADM. Finally, to reveal the dominance and supremacy of our proposed work, a benchmark dilemma was used for comparison with various prevailing techniques.

An optimized and intelligent metaverse intrusion detection system based on rough sets

The convergence of the Internet of Things (IoT) and the Metaverse is revolutionizing the digital world by providing immersive, interactive environments as well as new data transmission opportunities. However, this rapid integration raises complex security issues, including an increased risk of unlawful access and data breaches. Strong cybersecurity measures are required to identify and prevent these attacks, preserving the security and confidentiality of users. Finding significant features for recognizing malicious attacks and enhancing the accuracy of network intrusion detection in general, and particularly in the virtual environment, are some of the significant research needs. This paper introduces an intelligent intrusion detection system (IIDS) based on rough set-based electric eel foraging optimization (RSEEFO) in conjunction with the AdaBoost-based classification algorithm. The main objective of this system is to detect and recognize different types of attacks on the interaction and connectivity between the IoT and the metaverse. The proposed IIDS-RSEEFO consists of three phases, which are data pre-processing, multi-IoT attack classification, and evaluation. The main problems associated with the adopted dataset are handled in data pre-processing. Then, in the second phase, a one-versus-all approach is employed along with RSEEFO and AdaBoost to handle the multi-class classification problem. Finally, several evaluation metrics are employed to assess the reliability and robustness of the proposed IIDS-RSEEFO. The proposed IIDS was tested on CIC-IoT-2023 and validated on UNSWNB-15. It achieved high accuracy across all attack types of CIC-IoT-2023, with accuracies of 99.7 %, 100 %, 100 %, 99.8 %, 100 %, 100 %, 99.8 %, and 100 % for benign traffic, DDoS, brute force, spoofing, DoS, Mirai, recon, and web-Based respectively, accompanied by robust sensitivity, F1-Score, Specificity, G-Mean, and crossover-error rate metrics demonstrating its effectiveness in accurately predicting each attack type. Additionally, it obtained high accuracy for all attack types of UNSWNB-15, with accuracies of 96.48 %, 99.12 %, 99.24 %, 93.78 %, 92.55 %, 92.55 %, 92.55 %, 94.73 %, 94.73 %, 98.09 %, 98.39 %, 99.50 %, and 99.95 % for analysis, backdoor, DoS, exploits, fuzzers, generic, normal, reconnaissance, shellcode, and worms, respectively. In addition, the results evaluated that the proposed model is superior compared to the existing intrusion detection systems.

Exploring the Health Literacy Behavior Patterns of Male Patients Using an Interpretable Method.

Improving overall and individual health literacy is a major focus of national initiatives in China and similar initiatives globally. However, few studies have examined the identification and improvement of individual health literacy levels, especially among patients. To develop an interpretable method with decision rules to assess the health literacy levels of male patients and identify key factors influencing health literacy levels. Using a convenience sampling method, we conducted on-site surveys with 212 male patients of a hospital in China from July 2020 to September 2020. The questionnaire was developed by the Ministry of Health of the People's Republic of China. A total of 206 of the completed surveys were ultimately included for analyses in this study. The rough set theory was used to identify conditional attributes (ie, key factors) and decision attributes (ie, levels of health literacy) and to establish decision rules between them. These rules specifically describe how different combinations of conditional attributes can affect health literacy levels among men. Basic knowledge, concepts, and health skills are important in identifying whether male patients have health literacy. Health skills, scientific health concepts, healthy lifestyles and behaviors, infectious disease prevention and control literacy, basic medical literacy, and health information literacy can be identified as cognitive behaviors with varying degrees of health literacy among patients. This model can effectively identify the key factors and decision rules for male patients' health literacy. Simultaneously, it can be applied to clinical nursing practice, making it easier for hospitals to guide male patients to improve their health literacy.

A New Application with Conditional Risk Matrix and Decision Rules: An Assessment of the Sustainability and Performance Electric Power Company

Abstract The 2030 Agenda for Sustainable Development of the United Nations General Assembly focuses on economic development, poverty cessation, environmental sustainability, and good governance at all levels, including peace and safety. For electric power distribution concessionary companies in Brazil, it is necessary to evaluate their sustainability and performance according to the parameters laid by the National Electric Power Agency (ANEEL). For that purpose, sixty-two indicators were assembled that were directly and indirectly associated with sustainability for 38 companies in the period–2013-2021. This study proposes a new application with a conditional risk matrix and decision rules aimed at the integrated assessment of sustainability and performance of electric power companies using the conditional probability of indicators in the ascent or descent of the companies’ classification. A set of “if..., then...” decision rules were inferred by the algorithm VC-DomLEM using concepts from the Rough Sets Theory and the Dominance principle, Dominance-based Rough Set Approach (DRSA).