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This study introduces innovative operational laws, Einstein operations, and novel aggregation algorithms tailored for handling q-spherical fuzzy rough data. The research article presents three newly designed arithmetic averaging operators: q-spherical fuzzy rough Einstein weighted averaging, q-spherical fuzzy rough Einstein ordered weighted averaging, and q-spherical fuzzy rough Einstein hybrid weighted averaging. These operators are meticulously crafted to enhance precision and accuracy in arithmetic averaging. By thoroughly examining their characteristics and interrelations with existing aggregate operators, the article uncovers their distinct advantages and innovative contributions to the field. Furthermore, the study illustrates the actual implementation of these newly constructed operators in a variety of attribute decision-making scenarios employing q-SFR data, yielding useful insights. Our suite of decision-making tools, including these operators, is specifically designed to address complex and uncertain data. To validate our approach, this study offers a numerical example showcasing the real-world applicability of the proposed operators. The results not only corroborate the efficacy of the proposed method but also underscore its potential significance in practical decision-making processes dealing with intricate and ambiguous data. Additionally, comparative and sensitivity analyses are presented to assess the effectiveness and robustness of our proposed work relative to other approaches. The acquired knowledge enriches the current understanding and opens new avenues for future research.

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This paper introduces a refined and broadened version of decision-theoretic rough sets (DTRSs) named Generalized Sequential Decision-Theoretic Rough Set (GSeq-DTRS), which integrates the three-way decision (3WD) methodology. Operating through multiple levels, this iterative approach aims to comprehensively explore the boundary region. It introduces the concept of generalized granulation, departing from conventional equivalence-relation-based structures to incorporate similarity/tolerance relations. GSeq-DTRS addresses the limitations encountered by its predecessor, Seq-DTRS, particularly in managing sequential procedures and integrating new attributes. A notable advancement is its seamless handling of continuous-scale datasets through a defined Generalized Granular Structure (GGS), enabling classification across multiple levels without necessitating reduction of attributes. A refined version of conditional probability (CP), aligned with tolerance classes, enhances the approach, supported by a meticulously designed algorithm. Extensive experimental analysis conducted on two datasets sourced from https://www.kaggle.com demonstrates the efficacy of the procedure for both continuous and discrete datasets, effectively classifying probable elements into POS or NEG regions based on their membership. Unlike traditional Seq-DTRS, it does not require reduction of attributes at each new level. Additionally, the algorithm exhibits lower sensitivity to parametric values and yields results in fewer iterations. Thus, its potential impact on decision-making processes is readily apparent.

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The rapid evolution of rough-set theory has prompted the need for enhanced methodologies in medical diagnostics, particularly regarding COVID-19 variant detection. This study introduces refined mathematical techniques based on topological structures (called nearly initial-rough sets) derived directly from initial-rough sets. Four categories of rough-set methodologies are presented, demonstrating heightened accuracy through comprehensive comparisons against existing methods. By leveraging these techniques, a rule-based classification system for COVID-19 variants is established, achieving 100 % accuracy measures through rigorous testing against real-world and computer-generated data. The implications of these advancements in medical diagnosis hold promise for future research, offering accessible and precise tools for variant identification and prediction. Using a medical application as a case study, we demonstrate superiority through comparative analyses, aligning mathematical results with medical data and showcasing the potential for broader applications beyond experts in topology. Furthermore, the study outlines an algorithm simplifying implementation, particularly in MATLAB, and suggests future explorations in medical, economic, and diverse theoretical frameworks to enhance applicability.

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This study investigates advanced data collection methodologies and their implications for understanding employee and customer behavior within specific locations. Employing a comprehensive multi-criteria decision-making framework, we evaluate various technologies based on four distinct criteria and four technological alternatives. To identify the most effective technological solution, we employ the q-spherical fuzzy rough TOPSIS method, integrating three key parameters: lower set approximation, upper set approximation, and parameter q (where q ≥ 1). Our novel approach combines the TOPSIS method with q-spherical fuzzy rough set theory, providing deeper insights into data-driven decision-making processes in corporate environments. By comparing our proposed framework with existing multi-criteria decision-making methodologies, we demonstrate its strength and competitiveness. This research contributes to enhancing decision-making capabilities in corporate settings and beyond.

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q-spherical fuzzy rough set (q-SFRS) is also one of the fundamental concepts for addressing more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi-parameters. Taking this feature and the significance of the q-SFRSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the q-spherical fuzzy rough numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with applications for selecting a Cloud Service Provider and a Digital Transformation Vendor for digital transformation. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

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Schizophrenia (SZ) is a mental disorder that causes lifelong disorders based on delusions, cognitive deficits, and hallucinations. By visual assessment, SZ diagnosis is time-consuming and complicated, because brain states are more effectively revealed by electroencephalogram (EEG) signals, which are effectively used in SZ diagnosis. The application of existing deep learning methods in SZ detection is effective in the classification of 2-dimensional images, and these methods require more computational resources. Therefore, dimensionality reduction is necessary for SZ diagnosis using EEG signals. To reduce the dimensionality of the data, an improved CAO (ICAO) dimensionality reduction method is proposed, which integrates horizontal and vertical crossover approaches with AOA. The optimal feature subset is achieved by satisfying the ICAO conditions, and a fitness function is evaluated based on rough sets for improved accuracy in feature selection. Therefore a Crossover-boosted Archimedes optimization algorithm (AOA) with rough sets for Schizophrenia detection (CAORS-SD) was proposed using multichannel EEG signals from both SZ and normal patients. The signals are decomposed using multivariate empirical mode decomposition into multivariate intrinsic mode functions (MIMFs). Entropy metrics such as spectral entropy, permutation entropy, approximate entropy, sample entropy, and SVD entropy are evaluated on the MIMF domain to detect SZ. The processing time of the kernel support vector machine classifier is minimized with fewer features, reducing the risk Fof overfitting. Accuracy, sensitivity, specificity, precision, and F1-score of the CAORS-SD model should be conducted to diagnose SZ. Therefore, the proposed CAORS-SD method achieves the higher performance of accuracy, sensitivity, specificity, precision, and F1-score values of 96.34, 98.95, 96.86, 98.52, and 96.74% respectively. Also, the CAORS-SD method minimizes the error rate and significantly reduces the execution time.

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Calculating single-source shortest paths (SSSPs) rapidly and precisely from weighted digraphs is a crucial problem in graph theory. As a mathematical model of processing uncertain tasks, rough sets theory (RST) has been proven to possess the ability of investigating graph theory problems. Recently, some efficient RST approaches for discovering different subgraphs (e.g. strongly connected components) have been presented. This work was devoted to discovering SSSPs of weighted digraphs by aid of RST. First, SSSPs problem was probed by RST, which aimed at supporting the fundamental theory for taking RST approach to calculate SSSPs from weighted digraphs. Second, a heuristic search strategy was designed. The weights of edges can be served as heuristic information to optimize the search way of $ k $-step $ R $-related set, which is an RST operator. By using heuristic search strategy, some invalid searches can be avoided, thereby the efficiency of discovering SSSPs was promoted. Finally, the W3SP@R algorithm based on RST was presented to calculate SSSPs of weighted digraphs. Related experiments were implemented to verify the W3SP@R algorithm. The result exhibited that W3SP@R can precisely calculate SSSPs with competitive efficiency.

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Recently, research is emerging highlighting the potential of cannabinoids' beneficial effects related to anxiety, mood, and sleep disorders as well as pointing to an increased use of cannabinoid-based medicines since COVID-19 was declared a pandemic. The objective of this research is 3 fold: i) to evaluate the relationship of the clinical delivery of cannabinoid-based medicine for anxiety, depression and sleep scores by utilizing machine learning specifically rough set methods; ii) to discover patterns based on patient features such as specific cannabinoid recommendations, diagnosis information, decreasing/increasing levels of clinical assessment tools (CAT) scores over a period of time; and iii) to predict whether new patients could potentially experience either an increase or decrease in CAT scores. The dataset for this study was derived from patient visits to Ekosi Health Centres, Canada over a 2 year period including the COVID timeline. Extensive pre-processing and feature engineering was performed. A class feature indicative of their progress or lack thereof due to the treatment received was introduced. Six Rough/Fuzzy-Rough classifiers as well as Random Forest and RIPPER classifiers were trained on the patient dataset using a 10-fold stratified CV method. The highest overall accuracy, sensitivity and specificity measures of over 99% was obtained using the rule-based rough-set learning model. In this study, we have identified rough-set based machine learning model with high accuracy that could be utilized for future studies regarding cannabinoids and precision medicine.

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Conflict analysis is one of the most critical application domains whose importance is increasing rapidly nowadays. Attributes involving conflicts frequently occur with opinion, negotiations, and collaborators in decision-making. Taking advantage of the uncertainty present in decision-making, in this paper, we have proposed a system that can solve the problems involving conflicts more adequately.•A new interval-valued intuitionistic fuzzy rough set (IVIFRS) system is introduced to handle a decision-making problem involving a conflict of interests.•The proposed system exploits both the notions of rough set and interval-valued intuitionistic fuzzy set theories in sharpening the boundaries of conflicts.•In the IVIFRS system, the disputes amongst the objectives are measured by the novel conflict distance measure. Further, an interval-valued intuitionistic fuzzy conflict analysis system formulated on the IVIFRS is designed for deciding the conflicting attributesThe formulated system is then studied for weight vectors too. The intended conflict analysis system is studied with reference to the well-known existing intuitionistic fuzzy rough set system. The real-life socio-economic problems are dealt with, and the experimental results validate the efficacy of the proposed system.

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Everyone is making constant efforts to establish an effective diagnostic approach, therapy and control of the spread of the pandemic. Due to a flexible formulation, the parameters prior to the normal distributions and explicitly formulate assumptions on the transition probabilities between these categories over time. The spread of the COVID-19 pandemic represents a serious threat for scientists and academics, health professionals and even governments today. The Hospital wards are classified into Intensive Care Unit (ICU), Regular Wards (RW) with Recovered (R) and Deceased (D).. The formulation may be truncated to include particular hypotheses with an epidemiological interpretation. The principles of Three-Way Decision Theory could be used to anticipate and diagnose COVID-19 patients were classified into one of three zones based on their symptoms: Positive, Negative, or Boundary, and treatment are recommended if necessary. The thresholds that distinguish the three zones are determined using a variance-based criterion. Examine the impact of nonpharmaceutical interventions and the findings from data gathered during the second wave of the pandemic in Trivandrum, India.The Three-Way Decision Theory model has a good fit and gives good predictive performance, especially for RW and ICU patients, according to suitable discrepancy metrics that were created to assess and compare models. 95 percent accuracy increased and calculated values for 10 days to demonstrate the temporal aspects of the expected daily reproduction number R.

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In this article, we present a modification of the algorithm based on EAV (entity-attribute-value) model, for induction of decision rules, utilizing novel approach for attribute ranking. The selection of attributes used as premises of decision rules, is an important stage of the process of rules induction. In the presented approach, this task is realized using ranking of attributes based on standard deviation of attributes' values per decision classes, which is considered as a distinguishability level. The presented approach allows to work not only with numerical values of attributes but also with categorical ones. For this purpose, an additional step of data transformation into a matrix format has been proposed. It allows to transform data table into a binary one with proper equivalents of categorical values of attributes and ensures independence of the influence of the attribute selection function from the data type of variables. The motivation for the proposed method is the development of an algorithm which allows to construct rules close to optimal ones in terms of length, while maintaining enough good classification quality. The experiments presented in the paper have been performed on data sets from UCI ML Repository, comparing results of the proposed approach with three selected greedy heuristics for induction of decision rules, taking into consideration classification accuracy and length and support of constructed rules. The obtained results show that for the most part of datasests, the average length of rules obtained for 80% of best attributes from the ranking is very close to values obtained for the whole set of attributes. In case of classification accuracy, for 50% of considered datasets, results obtained for 80% of best attributes from the ranking are higher or the same as results obtained for the whole set of attributes.

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Aiming to optimize the diagnosis of pulmonary embolism (PE) in patients with acute exacerbation of chronic obstructive pulmonary disease (AECOPD), we conducted a retrospective study enrolling 185 AECOPD patients, of whom 90 were diagnosed with PE based on computed tomography pulmonary angiography (CTPA). Ten characteristic indicators and 27 blood indicators were extracted for each patient. First, we quantified the importance of each indicator for diagnosing PE in AECOPD using fuzzy rough sets (FRS) and selected the more important indicators to construct a support vector machine (SVM) diagnosis model called FRS-SVM. The performance of the proposed diagnosis model on the test sets was compared to that of the logistic regression model. The average accuracy and area under the curve (AUC) of the proposed model for the test sets in 10 independent trials were 94.67% and 0.944, respectively, compared to 80.41% and 0.809 for the logistic regression model. Thus, we validated the higher accuracy and stability of the FRS-SVM for PE diagnosis in patients with AECOPD. This model improved the prediction probability before CTPA and can be used in clinical practice to help doctors make decisions.

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The paper presents and evaluates an approach based on Rough Set Theory, and some variants and extensions of this theory, to analyze phenomena related to Information Disorder. The main concepts and constructs of Rough Set Theory, such as lower and upper approximations of a target set, indiscernibility and neighborhood binary relations, are used to model and reason on groups of social media users and sets of information that circulate in the social media. Information theoretic measures, such as roughness and entropy, are used to evaluate two concepts, Complexity and Milestone, that have been borrowed by system theory and contextualized for Information Disorder. The novelty of the results presented in this paper relates to the adoption of Rough Set Theory constructs and operators in this new and unexplored field of investigation and, specifically, to model key elements of Information Disorder, such as the message and the interpreters, and reason on the evolutionary dynamics of these elements. The added value of using these measures is an increase in the ability to interpret the effects of Information Disorder, due to the circulation of news, as the ratio between the cardinality of lower and upper approximations of a Rough Set, cardinality variations of parts, increase in their fragmentation or cohesion. Such improved interpretative ability can be beneficial to social media analysts and providers. Four algorithms based on Rough Set Theory and some variants or extensions are used to evaluate the results in a case study built with real data used to contrast disinformation for COVID-19. The achieved results allow to understand the superiority of the approaches based on Fuzzy Rough Sets for the interpretation of our phenomenon.

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Kolkata has a reputation for being one of the world's most polluted cities, particularly in the post-monsoon months of October, November, and December. Diwali, a Hindu festival, coincides with these months where a large number of firecrackers are set off followed by high emissions of air pollutants. As a result, the air quality index (AQI) deteriorates to "very poor" (301 ≤ AQI ≤ 400) and "poor" (201 ≤ AQI ≤ 300) categories. This situation stays for several days to a month. The present study aims to identify the thresholds for PM2.5 and PM10 that cause the AQI of Kolkata to deteriorate to "very poor" and "poor." For this purpose, we have used a rough set theory-based condition-decision support system to predict the aforementioned categories of AQI. We have developed a Z-number-based novel quantification measure of semantic information of AQI to assess the reliability of the outcomes, as generated from the condition-decision-based decision rules, during post-monsoon season. The result reveals the best possible forecast of AQI with linguistic summarization of the reliability or confidence for different threshold ranges of PM10 and PM2.5. Inverse-decision rules based on rough set theory are utilized to justify and validate the forecasts. The explainability of the condition-decision support system is demonstrated/visualized using a flow graph that maps rough-rule-based different decision paths between input and output with strength, certainty, and coverage. The investigation resulted in an advanced intelligent environmental decision support system (IEDSS) for air-quality prediction.

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In data analysis, data scientists usually focus on the size of data instead of features selection. Owing to the extreme growth of internet resources data are growing exponentially with more features, which leads to big data dimensionality problems. The high volume of features contains much of redundant data, which may affect the feature classification in terms of accuracy. In the current scenario, feature selection attracts the research community to identify and to remove irrelevant features with more scalability and accuracy. To accommodate this, in this research study, we present a novel feature selection framework that is implemented on Hadoop and Apache Spark platform. In contrast, the proposed model also includes rough sets and differential evolution (DE) algorithm, where rough sets are used to find the minimum features, but rough sets do not consider the degree of overlying in the data. Therefore, DE algorithm is used to find the most optimal features. The proposed model is studied with Random Forest and Naive Bayes classifiers on five well-known data sets and compared with existing feature selection models presented in the literature. The results show that the proposed model performs well in terms of scalability and accuracy.

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Gliomas develop and grow in the brain and central nervous system. Examining glioma grading processes is valuable for improving therapeutic challenges. One of the most extensive repositories storing transcriptomics data for gliomas is The Cancer Genome Atlas (TCGA). However, such big cohorts should be processed with caution and evaluated thoroughly as they can contain batch and other effects. Furthermore, biological mechanisms of cancer contain interactions among biomarkers. Thus, we applied an interpretable machine learning approach to discover such relationships. This type of transparent learning provides not only good predictability, but also reveals co-predictive mechanisms among features. In this study, we corrected the strong and confounded batch effect in the TCGA glioma data. We further used the corrected datasets to perform comprehensive machine learning analysis applied on single-sample gene set enrichment scores using collections from the Molecular Signature Database. Furthermore, using rule-based classifiers, we displayed networks of co-enrichment related to glioma grades. Moreover, we validated our results using the external glioma cohorts. We believe that utilizing corrected glioma cohorts from TCGA may improve the application and validation of any future studies. Finally, the co-enrichment and survival analysis provided detailed explanations for glioma progression and consequently, it should support the targeted treatment.

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The described application of granular computing is motivated because cardiovascular disease (CVD) remains a major killer globally. There is increasing evidence that abnormal respiratory patterns might contribute to the development and progression of CVD. Consequently, a method that would support a physician in respiratory pattern evaluation should be developed. Group decision-making, tri-way reasoning, and rough set-based analysis were applied to granular computing. Signal attributes and anthropomorphic parameters were explored to develop prediction models to determine the percentage contribution of periodic-like, intermediate, and normal breathing patterns in the analyzed signals. The proposed methodology was validated employing k-nearest neighbor (k-NN) and UMAP (uniform manifold approximation and projection). The presented approach applied to respiratory pattern evaluation shows that median accuracies in a considerable number of cases exceeded 0.75. Overall, parameters related to signal analysis are indicated as more important than anthropomorphic features. It was also found that obesity characterized by a high WHR (waist-to-hip ratio) and male sex were predisposing factors for the occurrence of periodic-like or intermediate patterns of respiration. It may be among the essential findings derived from this study. Based on classification measures, it may be observed that a physician may use such a methodology as a respiratory pattern evaluation-aided method.

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BACKGROUND: Machine learning involves strategies and algorithms that may assist bioinformatics analyses in terms of data mining and knowledge discovery. In several applications, viz. in Life Sciences, it is often more important to understand how a prediction was obtained rather than knowing what prediction was made. To this end so-called interpretable machine learning has been recently advocated. In this study, we implemented an interpretable machine learning package based on the rough set theory. An important aim of our work was provision of statistical properties of the models and their components. RESULTS: We present the R.ROSETTA package, which is an R wrapper of ROSETTA framework. The original ROSETTA functions have been improved and adapted to the R programming environment. The package allows for building and analyzing non-linear interpretable machine learning models. R.ROSETTA gathers combinatorial statistics via rule-based modelling for accessible and transparent results, well-suited for adoption within the greater scientific community. The package also provides statistics and visualization tools that facilitate minimization of analysis bias and noise. The R.ROSETTA package is freely available at https://github.com/komorowskilab/R.ROSETTA . To illustrate the usage of the package, we applied it to a transcriptome dataset from an autism case-control study. Our tool provided hypotheses for potential co-predictive mechanisms among features that discerned phenotype classes. These co-predictors represented neurodevelopmental and autism-related genes. CONCLUSIONS: R.ROSETTA provides new insights for interpretable machine learning analyses and knowledge-based systems. We demonstrated that our package facilitated detection of dependencies for autism-related genes. Although the sample application of R.ROSETTA illustrates transcriptome data analysis, the package can be used to analyze any data organized in decision tables.

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Neighborhood systems are used to approximate graphs as finite topological structures. Throughout this article, we construct new types of eight neighborhoods for vertices of an arbitrary graph, say, j-adhesion neighborhoods. Both notions of Allam et al. and Yao will be extended via j-adhesion neighborhoods. We investigate new types of j-lower approximations and j-upper approximations for any subgraph of a given graph. Then, the accuracy of these approximations will be calculated. Moreover, a comparison between accuracy measures and boundary regions for different kinds of approximations will be discussed. To generate j-adhesion neighborhoods and rough sets on graphs, some algorithms will be introduced. Finally, a sample of a chemical example for Walczak will be introduced to illustrate our proposed methods.

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Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.