Rough set theory has emerged as a robust soft computing paradigm for feature selection, commonly known as reduct computation. A decision system may contain multiple reducts of varying sizes, all offering equivalent classification capabilities. However, when model performance is a critical factor, the shortest reduct is generally preferred due to its simplicity and interpretability. The discernibility matrix method is a widely used technique for computing such reducts. Despite its effectiveness, this method is computationally intensive and classified as NP-hard, limiting its scalability for datasets where discernibility matrix computation becomes infeasible. This study addresses the limitations of traditional discernibility matrix-based approaches by introducing a novel method that combines a Breadth-First Search control strategy with an incremental approach to compute the absorbed discernibility matrix. The Breadth First Search strategy enables efficient exploration of the search space to identify the shortest optimal reduct early, while the incremental absorbed discernibility matrix enhances the computational scalability of the algorithm. To validate the proposed method, an experimental evaluation was conducted against two stateof-the-art algorithms: Breadth-First Search, representing the discernibility matrix-based strategy, and MinReduct, a benchmark for absorbed discernibility matrix-based approaches. Results demonstrate superior computational performance and earlier discovery of shortest reducts without compromising correctness or optimality.

The Fuzzy Min-Max Neural Network (FMNN) Classification algorithm gained prominence due to its distinct characteristics, such as adaptability for incremental learning, nonlinear classification, and single-pass training. There were many extensions to FMNN since it was incepted. Among them, a couple of works have been done to improve the scalability of FMNN. The MapReduce framework has been widely employed in recent years to scale machine learning algorithms. The existing MapReduce-based FMNN (MRCFMNN) that uses centroid for classification was found to have limitations regarding generalizability due to outliers. This work proposes medoid-based algorithms MRMFMNN_1 and MRMFMNN_2 to overcome the limitations associated with MRCFMNN. The Apache Spark cluster was used to perform the comparative experimental study between the proposed approaches MRMFMNN_1, MRMFMNN_2, and existing state-of-the-art approaches MRCFMNN, MRFMNN using benchmark large decision systems. The experimental outcomes empirically determine the supremacy of the proposed MRMFMNN_1 algorithm by accomplishing improved generalizability over existing MRCFMNN and MRFMNN.

The hybrid paradigm of fuzzy-rough set theory, which combines fuzzy and rough sets, has proven effective in attribute reduction for hybrid decision systems encompassing both numerical and categorical attributes. However, current parallel/distributed approaches are limited to handling datasets with either categorical or numerical attributes and often rely on fuzzy dependency measures. There exists little research on parallel/distributed attribute reduction for large-scale hybrid decision systems. The challenge of handling high-dimensional data in hybrid decision systems necessitates efficient distributed computing techniques to ensure scalability and performance. MapReduce, a widely used framework for distributed processing, provides an organized approach to handling large-scale data. Despite its potential, there is a noticeable lack of attribute reduction techniques that leverage MapReduce's capabilities with a fuzzy discernibility matrix, which can significantly improve the efficiency of processing high-dimensional hybrid datasets. This paper introduces a vertically partitioned fuzzy discernibility matrix within the MapReduce computation model to address the high dimensionality of hybrid datasets. The proposed MapReduce strategy for attribute reduction minimizes data movement during the shuffle and sort phase, overcoming limitations present in existing approaches. Furthermore, the method's efficiency is enhanced by integrating a feature known as SAT-region removal, which removes matrix entries that satisfy the maximum satisfiability conditions during the attribute reduction process. Extensive experimental analysis validates the proposed method, demonstrating its superior performance compared to recent parallel/distributed methods in attribute reduction.

In rough set-based feature selection, the discernibility matrix provides a mathematical framework for computing all or multiple reducts. However, for applications such as ensemble model induction, there is no need to generate an exhaustive set of reducts; instead, selecting a smaller subset with better individual performance and sufficient diversity tends to more effective. Diversity among base classifiers is critical for improving the predictive performance of ensemble models, yet most existing rough set-based methods do not explicitly address this aspect when generating multiple reducts. To overcome this limitation, this paper proposes two strategies that embed diversity directly into the reduct generation process. The first introduces a novel partition refinement cardinality heuristic that selects mutually exclusive reducts with maximum partition cardinality differences to promote classifier diversity. The second presents an efficient adaptation of an existing least overlap heuristic, combined with an incremental construction of the absorbed discernibility matrix to ensure scalability for large datasets where conventional discernibility matrix construction is infeasible. Finally, empirical analysis with state-of-the-art algorithms demonstrates that the diverse reducts generated by the proposed methods successfully achieve their goal of enhancing ensemble model performance through improved diversity and predictive accuracy.

Fuzzy Rough Set Theory (FRS) is an effective method for feature subset selection (reduct computation) for numeric decision systems. Several Fuzzy Rough Set reduct computation approaches were proposed using Fuzzy Similarity Matrix (FSM) or Fuzzy Discernibility Matrix (FDM) constructed on object space. However, constructing FDM or FSM on object space increases the complexity of the algorithm. In a stand-alone scenario, a representative instance-based reduct computation approach is useful in increasing the scalability while computing an approximate reduct. The FMNN-FRS algorithm is one such approach where the given dataset is represented by a much smaller interval-valued decision system using Fuzzy Min-Max Neural Network (FMNN) pre-processing. This work aims to further increase the scalability of FMNN-FRS by designing a novel MapReduce approach (MR_FMNN_FRRC) using centroid-based FMNN. We also proposed two more representative instances-based approaches using MapReduce through FMNN pre-processing. The relevance of the proposed approaches is assessed through a comparative experimental analysis with state-of-the-art Fuzzy Discernibility Matrix (FDM)-based MapReduce algorithm(MR_IFDMFS), Distributed Fuzzy Rough Set (DFRS)based feature selection, MapReduce based Approach for Fuzzy Decision Reduct Computation (MR_IMQRA), and Hybrid-FMNN-FRS. The results amply validate that the proposed approaches achieve higher scalability with an ability to induce generalizable classification models while achieving dependency measures almost equal to 1.

Selecting a compact and relevant feature subset for hybrid decision systems is a key task in decision-making. Fuzzy rough set (FRS) is an effective method for this purpose, but its space complexity can be a hindrance when dealing with large data sets. A scalable FRS-based feature subset selection framework, FDM-FMFRS, was proposed earlier. This framework integrates FRS with fuzzy min-max neural network (FMNN) as a preprocessing step to handle large datasets. FMNN model transforms object space into hyperbox space. However, its implementation requires all input variables to be numeric. One way to handle categorical data is to replace them with numerical values, but this method may define an unsuitable metric for the categories. This article presents an extended version of FDM-FMFRS, called Hybrid-FDM-FMFRS, which is applicable to both numeric and categorical variables by incorporating set-valued data for categorical attributes. A weighted set is presented to represent the frequency distribution of distinct categories within the hyperbox, helping to create set-valued data for categorical attributes and providing the proposed approach greater flexibility and broader applications on definite space. A comprehensive comparative analysis is conducted on hybrid benchmark datasets, and it is established that the proposed algorithm obtained relevant reduct while preserving satisfactory classification accuracy in much less computational time. In addition, the proposed approach retains the scalability benefits of FDM-FMRS, allowing it to handle large datasets where the compared algorithms fail to compute reducts.

Feature selection (FS) is an important pre-processing step in building machine learning models. minimum Redundancy and Maximum Relevance (mRMR) approach has emerged as one of the successful algorithms in obtaining irredundant feature subset involving only bivariate computations. In the current digital age, owing to the prevalence of very large scale datasets, an imminent need has arisen for scalable solutions using distributed/parallel algorithms. MapReduce solutions are proven to be one of the best approaches to design fault-tolerant and scalable solutions. This work analyses the existing Horizontal MapReduce approaches for mRMR feature selection and identifies the limitations thereof. It is observed that existing approaches involve redundant and repetitive computations and lacks a metadata framework to diminish them. This motivated us to propose Horizontal partitioning based MapReduce solutions namely HMR_mRMR, is an Iterative MapReduce algorithms and is designed under Apache Spark. Appropriate usage of metadata framework and solution formulation optimizes the computations in the proposed approaches. The comparative experimental study is conducted with existing approaches to establish the importance of HMR_mRMR.

Feature selection stands out to be an important preprocessing step that is used to handle the uncertainty and vagueness in the data. In recent times, the minimum Redundancy and Maximum Relevance (mRMR) approach has been proven to be effective in obtaining the irredundant feature subset. Owing to the generation of voluminous datasets, it is essential to design scalable solutions using distributed/parallel paradigms. MapReduce solutions are proven to be one of the best approaches to designing fault-tolerant and scalable solutions. This work analyses the existing vertical partitioning MapReduce approaches for mRMR feature selection and identifies the limitations thereof. In the current study, we proposed VMR_mRMR, an efficient vertical partitioning-based approach using a memorization approach thereby overcoming the extant approaches limitations. The experiment analysis says that VMR_mRMR significantly outperformed extant approaches and achieved a better computational gain (C.G). We also conducted a comparative analysis with the horizontal partitioning approach HMR_mRMR to assess the strengths and limitations of the proposed approach.

Fuzzy Min-Max Neural Network (FMNN) Classifier has acquired significance owing to its unique properties of single-pass training, non-linear classification, and adaptability for incremental learning. Since its inception in 1992, FMNN has witnessed several extensions, modifications, and utilization in various applications. But very few works are done in the literature for enhancing the scalability of FMNN. In recent years, MapReduce framework is used extensively for scaling machine learning algorithms. The existing MapReduce approach for FMNN (MRFMNN) is found to be having limitations in load balancing and in achieving good generalizability. This work proposes MRCFMNN Algorithm for overcoming these limitations. MRCFMNN induces an ensemble of centroid-based FMNN Classifiers for achieving higher generalizability with load balancing. Four ensemble strategies are proposed for combining the individual classifier results. The comparative experimental results using benchmark large decision systems were conducted on Apache Spark MapReduce cluster. The results empirically establish the relevance of the proposed MRCFMNN by achieving significantly better classification accuracy in most of the datasets over MRFMNN.

Traditionally, the shortest length has been used as the optimality criterion in rough set based optimal / near-optimal reduct computation. A more generalizable alternative to the optimal reduct computation approach was recently introduced, with the coarsest granular space as the optimality criterion. However, owing to exponential time complexity, it is not scalable to even moderate-sized data sets. This article investigates to formulate two near-optimal reduct computation alternatives for scaling comparatively larger data sets. The first algorithm employs a controlled A ∗ search based strategy to find a near-optimal reduct while reducing both space utilization and computational time. Whereas, the second algorithm employs a greedy sequential backward elimination ( SBE ) strategy on the higher granular space attribute ordering for achieving coarsest granular space based near-optimal reduct. The comparative experimental study is conducted among the proposed approaches with the coarsest granular space based optimal reduct algorithm A ∗ R S O R and state-of-the-art shortest length based optimal and near-optimal reduct algorithms. The experimental study amply validates the relevance of the proposed approaches in obtaining near-optimal reduct with increased scalability and comparable or improved generalizable classification models induction.

The optimal reduct computation problem aims to obtain the best reduct out of all possible reducts of a given decision system. In the rough set literature, two optimality criteria exist for computing an optimal reduct: shortest length based and coarsest granular space based. The coarsest granular space-based optimal reduct has the ability to induce a better generalizable classification model. The A* RSOR is an existing A* search-based optimal reduct computation algorithm that uses the coarsest granular space as an optimality criterion. This article proposes an improved coarsest granularity-based optimal reduct approach MA*_RSOR through analyzing the search process's behaviour in A*_RSOR algorithm. To minimize the search space utilization and arrive at an optimal reduct in less time, suitable modifications are incorporated using the domain knowledge of rough set theory. The relevance of MA*_RSOR is demonstrated through theoretical analysis and comparative experimental validation with state-of-the-art algorithms. The experimental results with benchmark data sets established that MA*_RSOR achieves significant computational time gain (49 - 99%) and space reduction (37 - 96%) over A*_RSOR. The MA*_RSOR could induce classification models with significantly better classification accuracies than state-of-the-art shortest length-based optimal/near-optimal reduct computation algorithms. In addition, a coefficient of variation based CVNonCore heuristic is proposed for predicting when the MA*_RSOR algorithm is appropriate to use. Experimental results validate the relevance of the heuristic as its prediction turned out correctly in 8 out of 10 data sets.

While building machine learning models, Feature selection (FS) stands out as an essential preprocessing step used to handle the uncertainty and vagueness in the data. Recently, the minimum Redundancy and Maximum Relevance (mRMR) approach has proven to be effective in obtaining the irredundant feature subset. Owing to the generation of voluminous datasets, it is essential to design scalable solutions using distributed/parallel paradigms. MapReduce solutions are proven to be one of the best approaches to designing fault-tolerant and scalable solutions. This work analyses the existing MapReduce approaches for mRMR feature selection and identifies the limitations thereof. In the current study, we proposed VMR_mRMR, an efficient vertical partitioning-based approach using a memorization approach, thereby overcoming the extant approaches limitations. The experiment analysis says that VMR_mRMR significantly outperformed extant approaches and achieved a better computational gain (C.G). In addition, we also conducted a comparative analysis with the horizontal partitioning approach HMR_mRMR [1] to assess the strengths and limitations of the proposed approach.

The scale of the data collected today from applications in the real-world is massive. Sometimes this data can also include missing (incomplete) values that give rise to large-scale incomplete decision systems (IDS). Parallel attribute reduction in big data is an essential preprocessing step for scalable machine learning model construction. Rough set theory has been used as a powerful tool for attribute reduction in complete decision systems (CDS). Furthermore extensions to classical rough set theory have been proposed to deal with IDS. A lot of research works have been done on efficient attribute reduction in IDS using these extensions, but no parallel/distributed approaches have been proposed for attribute reduction in large-scale IDS. Since, owing to its two challenges, large-scale and incompleteness, the processing of large-scale IDS is difficult. To address these challenges, we propose MapReduce based parallel/distributed approaches for attribute reduction in massive IDS. The proposed approaches resolve the challenge of incompleteness with the existing Novel Granular Framework (NGF). And each proposed approach follows a different data partitioning strategy to handle the data sets that are large-scale in terms of number of objects and attributes. One of the proposed approaches adopts an alternative representation of the NGF and uses a horizontal partitioning (division in object space) of the data to the nodes of cluster. Another approach embraces the existing NGF and uses a vertical partitioning (division in attribute space) of the data. Extensive experimental analysis carried out on various data sets with different percentages of incompleteness in the data. The experimental results show that the horizontal partitioning based approach performs well for the massive object space data sets. And the vertical partitioning based approach is relevant and scales well for extremely high dimensional data sets.

Fuzzy rough sets (FRS) provides effective ways for selecting the compact/relevant feature subset for hybrid decision systems. However, the underlying complexity of the existing FRS methods through batch processing is often costly or intractable on large data and also suffer from continuous model adaptation on dynamic data. This paper proposes a FRS based incremental feature subset selection (IvFMFRS) framework using fuzzy min-max neural network (FMNN) as a preprocessor step in aiding to deal with data dynamically without sacrificing classification performance. FMNN is a single epoch learning algorithm employed to construct fuzzy hyperboxes (information granules) of pattern spaces very fast. Fuzzy hyperboxes facilitate the formation of interval-valued decision system (IDS) from the numerical decision system of much smaller size. In IvFMFRS, on each sample subset arrival, an incremental mechanism for updating fuzzy discernibility matrix (FDM) based on constructed IDS is first formulated and then update feature subset by adding and deleting features based on updated FDM. A comparative analysis has been conducted comprehensively to assess the performance of the proposed algorithm with the existing FRS methods on numerical datasets. And, the results show that the IvFMFRS obtained the relevant feature subsets with similar classification accuracy with significantly less computational time than existing FRS methods.

Fuzzy-rough set theory is an efficient method for attribute reduction. It can effectively handle the imprecision and uncertainty of the data in the attribute reduction. Despite its efficacy, current approaches to fuzzy-rough attribute reduction are not efficient for the processing of large data sets due to the requirement of higher space complexities. A limited number of accelerators and parallel/distributed approaches have been proposed for fuzzy-rough attribute reduction in large data sets. However, all of these approaches are dependency measure based methods in which fuzzy similarity matrices are used for performing attribute reduction. Alternative discernibility matrix based attribute reduction methods are found to have less space requirements and more amicable to parallelization in building parallel/distributed algorithms. This paper therefore introduces a fuzzy discernibility matrix-based attribute reduction accelerator (DARA) to accelerate the attribute reduction. DARA is used to build a sequential approach and the corresponding parallel/distributed approach for attribute reduction in large data sets. The proposed approaches are compared to the existing state-of-the-art approaches with a systematic experimental analysis to assess computational efficiency. The experimental study, along with theoretical validation, shows that the proposed approaches are effective and perform better than the current approaches.

Rough set theory has emerged as an influential soft-computing approach for feature subset selection (reduct computation) in the decision system amidst incompleteness and inconsistency. Multiple reducts computation using rough sets provide an elegant way for construction of ensemble classifier for better and stable classification. The existing approaches for multiple reducts computation are primarily based on the genetic algorithm and select diverse multiple reducts after generation of abundant candidate reducts. This work proposes an MRGA_MRC algorithm for multiple reducts computation by utilizing the systematically evolving search space of all reducts computation in the MRGA algorithm without generation of many candidate reducts. A novel heuristic is introduced for selection of diverse multiple reducts. Experiments conducted on the benchmark decision systems have established the relevance of the proposed approach in comparison to the genetic algorithm based multiple reducts computation approach REUCS.

Fuzzy rough sets (FRS) framework is proven to be useful in computing predictive features in the presence of incompleteness and uncertainty in hybrid systems. However, the existing FRS methods for feature subset selection (reduct computation) are not scalable to large datasets due to higher space and time complexities. Towards increasing the scalability of FRS reduct computation, FMNN-FRS approach is proposed earlier, utilizing fuzzy min–max neural network (FMNN) preprocessing to enable reduct computation in fuzzy hyperbox space instead of object space. FMNN-FRS approach considers fuzzy discernibility matrix (DM) for computation of an approximate reduct. However, it is observed that the space utilization of fuzzy DM limits the scalability of FMNN-FRS. To further increase the scalability of FMNN-FRS method by the reduction in the space complexity, in this work, a novel way of crisp DM construction is proposed from the knowledge derived from FMNN preprocessing (CDM-FMFRS). Extended overlapping criteria, with tolerance parameter, are also designed for arriving at the crisp discernibility relation through fuzzy hyperboxes. The proposed CDM-FMFRS approach computes an approximate reduct using SFS strategy on the generated crisp DM. Empirically, the experimental results established that the classifiability of the induced model from the proposed algorithm is similar or better than FMNN-FRS and other state-of-the-art FRS reduct approaches with a significant reduction in computational time. Results also established better scalability achieved by CDM-FMFRS than FMNN-FRS.

Fuzzy Min-Max Neural Networks (FMNN) is a single epoch learning Pattern Classification algorithm with several advantages for online learning. The information loss due to Contraction step of FMNN leads to several improvements in literature such as MLF, FMCN etc. These approaches do not use Contraction step and provide additional structures in FMNN for decision making in overlapped regions overcoming the problem of Contraction with the cost of an increase in training complexity of FMNN. This work proposes a hybridization of FMNN with kNN algorithm for achieving the ability to handle decision making in overlapped regions without altering the structure of FMNN. Comparative studies with existing approaches over benchmark decision systems have proved the utility of the proposed kNN-FMNN approach.

Feature subset selection or reduct computation is a prominent domain for the classical rough set theory, which can preserve the most predictive features of a decision system. A given decision system has several reducts. Computation of all possible reducts was achieved through the computing prime implicants of the discernibility function. Currently, an optimal reduct based on any optimality criteria can only be achieved post-generation of all possible reducts. Indeed, it is an NP-hard problem. Several researchers have extended the alternative aspects with search strategies such as Genetic Algorithm, Ant Colony Optimization, Simulated Annealing, etc., for obtaining near-optimal reducts. In this paper, we propose an admissible and consistent heuristic for computing the optimal reduct having least number of induced equivalence classes or granules. A* RSOR reduct computation algorithm is developed using the proposed consistent heuristic in A* search. The proposed approach is validated both theoretically and experimentally. The comparative results establish the relevance of the proposed optimality criterion as the achieved optimal reduct has obtained significantly better accuracies with different classifiers.

Fuzzy-rough set theory, an extension to classical rough set theory, is effectively used for attribute reduction in hybrid decision systems. However, it’s applicability is restricted to smaller size datasets because of higher space and time complexities. In this work, an algorithm MR_IMQRA is developed as a MapReduce based distributed/parallel approach for standalone fuzzy-rough attribute reduction algorithm IMQRA. This algorithm uses a vertical partitioning technique to distribute the input data in the cluster environment of the MapReduce framework. Owing to the vertical partitioning, the proposed algorithm is scalable in attribute space and is relevant for scalable attribute reduction in the areas of Bioinformatics and document classification. This technique reduces the complexity of movement of data in shuffle and sort phase of MapReduce framework. A comparative and performance analysis is conducted on larger attribute space (high dimensional) hybrid decision systems. The comparative experimental results demonstrated that the proposed MR_IMQRA algorithm obtained good sizeup/speedup measures and induced classifiers achieving better classification accuracy.