Rudiments of rough sets

Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes

In this paper, we consider classes of decision tables with many-valued decisions closed under operations of the removal of columns, the changing of decisions, the permutation of columns, and the duplication of columns. We study relationships among three parameters of these tables: the complexity of a decision table (if we consider the depth of the decision trees, then the complexity of a decision table is the number of columns in it), the minimum complexity of a deterministic decision tree, and the minimum complexity of a nondeterministic decision tree. We consider the rough classification of functions characterizing relationships and enumerate all possible seven types of relationships.

A progressive approach to multi-criteria group decision-making: N-bipolar hypersoft topology perspective

This paper investigates N-bipolar hypersoft topology (N-BHST), a novel extension of both the well-established N-hypersoft topology (N-HST) and hypersoft topology (HST). Deviating significantly from its precursor, the N-bipolar hypersoft (N-BHS) set, N-BHST introduces a multi-opinion approach to decision-making, augmenting robustness and adaptability. This innovative framework addresses identified limitations in N-bipolar soft topology (N-BST), especially in managing multi-argument approximate functions. The study analyzes various operators (closure, interior, exterior, and boundary) within the N-BHST framework, elucidating their interrelationships. Additionally, an examination is carried out on the enhancement of multi-criteria group decision-making (MCGDM) using N-BHST, setting it apart from existing models. A numerical example is presented to illustrate its application in real-world decision scenarios.

Azolla Pinnata: Sustainable Floating Oil Cleaner of Water Bodies

Various plant-based materials effectively absorb oil contaminants at the water/air interface. These materials showcase unparalleled efficiency in purging oil contaminants, encompassing rivers, lakes, and boundless oceans, positioning them as integral components of environmental restoration endeavors. In addition, they are biodegradable, readily available, and eco-friendly, thus making them a preferable choice over traditional oil cleaning materials. This study explores the phenomenal properties of the floating Azolla fern (Azolla pinnata), focusing on its unique hierarchical leaf surface design at both the microscale and nanoscale levels. These intricate structures endow the fern with exceptional characteristics, including superhydrophobicity, high water adhesion, and remarkable oil or organic solvent absorption capabilities. Azolla's leaf surface exhibits a rare combination of dual wettability, where hydrophilic spots on a superhydrophobic base enable the pinning of water droplets, even when positioned upside-down. This extraordinary property, known as the parahydrophobic state, is rare in floating plants, akin to the renowned Salvinia molesta, setting Azolla apart as a natural wonder. Submerged in water, Azolla leaves excel at absorbing light oils at the air-water interface, demonstrating a notable ability to extract high-density organic solvents. Moreover, Azolla's rapid growth, doubling in the area every 4-5 days, especially in flowing waters, positions it as a sustainable alternative to traditional synthetic oil-cleaning materials with long-term environmental repercussions. This scientific lead could pave the way for more environmentally friendly approaches to mitigate the negative impacts of oil spills and promote a cleaner water ecosystem.

A hybridized red deer and rough set clinical information retrieval system for hepatitis B diagnosis

Healthcare is a big concern in the current booming population. Many approaches for improving health are imposed, such as early disease identification, treatment, and prevention. Therefore, knowledge acquisition is highly essential at different stages of decision-making. Inferring knowledge from the information system, which necessitates multiple steps for extracting useful information, is one technique to address this problem. Handling uncertainty throughout data analysis is also another challenging task. Computer intelligence is a step forward to this end while selecting characteristics, classification, clustering, and developing clinical information retrieval systems. According to recent studies, swarm optimization is a useful technique for discovering key features while resolving real-world issues. However, it is ineffective in managing uncertainty. Conversely, a rough set helps a decision system generate decision rules. This produces decision rules without any additional information. In order to assess real-world information systems while managing uncertainties, a hybrid strategy that combines a rough set and red deer algorithm is presented in this research. In the red deer optimization algorithm, the suggested method selects the optimal characteristics in terms of the degree of dependence on the rough set. In order to determine the decision rules, further a rough set is used. The efficiency of the suggested model is also contrasted with that of the decision tree algorithm and the conventional rough set. An empirical study on hepatitis disease illustrates the viability of the proposed research as compared to the decision tree and crisp rough set. The proposed hybridization of rough set and red deer algorithm achieves an accuracy of 91.7% accuracy. The acquired accuracy for the decision tree, and rough set methods is 82.9%, and 88.9%, respectively. It suggests that the proposed research is viable.

On Complexity of Deterministic and Nondeterministic Decision Trees for Conventional Decision Tables from Closed Classes

In this paper, we consider classes of conventional decision tables closed relative to the removal of attributes (columns) and changing decisions assigned to rows. For tables from an arbitrary closed class, we study the dependence of the minimum complexity of deterministic and nondeterministic decision trees on the complexity of the set of attributes attached to columns. We also study the dependence of the minimum complexity of deterministic decision trees on the minimum complexity of nondeterministic decision trees. Note that a nondeterministic decision tree can be interpreted as a set of true decision rules that covers all rows of the table.

Ontology-Based Semantic Modeling of Coal Mine Roof Caving Accidents

The frequency of roof-caving accidents ranks first among all coal mine accidents. However, the scattered knowledge system in this field and the lack of standardization exacerbate the difficulty of analyzing roof fall accidents. This study proposes an ontology-based semantic modeling method for roof fall accidents to share and reuse roof fall knowledge for intelligent decision-making. The crucial concepts of roof fall accidents and the correlations between concepts are summarized by analyzing the roof fall knowledge, providing a standard framework to represent the prior knowledge in this field. Besides, the ontology modeling tool Protégé is used to construct the ontology. As for ontology-based deep information mining and semantic reasoning, semantic rules based on expert experience and data fusion technology are proposed to evaluate mines’ potential risks comprehensively. In addition, the roof-falling rules are formalized based on the Jena syntax to make the ontology uniformly expressed in the computer. The Jena reasoning engine is utilized to mine potential tacit knowledge and preventive measures or solutions. The proposed method is demonstrated using roof fall cases, which confirms its validity and practicability. Results indicate that this method can realize the storage, management, and sharing of roof fall accident knowledge. Furthermore, it can provide accurate and comprehensive experience knowledge for the roof fall knowledge requester.

Designing face resemblance technique using near set theory under varying facial features

Near sets (also called Descriptively Near Sets) classify nonempty sets of objects based on object feature values. The Near Set Theory provides a framework for measuring the similarity of objects based on features that describe them in much the same way humans perceive the similarity of objects. This paper presents a novel approach for face recognition using Near Set Theory that takes into account variations in facial features due to varying facial expressions, and facial plastic surgery. In the proposed work, we demonstrate two-fold usage of Near set theory; firstly, Near Set Theory as a feature selector to select the plastic surgery facial features with the help of tolerance classes, and secondly, Near Set Theory as a recognizer that uses selected prominent intrinsic facial features which are automatically extracted through the deep learning model. Extensive experimentation was performed on various facial datasets such as YALE, PSD, and ASPS. Experimentation demonstrates 93% of accuracy on the YALE face dataset, 98% of accuracy on the PSD dataset, and 98% of accuracy on the ASPS dataset. A detailed comparative analysis of the proposed work of facial resemblance with other state-of-the-art algorithms is presented in this paper. The experimentation results effectively classify face resemblance using Near Set Theory, which has outperformed several state-of-the-art classification approaches.

A hybrid rough set shuffled frog leaping knowledge inference system for diagnosis of lung cancer disease

Abundant medical data are generated in the digital world every second. However, gathering helpful information from these data is difficult. Gathering useful information from the dataset is very advantageous and demanding. Besides, such data also contain many extraneous features that do not influence the foreboding accuracy while diagnosing a disease. The data must eliminate these extraneous features to get a better diagnosis. Ultimately, the minimized information system will lead to a better diagnosis. In this paper, we have introduced an incremental rough set shuffled frog leaping algorithm for knowledge inference. The proposed algorithm helps find minimum features from an information system while handling complex databases with uncertainty and incompleteness. The proposed rough set shuffled frog leaping knowledge inference model works in two phases. In the initial phase, the incremental rough set shuffled frog leaping algorithm is used to get the most relevant features. Identifying the relevant features is carried out using a fitness function, which uses the rough degree of dependency. The use of the fitness function identifies the much information with the minimum number of features. The purpose of feature selection is to identify a feature subset from an original set of features without reducing the predictive accuracy and to scale back the computation overhead in the data processing. In the second phase, a rough set is utilized for knowledge discovery in perception with rule generation. The selection of decision rules is carried out based on the accuracy of the decision rule and a predefined threshold value. An empirical analysis of the lung disease information system and a comparative study is conducted. Experimental outcomes exhibit that hybrid techniques express the feasibility of the proposed model while achieving better classification accuracy.

Rough-set based learning: Assessing patterns and predictability of anxiety, depression, and sleep scores associated with the use of cannabinoid-based medicine during COVID-19

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.

RAGOSRA: Rough attributed goal oriented software requirements analysis method

Goal oriented software requirements analysis method is used for the analysis of elicited functional goals (FGs) and non-functional goals (NFGs) of a system in which goals are decomposed and refined into sub-goals until requirements from the sub-goals are identified. Based on the critical analysis, we found that most of the attention of goal-oriented methods is on the crisp and fuzzy logic during the analysis of the software goals or requirements. In these methods’ prior information about the type of membership function is required; and the selection of membership function depends on the subjective justification. As a result, it lacks objectivity and may affect the ranking values of the goals or requirements during the analysis. Therefore, this paper presents a rough attributed goal-oriented software requirements analysis (RAGOSRA) method in which rough preference matrix has been used to capture the opinions of different stakeholders. The result of the RAGOSRA method is compared by considering the following criteria, i.e., goal types, goal links, types of data used in the analysis, stakeholder perceptions and time complexity with some fuzzy based methods. Based on the time complexity analysis, it is found that RAGOSRA method requires only 4 operations for the selection of goals for the dataset having NFGs and FGs of an institute examination system. On the other hand, FAGOSRA method, fuzzy TOPSIS method, and fuzzy AHP method requires 36, 200, and 240 operations respectively.

Improved EAV-Based Algorithm for Decision Rules Construction

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.

Selected Data Mining Tools for Data Analysis in Distributed Environment

In this paper, we deal with distributed data represented either as a finite set T of decision tables with equal sets of attributes or a finite set I of information systems with equal sets of attributes. In the former case, we discuss a way to the study decision trees common to all tables from the set T: building a decision table in which the set of decision trees coincides with the set of decision trees common to all tables from T. We show when we can build such a decision table and how to build it in a polynomial time. If we have such a table, we can apply various decision tree learning algorithms to it. We extend the considered approach to the study of test (reducts) and decision rules common to all tables from T. In the latter case, we discuss a way to study the association rules common to all information systems from the set I: building a joint information system for which the set of true association rules that are realizable for a given row ρ and have a given attribute a on the right-hand side coincides with the set of association rules that are true for all information systems from I, have the attribute a on the right-hand side, and are realizable for the row ρ. We then show how to build a joint information system in a polynomial time. When we build such an information system, we can apply various association rule learning algorithms to it.

Approximation operators via TD-matroids on two sets

Rough set theory is an extension of set theory with two additional unary set-theoretic operators known as approximation in order to extract information and knowledge. It needs the basic, or say definable, knowledge to approximate the undefinable knowledge in a knowledge space using the pair of approximation operators. Many existed approximation operators are expressed with unary form. How to mine the knowledge which is asked by binary form with rough set has received less research attention, though there are strong needs to reveal the answer for this challenging problem. There exist many information with matroid constraints since matroid provides a platform for combinatorial algorithms especially greedy algorithm. Hence, it is necessary to consider a matroidal structure on two sets no matter the two sets are the same or not. In this paper, we investigate the construction of approximation operators expressed by binary form with matroid theory, and the constructions of matroidal structure aided by a pair of approximation operators expressed by binary form.

First, we provide a kind of matroidal structure—TD-matroid defined on two sets as a generalization of Whitney classical matroid.

Second, we introduce this new matroidal construction to rough set and construct a pair of approximation operators expressed with binary form.

Third, using the existed pair of approximation operators expressed with binary form, we build up two concrete TD-matroids.

Fourth, for TD-matroid and the approximation operators expressed by binary form on two sets, we seek out their properties with aspect of posets, respectively.

Through the paper, we use some biological examples to explain and test the correct of obtained results. In summary, this paper provides a new approach to research rough set theory and matroid theory on two sets, and to study on their applications each other.

Abawajy J, Shah H, Husaini NA, Zeb A. Rough set based information theoretic approach for clustering uncertain categorical data

Motivation

Many real applications such as businesses and health generate large categorical datasets with uncertainty. A fundamental task is to efficiently discover hidden and non-trivial patterns from such large uncertain categorical datasets. Since the exact value of an attribute is often unknown in uncertain categorical datasets, conventional clustering analysis algorithms do not provide a suitable means for dealing with categorical data, uncertainty, and stability.

Problem statement

The ability of decision making in the presence of vagueness and uncertainty in data can be handled using Rough Set Theory. Though, recent categorical clustering techniques based on Rough Set Theory help but they suffer from low accuracy, high computational complexity, and generalizability especially on data sets where they sometimes fail or hardly select their best clustering attribute.

Objectives

The main objective of this research is to propose a new information theoretic based Rough Purity Approach (RPA). Another objective of this work is to handle the problems of traditional Rough Set Theory based categorical clustering techniques. Hence, the ultimate goal is to cluster uncertain categorical datasets efficiently in terms of the performance, generalizability and computational complexity.

Methods

The RPA takes into consideration information-theoretic attribute purity of the categorical-valued information systems. Several extensive experiments are conducted to evaluate the efficiency of RPA using a real Supplier Base Management (SBM) and six benchmark UCI datasets. The proposed RPA is also compared with several recent categorical data clustering techniques.

Results

The experimental results show that RPA outperforms the baseline algorithms. The significant percentage improvement with respect to time (66.70%), iterations (83.13%), purity (10.53%), entropy (14%), and accuracy (12.15%) as well as Rough Accuracy of clusters show that RPA is suitable for practical usage.

Conclusion

We conclude that as compared to other techniques, the attribute purity of categorical-valued information systems can better cluster the data. Hence, RPA technique can be recommended for large scale clustering in multiple domains and its performance can be enhanced for further research.

Fuzzy set-valued information systems and their homomorphisms based on data compression

A fuzzy set-valued information system (FSVIS) is a special information system (IS) where the value of an object under each attribute or each attribute value is a fuzzy set. Homomorphism is a powerful mathematical tool to deal with FSVISs, which can be used to study relationships among them. Based on data compression, we obtain some characterizations about FSVISs and their homomorphisms. First, some homomorphisms between FSVISs are introduced. After that, attribute reduction based on tolerance relation in a FSVIS is studied. Eventually, we get invariant characterizations of FSVISs based on some special homomorphisms under data compression.

Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China

The material foundation of soil and water conservation is built on the integrity of the highway plant slope. The proportional relevance of the components that affect slope quality was evaluated based on an environmental assessment and the actual characteristics of the highway slope. A system of four major indexes and twelve secondary indexes comprising plant traits, geometric factors, hydrological conditions, and vegetation conditions was developed to assess the stability of roadway plant slopes. The rough set theory approach and the analytic hierarchy process were used to solve the weights of the slope evaluation indexes. Based on a rough set and an analytic hierarchy process, an evaluation model is proposed. The model eliminates the inconsistency and uncertainty in the evaluated factors that are used to calculate the slope. The study was conducted in China. The highway plant slope of the Taihang Mountain highway in the Hebei province was evaluated using the assessment model after dividing the highway plant slope stability into four grades. According to the evaluation results, the model can be used as a reference highway plant slope stability study and provide technical help to prevent and lower slope safety accidents. The evaluation model can predict the slope quality of highway plants, demonstrating the efficacy and reliability of the evaluation methodology and approach.

Rough-Set-Theory-Based Classification with Optimized k-Means Discretization

The discretization of continuous attributes in a dataset is an essential step before the Rough-Set-Theory (RST)-based classification process is applied. There are many methods for discretization, but not many of them have linked the RST instruments from the beginning of the discretization process. The objective of this research is to propose a method to improve the accuracy and reliability of the RST-based classifier model by involving RST instruments at the beginning of the discretization process. In the proposed method, a k-means-based discretization method optimized with a genetic algorithm (GA) was introduced. Four datasets taken from UCI were selected to test the performance of the proposed method. The evaluation of the proposed discretization technique for RST-based classification is performed by comparing it to other discretization methods, i.e., equal-frequency and entropy-based. The performance comparison among these methods is measured by the number of bins and rules generated and by its accuracy, precision, and recall. A Friedman test continued with post hoc analysis is also applied to measure the significance of the difference in performance. The experimental results indicate that, in general, the performance of the proposed discretization method is significantly better than the other compared methods.

A Distributed Attribute Reduction Algorithm for High-Dimensional Data under the Spark Framework

Attribute reduction is an important issue in rough set theory. However, the rough set theory-based attribute reduction algorithms need to be improved to deal with high-dimensional data. A distributed version of the attribute reduction algorithm is necessary to enable it to effectively handle big data. The partition of attribute space is an important research direction. In this paper, a distributed attribution reduction algorithm based on cosine similarity (DARCS) for high-dimensional data pre-processing under the Spark framework is proposed. First, to avoid the repeated calculation of similar attributes, the algorithm gathers similar attributes based on similarity measure to form multiple clusters. And then one attribute is selected randomly as a representative from each cluster to form a candidate attribute subset to participate in the subsequent reduction operation. At the same time, to improve computing efficiency, an improved method is introduced to calculate the attribute dependency in the divided sub-attribute space. Experiments on eight datasets show that, on the premise of avoiding critical information loss, the reduction ability and computing efficiency of DARCS have been improved by 0.32 to 39.61% and 31.32 to 93.79% respectively compared to the distributed version of attribute reduction algorithm based on a random partitioning of the attributes space.

A wind power plant site selection algorithm based on q-rung orthopair hesitant fuzzy rough Einstein aggregation information

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method’s capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.

Rough Set-Game Theory Information Mining Model Considering Opponents’ Information

In multi-strategy games, the increase in the number of strategies makes it difficult to make a solution. To maintain the competition advantage and obtain maximal profits, one side of the game hopes to predict the opponent’s behavior. Building a model to predict an opponent’s behavior is helpful. In this paper, we propose a rough set-game theory model (RS-GT) considering uncertain information and the opponent’s decision rules. The uncertainty of strategies is obtained based on the rough set method, and an accurate solution is obtained based on game theory from the rough set-game theory model. The players obtain their competitors’ decision rules to predict the opponents’ behavior by mining the information from repeated games in the past. The players determine their strategy to obtain maximum profits by predicting the opponent’s actions, i.e., adopting a first-mover or second-mover strategy to build a favorable situation. The result suggests that the rough set-game theory model helps enterprises avoid unnecessary losses and allows them to obtain greater profits.

On the Depth of Decision Trees with Hypotheses

In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change.

A study of uncertain multi-objective nonlinear programming problems for rough intervals

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

Multi-granularity belief interval-valued soft set

A new model named multi-granularity belief interval-valued soft set is introduced in this paper. Some basic properties about it are presented and illustrated. The improved concepts of the soft belief value and soft belief degree are proposed, which provided an easier and better compared horizontally and vertically method among the different objects and different parameters. An algorithm for decision-making problems on multi-granularity belief interval-valued soft set is put forward and its validity is proved by the application of an example. Moreover, the newly proposed algorithm is compared with existing method to indicate its extensive application.

Decision Rules Derived from Optimal Decision Trees with Hypotheses

Conventional decision trees use queries each of which is based on one attribute. In this study, we also examine decision trees that handle additional queries based on hypotheses. This kind of query is similar to the equivalence queries considered in exact learning. Earlier, we designed dynamic programming algorithms for the computation of the minimum depth and the minimum number of internal nodes in decision trees that have hypotheses. Modification of these algorithms considered in the present paper permits us to build decision trees with hypotheses that are optimal relative to the depth or relative to the number of the internal nodes. We compare the length and coverage of decision rules extracted from optimal decision trees with hypotheses and decision rules extracted from optimal conventional decision trees to choose the ones that are preferable as a tool for the representation of information. To this end, we conduct computer experiments on various decision tables from the UCI Machine Learning Repository. In addition, we also consider decision tables for randomly generated Boolean functions. The collected results show that the decision rules derived from decision trees with hypotheses in many cases are better than the rules extracted from conventional decision trees.

An improved density-based approach to risk assessment on railway investment

Purpose

Density-based spatial clustering of applications with noise (DBSCAN) is the most commonly used density-based clustering algorithm, while it cannot be directly applied to the railway investment risk assessment. To overcome the shortcomings of calculation method and parameter limits of DBSCAN, this paper proposes a new algorithm called Improved Multiple Density-based Spatial clustering of Applications with Noise (IM-DBSCAN) based on the DBSCAN and rough set theory.

Design/methodology/approach

First, the authors develop an improved affinity propagation (AP) algorithm, which is then combined with the DBSCAN (hereinafter referred to as AP-DBSCAN for short) to improve the parameter setting and efficiency of the DBSCAN. Second, the IM-DBSCAN algorithm, which consists of the AP-DBSCAN and a modified rough set, is designed to investigate the railway investment risk. Finally, the IM-DBSCAN algorithm is tested on the China–Laos railway's investment risk assessment, and its performance is compared with other related algorithms.

Findings

The IM-DBSCAN algorithm is implemented on China–Laos railway's investment risk assessment and compares with other related algorithms. The clustering results validate that the AP-DBSCAN algorithm is feasible and efficient in terms of clustering accuracy and operating time. In addition, the experimental results also indicate that the IM-DBSCAN algorithm can be used as an effective method for the prospective risk assessment in railway investment.

Originality/value

This study proposes IM-DBSCAN algorithm that consists of the AP-DBSCAN and a modified rough set to study the railway investment risk. Different from the existing clustering algorithms, AP-DBSCAN put forward the density calculation method to simplify the process of optimizing DBSCAN parameters. Instead of using Euclidean distance approach, the cutoff distance method is introduced to improve the similarity measure for optimizing the parameters. The developed AP-DBSCAN is used to classify the China–Laos railway's investment risk indicators more accurately. Combined with a modified rough set, the IM-DBSCAN algorithm is proposed to analyze the railway investment risk assessment. The contributions of this study can be summarized as follows: (1) Based on AP, DBSCAN, an integrated methodology AP-DBSCAN, which considers improving the parameter setting and efficiency, is proposed to classify railway risk indicators. (2) As AP-DBSCAN is a risk classification model rather than a risk calculation model, an IM-DBSCAN algorithm that consists of the AP-DBSCAN and a modified rough set is proposed to assess the railway investment risk. (3) Taking the China–Laos railway as a real-life case study, the effectiveness and superiority of the proposed IM-DBSCAN algorithm are verified through a set of experiments compared with other state-of-the-art algorithms.

Using Rough Set Theory to Find Minimal Log with Rule Generation

Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and reduce the attributes without the need for further information. In RST, the discernibility matrix is the mathematical foundation for computing such reducts. Although it proved its efficiency in feature selection, unfortunately it is computationally expensive on high dimensional data. Algorithm complexity is related to the search of the minimal subset of attributes, which requires computing an exponential number of possible subsets. To overcome this limitation, many RST enhancements have been proposed. Contrary to recent methods, this paper implements RST concepts in an iterated manner using R language. First, the dataset was partitioned into a smaller number of subsets and each subset processed independently to generate its own minimal attribute set. Within the iterations, only minimal elements in the discernibility matrix were considered. Finally, the iterated outputs were compared, and those common among all reducts formed the minimal one (Core attributes). A comparison with another novel proposed algorithm using three benchmark datasets was performed. The proposed approach showed its efficiency in calculating the same minimal attribute sets with less execution time.

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

Mining Knowledge of Respiratory Rate Quantification and Abnormal Pattern Prediction

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.

Decompose Boolean Matrices with Correlation Clustering

One of the tasks of data science is the decomposition of large matrices in order to understand their structures. A special case of this is when we decompose relations, i.e., logical matrices. In this paper, we present a method based on the similarity of rows and columns, which uses correlation clustering to cluster the rows and columns of the matrix, facilitating the visualization of the relation by rearranging the rows and columns. In this article, we compare our method with Gunther Schmidt’s problems and solutions. Our method produces the original solutions by selecting its parameters from a small set. However, with other parameters, it provides solutions with even lower entropy.