Intuitionistic Fuzzy Rough Sets Research Articles

A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy C-means clustering to handle imbalanced datasets

Due to advancement of internet and lab based technologies, large volume of high dimensional data are generated every day. These data usually consisted of several issues such as class imbalance, noise, later uncertainty, irrelevant and/or redundant features, and redundancy in size. These issues degrade the overall performance measures of the various machine learning algorithms. An efficient method to cope with such issues for a large sized datasets is to apply efficient data reduction techniques. In the recent years, numerous data reduction techniques have been presented based on fuzzy rough set theory to tackle these obstacles. However, building such a method that can handle all the above mentioned issues simultaneously is still a challenging task. In this study, we handle all these obstacles simultaneously by introducing a novel approach to obtain the reduced dataset by combining kernelized intuitionistic fuzzy C-means with intuitionistic fuzzy rough set model. Intuitionistic fuzzy rough set handles the vagueness and uncertainty in a better way than fuzzy set aided models as it takes use of membership, non-membership as well as hesitancy to capture the uncertainty of real-valued datasets. To generate the membership and non-membership grades, kernelized intuitionistic fuzzy C- means based notion is introduced. Further, an intuitionistic fuzzy rough set model is established by addressing lower and upper approximations based on a novel similarity relation. Moreover, all the necessary conditions are justified with the relevant mathematical theorems. Next, this model is employed for dimensionality reduction based on the concept of discernibility matrix by using the idea of different classes’ ratios to avoid the noise. Thereafter, positive region is defined with the help of lower approximation. The positive region information is applied to tackle problematic instances available in both minority and majority class for the imbalanced dataset after generation of artificial samples by synthetic minority oversampling technique (SMOTE). A comprehensive experimental study is added to show the effectiveness of the proposed technique. Finally, a framework is established to improve the prediction of animal toxin peptides.

An intuitionistic fuzzy rough model for maritime transportation chains under disaster effects: the case of COVID-19

The outbreak of COVID-19 has caused disruptions in port transport infrastructure and shipping, resulting in higher shipping rates in 2022. This article aims to assess the extent of COVID-19 risks on the capacity and concentration of traffic flows, and evaluate the degree of imbalance in the transport system during 2020-2021 compared to the previous period of 2018-2019. The data is analyzed using the Intuitionistic Fuzzy Rough set, which allows the evaluation of multiple heterogeneous measures to produce an aggregate outcome. The model is based on the intensity of non-stationary incoming and outgoing traffic, as well as the intervals between separate ship calls. The data obtained from the study shows the dynamics of changes in traffic flows under the influence of COVID-19. The results indicate a minimal degree of its influence, which did not lead to any failures or modifications in the composition of traffic flows. The method can also allow for the development of complex simulation models to assess the limit of potential deviations, after which, with a high degree of probability, deformation of traffic flows is possible.

A novel (alpha, beta)-indiscernibility-assisted intuitionistic fuzzy-rough set model and its application to dimensionality reduction

An intuitionistic fuzzy (IF) set is an interesting extension of a fuzzy set (FS) that includes more accurate expression of the uncertainty in contrast to conventional FS theory. By considering positive, negative, and hesitancy degree concurrently, IF set appears as an effective notion to deal with the uncertainty included by both the judgement and identification. In this article, we propose an innovative IF rough set (IFRS) framework that integrates IF set and rough set (RS) with the concept of (alpha, beta)-indiscernibility, which incorporates two thresholds to avoid noise. In addition, we utilize the supporting proofs to defend the suggested framework. Thereafter, a feature selection method is presented by using the proposed framework, and an appropriate algorithm is provided to determine the reduct for the high-dimensional datasets. Moreover, a concrete illustration using a sample information system depicts the efficacy of the suggested idea. Then, the proposed method is applied on the benchmark datasets to produce the reduced datasets. Furthermore, performance measures of numerous machine learning techniques are evaluated over these reduced datasets. Finally, a comparative study with the recently discussed fuzzy rough set (FRS) and IFRS-assisted methods is presented to justify the superiority of the established technique.

A new type of cosine similarity measures based on intuitionistic hesitant fuzzy rough sets for the evaluation of volatile currency: evidence from the Pakistan economy

A new type of cosine similarity measures based on intuitionistic hesitant fuzzy rough sets for the evaluation of volatile currency: evidence from the Pakistan economy

Representations of L-fuzzy rough approximation operators

In recent years, there has been tremendous interest in developing lattice-valued rough set theory. In this framework, we primarily take into account the following two problems. Firstly, we include the well-known intuitionistic, interval-valued, neutrosophic and Pythagorean fuzzy rough sets into the framework of lattice-valued rough sets. Specifically, the four kinds of rough sets can be considered as special lattice-valued rough sets. Secondly, based on a completely distributive lattice L, we provide representations of the upper and lower L-fuzzy rough approximation operators by using four kinds of cut sets of an L-fuzzy set and an L-fuzzy relation, which generalizes the existing results in the case that L=[0,1]. In particular, we show that representations of intuitionistic and interval-valued fuzzy rough approximation operators provided by Zhou and Sun are special examples of our proposed representations.

An approach to multi-attribute decision making based on intuitionistic fuzzy rough Aczel-Alsina aggregation operators

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed.

Asymmetric models of intuitionistic fuzzy rough sets and their applications in decision-making

Asymmetric models of intuitionistic fuzzy rough sets and their applications in decision-making

A Novel Fuzzy Covering Rough Set Model Based on Generalized Overlap Functions and Its Application in MCDM

As nonassociative fuzzy logic connectives, it is important to study fuzzy rough set models using overlap functions that replace the role of t-norms. Overlap functions and t-norms are logical operators with symmetry. Recently, intuitionistic fuzzy rough set and multi-granulation fuzzy rough set models have been proposed based on overlap functions. However, some results (that contain five propositions, two definitions, six examples and a proof) must be improved. In this work, we improved the existing results. Moreover, to extend the existing fuzzy rough sets, a new fuzzy covering rough set model was constructed by using the generalized overlap function, and it was applied to the diagnosis of medical diseases. First, we improve some existing results. Then, in order to overcome the limitations of the fuzzy covering rough set model based on overlap functions, a fuzzy β-covering rough set model based on generalized overlap functions was established. Third, some properties of the fuzzy β-covering rough set model based on generalized overlap functions are discussed. Finally, a multi-criteria decision-making (MCDM) method of the fuzzy β-covering rough set based on generalized overlap functions was proposed. Taking medical disease diagnosis as an example, the comparison with other methods shows that the proposed method is feasible and effective.

Enhanced tolerance-based intuitionistic fuzzy rough set theory feature selection and ResNet-18 feature extraction model for arrhythmia classification

Arrhythmia classification on Electrocardiogram (ECG) signals is an important process for the diagnosis of cardiac disease and arrhythmia disease. The existing researches in arrhythmia classification have limitations of imbalance data problem and overfitting in classification. This research applies Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) for feature selection in arrhythmia classification. The selected features from FCM-ETIFRST were applied to the Multi-class Support Vector Machine (MSVM) for arrhythmia classification. The ResNet18 – Convolution Neural Network (CNN) was applied for feature extraction in input signal to overcome imbalance data problem. Conventional feature extraction along with CNN features are applied for FCM-ETIFRST feature selection process. The FCM-ETIFRST method in arrhythmia classification is evaluated on MIT-BIH and CPCS 2018 dataset. The FCM-ETIFRST has 98.95% accuracy and Focal loss-CNN has 98.66% accuracy on MIT-BIH dataset. The FCM-ETIFRST method has 98.45% accuracy and Explainable Deep learning Model (XDM) method have 93.6% accuracy on CPCS 2018 dataset.

Q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems

<abstract> <p>This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.</p> </abstract>

Interval-valued intuitionistic fuzzy rough set system over a novel conflict distance measure with application to decision-making

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.

Confidence Level Aggregation Operators Based on Intuitionistic Fuzzy Rough Sets With Application in Medical Diagnosis

In recent days, due to the complexities of different diseases of similar types, it becomes very difficult to diagnose an accurate type of disease, and so medical diagnosis becomes a difficult task for the experts working in health departments. Many researchers try to develop new methods and techniques to over the difficulties that come across in the way of medical diagnosis. In this paper, we try to develop some novel techniques that will help experts to diagnose diseases accurately. Based on a more advanced structure of intuitionistic fuzzy rough sets, in this article, we establish confidence-level intuitionistic fuzzy average/geometric aggregation operators to incorporate the familiarity degree of experts with evaluated objects for an initial assessment while intuitionistic fuzzy rough average/geometric aggregation operators cannot do so. Moreover, we have given some basic properties of the initiated operators. To show the effective use of these operators we have proposed an algorithm with an illustrative example. Furthermore, based on the intuitionistic fuzzy rough model, we have also established a medical diagnosis model to incorporate the difficulty that occurs in the diagnosis of disease. Furthermore, a comparative analysis demonstrates the efficiency of our proposed methods.

Incomplete Dominance-Based Intuitionistic Fuzzy Rough Sets and Their Application in Estimation of Inflation Rates in the Least Developed Countries

Incomplete Dominance-Based Intuitionistic Fuzzy Rough Sets and Their Application in Estimation of Inflation Rates in the Least Developed Countries

Intuitionistic Fuzzy Rough Aczel-Alsina Average Aggregation Operators and Their Applications in Medical Diagnoses

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach.

A novel intuitionistic fuzzy rough set model and its application to enhance umami peptide prediction

Datasets mainly consist of ambiguous objects, redundant and uncertain attribute values which increase complexity, time and cost in Knowledge Discovery in Databases (KDD) process. Rough set-based attribute reduction techniques deals with ambiguity but fails to handle uncertainty available in a real-valued dataset. Combining rough set with intuitionistic fuzzy set provides a great opportunity to the researchers working on attribute reduction of real-valued datasets as it provides better results when compared to the traditional fuzzy rough set theory. In this paper, we present a new intuitionistic fuzzy rough set model for attribute reduction to avoid misclassification and perturbation by handling hesitancy, ambiguity and uncertainty present in a dataset. We define an intuitionistic fuzzy tolerance relation between two objects along with lower and upper approximations based on that relation. Next, the concept of Degree of dependency is utilized to present attribute reduction by using model due to its better performing nature over other methods. The algorithm of the proposed technique is applied on benchmark datasets to perform a comparative study with recent approaches. We obtain the best result for the reduced Breast Cancer dataset by our proposed approach, with an accuracy of 98.96% along with 0.90 standard deviation by using SMO classifier. Finally, our proposed method is used to present a methodology to improve the prediction of umami peptides. Here, we record the best results with sensitivity, specificity, accuracy, AUC, and MCC of 96.8%, 93.6%, 97.7%, 0.988, and 0.899, respectively. From the experiments, it can be concluded that our method outperforms the existing methods.

Attribute reduction based on observational consistency in intuitionistic fuzzy multi-covering decision systems

Attribute reduction is an important issue in data mining, machine learning and other applications of big data processing. Covering-based rough set and intuitionistic fuzzy (IF) set models are both the effective theoretical tools of uncertainty or imprecise computation, and thus IF covering rough set model has been acknowledged as a positive approach to attribute reduction. Based on IF covering rough set model, this study explores a kind of parameterized IF observational consistency in IF multi-covering decision system, and proposes an attribute reduction method. This article firstly defines the concepts of regular IF β-covering, parameterized IF observational sets on the regular IF β-covering approximation space. Secondly, the parameterized IF observational consistency is defined to be the principal of attribute reduction in the IF multi-covering decision system, and the related IF discernibility matrix is developed to provide a way of attribute reduction. For multi-observational consistency corresponding to an observational parameters set, an unified multi-observational discernibility matrix is constructed, which avoids the disadvantage of needing to construct multiple corresponding discernibility matrices separately. Furthermore, an attribute reduction algorithm based on iterative dissolving of unified multi-observational discernibility matrix is proposed, and the experiment to demonstrate effectiveness of algorithm is presented. Experiments with UCI datasets shows that, the proposed method is a good way for improving both the rates of attribute-reduced and the classification accuracy of reduced datasets.

Uncertainty Measure for Multisource Intuitionistic Fuzzy Information System

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods.

An intuitionistic fuzzy bireduct model and its application to cancer treatment

Due to technological advancement, data size has seen a significant increase both in terms of features and instances. An efficient way to handle large sized datasets is to apply data reduction technique to ease the computational intractability of learning algorithms. Intuitionistic fuzzy rough and fuzzy rough sets based approaches provide a handful of solution, but the applicability is mostly restricted to reduction in terms of feature size. However, reduction in terms of instance size has not been handled by any of the existing intuionistic fuzzy set approaches. The present paper introduces the notion of bireducts in intuitionistic fuzzy framework that can be used for simultaneous reduction of instances and features. A robust lower approximation formulation is employed along with laying the foundation for the variants of instance selection technique. The proposed model is therefore robust to noise and can very effectively handle uncertainities due to judgement as well as identification. Further, an efficient instance selection technique in bireduct formulation enhances the performance. The experimental evaluation on benchmark datasets demonstrates the applicability and robustness of the proposed bireducts. It significantly reduces data size both in terms of instances and features whilst maintaining high performances. Further, the model is applied in the challenging domain of cancer treatment by enhancing the prediction performance of anti-angiogenic peptides. A comparative analysis demonstrates the superiority of the proposed methodology.

Pessimistic Multigranulation Rough Set of Intuitionistic Fuzzy Sets Based on Soft Relations

Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm.

Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making Problem.

It has been found that fuzzy sets, rough sets and soft sets are closely related concepts. Many complicated problems in economics, engineering, social sciences, medical science and many other fields involve uncertain data. These problems, which one comes in real life, cannot be solved using classical mathematical methods. There are several well-known theories to describe uncertainty, for instance, fuzzy set theory, rough set theory, and other mathematical tools. But all of these theories have their inherit difficulties as pointed out by D. Molodtsov. In 1999, D. Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. The concept of rough sets, proposed by Z. Pawlak as a framework for the construction of approximations of concepts. It is a formal tool for modeling and processing insufficient and incomplete information. Zhou and Wu first proposed the concept of intuitionistic fuzzy rough sets (IFrough sets). The aim of this paper is to introduce the concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets). We also investigate some properties of IVIFS rough approximation operators. Some basic operations and properties are studied. Lastly applications have been shown in decision making problems.