Fuzzy Rough Approximation Research Articles

Fuzzy rough set models over two universes using textures

The purpose of this paper is twofold: firstly, to exhibit the existence of a reasonable connection between fuzzy relations and (textural) fuzzy direlations in terms of fuzzy logical connectives; and secondly, to give a new perspective with respect to approximation operators due to fuzzy rough set models over two universes using textures. To this end, we investigate the serialities of fuzzy relations in terms of fuzzy logic connectives using fuzzy direlations. For different fuzzy logic systems, we show that the textural serialities provide alternative descriptions of the serialities of a fuzzy relation in terms of parameters. Without considering the motivation of the semantic link with the classical Pawlak rough sets, we obtain and discuss the natural fuzzifications of rough set models over two universes. Further, we execute that a textural fuzzy rough set model is an efficient template for the basic properties of the various fuzzy rough set models over two universes. For instance, we prove that the revised fuzzy rough set approximations with two universes are the natural extensions of the loose and tight approximations of De Cock et al.

Axiomatic characterizations of [formula omitted]-valued rough sets using a single axiom

Fuzzy rough approximation operators are the underlying concepts in fuzzy rough set theory. There are at least two approaches to develop these primary concepts, i.e., the constructive approach and the axiomatic approach. Single axiomatic characterizations of fuzzy rough approximation operators have got tons of attention. In this paper, considering L being a GL-quantale, we will develop the theory of L-valued rough sets with an L-set as the basic universe of defining L-valued rough approximation operators. Adopting the idea of single axiomatic characterizations of fuzzy rough sets, we will present the axiomatic characterizations of L-valued upper and lower rough approximation operators on an L-set with respect to reflexive, symmetric, transitive L-valued relations on an L-set as well as their compositions. Choosing an L-set as the universe will break the rules that adopting Zadeh’s fuzzy sets as the universe. By these results, we will further provide a new framework of axiomatic research of fuzzy rough set theory.

Granular representation of OWA-based fuzzy rough sets

Granular representations of crisp and fuzzy sets play an important role in rule induction algorithms based on rough set theory. In particular, arbitrary fuzzy sets can be approximated using unions of simple fuzzy sets called granules. These granules, in turn, have a straightforward interpretation in terms of human-readable fuzzy “if..., then...” rules. In this paper, we are considering a fuzzy rough set model based on ordered weighted average (OWA) aggregation over considered values. We show that this robust extension of the classical fuzzy rough set model, which has been applied successfully in various machine learning tasks, also allows for a granular representation. In particular, we prove that when approximations are defined using a directionally convex t-norm and its residual implicator, the OWA-based lower and upper approximations are definable as unions of fuzzy granules. This result has practical implications for rule induction from such fuzzy rough approximations.

DTI-SNNFRA: Drug-target interaction prediction by shared nearest neighbors and fuzzy-rough approximation.

In-silico prediction of repurposable drugs is an effective drug discovery strategy that supplements de-nevo drug discovery from scratch. Reduced development time, less cost and absence of severe side effects are significant advantages of using drug repositioning. Most recent and most advanced artificial intelligence (AI) approaches have boosted drug repurposing in terms of throughput and accuracy enormously. However, with the growing number of drugs, targets and their massive interactions produce imbalanced data which may not be suitable as input to the classification model directly. Here, we have proposed DTI-SNNFRA, a framework for predicting drug-target interaction (DTI), based on shared nearest neighbour (SNN) and fuzzy-rough approximation (FRA). It uses sampling techniques to collectively reduce the vast search space covering the available drugs, targets and millions of interactions between them. DTI-SNNFRA operates in two stages: first, it uses SNN followed by a partitioning clustering for sampling the search space. Next, it computes the degree of fuzzy-rough approximations and proper degree threshold selection for the negative samples’ undersampling from all possible interaction pairs between drugs and targets obtained in the first stage. Finally, classification is performed using the positive and selected negative samples. We have evaluated the efficacy of DTI-SNNFRA using AUC (Area under ROC Curve), Geometric Mean, and F1 Score. The model performs exceptionally well with a high prediction score of 0.95 for ROC-AUC. The predicted drug-target interactions are validated through an existing drug-target database (Connectivity Map (Cmap)).

On (IO,O)-fuzzy rough sets based on overlap functions

In the last past years, as a class of continuous binary aggregation functions, there are many scholars keeping a watchful focus on overlap functions for their widely applicability in various actual problems. On the other side, after that rough sets were presented as a formal tool to handle indetermination and inaccuracy in the analysis of data, there arise many works concerning the extension study of rough approximation operators in rough set model. This paper mainly discusses the so-called (IO,O)-fuzzy rough set model obtained through extending the classical conjunction operator in rough approximation operator to overlap functions. Firstly, we investigate a number of essential properties of (IO,O)-fuzzy rough sets, especially for the connections between the obtained new fuzzy rough approximation operators and fuzzy relations. Secondly, we give the topological properties of (IO,O)-fuzzy rough sets. Finally, we show a brief comparison of the (IO,O)-fuzzy rough sets with other common fuzzy rough set models.

Attribute reduction with fuzzy rough self-information measures

The fuzzy rough set is one of the most effective methods for dealing with the fuzziness and uncertainty of data. However, in most cases this model only considers the information provided by the lower approximation of a decision when it is used to attribute reduction. In a realistic environment, the uncertainty of information is related to lower approximation as well as upper approximation. In this study, we construct four kinds of uncertainty measures by combining fuzzy rough approximations with the concept of self-information. These uncertainty measures can be employed to evaluate the classification ability of attribute subsets. The relationships between these measures are discussed in detail. It is proven that the fourth measure, called relative decision self-information, is better for attribute reduction than the other measures because it considers both the lower and upper approximations of a fuzzy decision. The proposed measures are generalizations of classical measures based on fuzzy rough sets. Finally, we have designed a greedy algorithm for attribute reduction. We validate the effectiveness of the proposed method by comparing the experimental results for efficiency and accuracy with those of three other algorithms using fundamental data.

Classification of gene expression patterns using a novel type-2 fuzzy multigranulation-based SVM model for the recognition of cancer mediating biomarkers

In this article, we propose a novel type-2 fuzzy multigranulation-based SVM model for gene expression pattern classification on human breast cancer dataset. Firstly, a type-2 fuzzy multigranulation system has been designed for the classification task dealing with noisy and nonlinear microarray gene expression patterns. Thereafter, the fuzzy if–then rules have been devised on the feature vectors of microarray to enable accurate bilinear classification process. The fuzzy if–then rules in the domain of type-2 fuzzy multigranulation system are able to identify efficient expression patterns that have been deferentially expressed from normal state to carcinogenic state. The proposed method reduces the structural complexity of the fuzzy if–then rules (type 1) since it works on upper and lower membership functions instead of a single membership function. In addition, a fuzzy rough approximation has been utilized in the model to reduce the computational cost. Lastly, the association among genes consisting of significantly different expression patterns from normal state to malignant state has been recognized with respect to their nature. The effectiveness of the proposed method has been implemented on eight microarray gene expression datasets for human breast cancer patients. Moreover, we have validated the results by F-score and NCBI database which signify that the proposed model performs better in comparison with the existing methods.

Single axioms for (S, T)-fuzzy rough approximation operators with fuzzy product operations

There are two different perspectives to study single axioms for (S, T)-fuzzy rough approximation operators, that is, ordinary fuzzy operations and fuzzy product operations. However, it is too complex and tedious to characterize (S, T)-fuzzy rough approximation operators with ordinary fuzzy operations, such as intersection, union and so on. To remedy these defects, this paper further investigates single axioms for (S, T)-fuzzy rough approximation operators with fuzzy product operations, where fuzzy relation is not limited into either a general fuzzy relation or a symmetric one. Considering a left-continuous t-norm T, we describe T-upper fuzzy rough approximation operators with fuzzy product operations by only one axiom. When t-conorm S is right-continuous and fuzzy negation N is strict, S-lower fuzzy rough approximation operators are characterized with fuzzy product operations by a single axiom.

Belief function of Pythagorean fuzzy rough approximation space and its applications

Rough set theory and evidence theory are two approaches to handle decision making and reduction problems of imprecise and uncertain knowledge. It is motivated that Pythagorean fuzzy set excels at describing the situation where the sum of non-membership degree and membership degree is greater than 1, and may have wider applications than intuitionistic fuzzy set. So in this paper we study probability measure of Pythagorean fuzzy sets and belief structure of Pythagorean fuzzy information systems based on rough set theory, and discuss the reduction of Pythagorean fuzzy information systems. First, we review the properties of Pythagorean fuzzy sets and the upper and lower Pythagorean fuzzy rough approximation operators on the level sets. Then using these properties, probability measure of Pythagorean fuzzy sets are constructed. And the belief and plausibility functions are studied by using the Pythagorean fuzzy rough upper and lower approximation operators. Finally, we apply the belief function to construct an attribute reduction algorithm, and an example is employed to illustrate the feasibility and validity of the algorithm.

Certain models of granular computing based on rough fuzzy approximations

An extraction of granular structures using graphs is a powerful mathematical framework in human reasoning and problem solving. The visual representation of a graph and the merits of multilevel or multiview of granular structures suggest the more effective and advantageous techniques of problem solving. In this research study, we apply the combinative theories of rough fuzzy sets and rough fuzzy digraphs to extract granular structures. We discuss the accuracy measures of rough fuzzy approximations and measure the distance between lower and upper approximations. Moreover, we consider the adjacency matrix of a rough fuzzy digraph as an information table and determine certain indiscernible relations. We also discuss some general geometric properties of these indiscernible relations. Further, we discuss the granulation of certain social network models using rough fuzzy digraphs. Finally, we develop and implement some algorithms of our proposed models to granulate these social networks.

Interval-valued pythagorean fuzzy rough approximation operators and its application

By combining interval-valued Pythagorean fuzzy sets with rough sets, the interval-valued Pythagorean fuzzy rough set model is first constructed in this paper. The connections between special interval-valued Pythagorean fuzzy relations and interval-valued Pythagorean fuzzy approximation operators are established subsequently. Then, we study the axiomatic characterizations of interval-valued Pythagorean fuzzy lower and upper approximation operators. Different axiom sets of interval-valued Pythagorean fuzzy set-theoretic operators ensure the existence of different types of interval-valued Pythagorean fuzzy relations producing the same operators. Finally, we give an example to illustrate the practical application of the newly proposed model.

Fuzzy Rough Attribute Reduction for Categorical Data

Classical rough set theory is considered a useful tool for dealing with the uncertainty of categorical data. The major deficiency of this model is that the classical rough set model is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy similarity relations was introduced to describe the similarity between samples with categorical attributes. However, these kinds of similarity relations also have deficiencies when they are used in fuzzy rough computation. In this article, we propose a new fuzzy-rough-set model for categorical data by introducing a variable parameter to control the similarity of samples. This model employs the iterative computation strategy to define fuzzy rough approximations and dependence functions. It is proved that the proposed rough dependence function is monotonic. Finally, the proposed model is applied to the attribute reduction of categorical data. The experimental results indicate that the proposed model is more effective for categorical data than some existing algorithms.

Some Algebraic Properties of Generalized Fuzzy Rough Approximations Derived by Fuzzy Set-Valued Homomorphism of LA-G-Semigroups

In this paper we define the concept of fuzzy set valued homomorphism of LA- G-semigroups and mention some features of them. We also investigate the approximations of a generalized fuzzy approximation space constructed on LA-G-semigroups and derived by fuzzy set valued homomorphisms of LA-G-semigroups. Especially, we focus on some algebraic properties of fuzzy subsets in terms of protection of some properties under these approximations.

A characterization of novel rough fuzzy sets of information systems and their application in decision making

AbstracVVt A novel concept of α-rough fuzzy sets is proposed as a generalization of rough fuzzy sets in information systems. A pair of rough fuzzy approximation operators is presented based on one type of correlation between attributes, namely, α-correlative relation. In addition, the properties of α-rough fuzzy sets are investigated. Finally, we develop an approach for decision-making problems based on lower and upper α-approximations and provide an actual example.

A Hesitant Soft Fuzzy Rough Set and its Applications

The difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Basic properties of hesitant soft fuzzy rough sets are investigated in detail. We obtain a decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set. Indeed, a hesitant fuzzy soft set can induce a hesitant fuzzy binary relation. Then we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets. In addition, we prove a characterization theorem for the hesitant soft fuzzy rough set model, which shows that the lower and upper hesitant soft fuzzy rough approximations can be equivalently defined by using level sets of the hesitant fuzzy soft set. Finally, by analyzing the limitations and advantages in the existing literatures, we establish an approach to decision making problem based on the hesitant soft fuzzy rough set model proposed in this paper and give a practical example to illustrate the validity of the novel method.

Distinguishing Vagueness from Ambiguity in Rough Set Approximations

In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of “imperfect” knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology.

New generalized fuzzy soft rough approximations applied to fuzzy topological spaces

New generalized fuzzy soft rough approximations applied to fuzzy topological spaces

Three-way decisions with reflexive probabilistic rough fuzzy sets

The theory of three-way decisions is used to classify a set of objects into the three disjoint parts of the positive, negative and boundary regions. This paper mainly studies three-way decisions with reflexive probabilistic rough fuzzy sets. We first discuss reflexive probabilistic rough sets in a reflexive probabilistic approximation space. For any fuzzy set and a level value, reflexive probabilistic rough fuzzy sets are introduced based on a pair of thresholds and a reflexive binary relation. Related properties of them are investigated. The lower and upper reflexive probabilistic rough fuzzy approximations are monotonic when the two thresholds and the level value increase or decrease. To give the physical interpretation of the required thresholds in reflexive probabilistic rough fuzzy sets, a set of states is constructed based on any fuzzy set and a level value. Three-way classifications in reflexive probabilistic rough fuzzy sets are then discussed. This method gives the values of the pair of thresholds using the loss functions. Meanwhile, using the minimum-risk decision rules, the lower and upper reflexive probabilistic rough fuzzy sets are constructed, which are consistent with the meaning of the lower and upper approximations in rough set theory. Related algorithm and example are also shown to explain the proposed method.

A novel feature selection method using fuzzy rough sets

The fuzzy set theory and the rough set theory are two distinct but complementary theories that deal with uncertainty in data. The salient features of both the theories are encompassed in the domain of the fuzzy rough set theory so as to cope with the problems of vagueness and indiscernibility in real world data. This hybrid theory has been found to be a potential tool for data mining, particularly useful for feature selection. Most of the existing approaches to fuzzy rough sets are based on fuzzy relations. In this paper, a new definition for fuzzy rough sets in an information system based on the divergence measure of fuzzy sets is introduced. The properties of the fuzzy rough approximations are explored. Moreover, an algorithm for feature selection using the proposed approximations is presented and experimented using real data sets.

Labeled fuzzy approximations based on bisimulations

This paper focuses on the labeled fuzzy approximation space, which is considered as a relational structure consisting of a nonempty universal set and some fuzzy relations. To deduce knowledge hidden in the labeled fuzzy approximation space, based on the notion of bisimulations, lower and upper fuzzy rough approximation operators are constructed. Then basic properties of the fuzzy rough approximation operators are investigated. When the largest bisimulation is a trivial identity relation in some cases, the concept of simulations is proposed. Moreover, the lower and upper fuzzy rough relation approximation operators are first proposed and properties of the new operators are examined. Finally, the relationships between two kinds of approximations are discussed.