Multi-granulation Rough Set Model Research Articles

Covering based multi-granulation rough fuzzy sets with applications to feature selection

Feature selection acts as an important preprocessing method to reduce redundant information. In order to effectively evaluate the classification information hidden in a given attribute subset, a novel rough set model is put forth via integrating covering based rough fuzzy sets with multi-granulation rough sets. In view of this, fuzzy β-neighborhood is employed to describe the information representation and knowledge fusion of covering families, by which a pair of approximation operators are formulated and a new multi-granulation rough fuzzy set model is introduced. The generalized model gives a unified perspective for existing rough set models. We then investigate the axiomatic characterizations by view of optimism and pessimism. Finally, the data reduction is processed from the point of keeping the discrimination ability. The multi-granulation significance function of a candidate attribute in term of fuzzy decisions is defined, using which a greedy algorithm is developed for multi-granulation feature selection. Experiments on twelve different types of datasets show that our model is efficient and superior to three popular algorithms in terms of reduction rate and classification performance.

A multigranulation rough set model based on variable precision neighborhood and its applications

A multigranulation rough set model based on variable precision neighborhood and its applications

Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

Two important mathematical methods for addressing uncertainty in data processing are multigranulation rough set (MGRS) and fuzzy bipolar soft set (FBSS). This paper describes a certain kind of multigranulation rough set in the context of multiple soft binary relations. We first define the multigranulation roughness of fuzzy bipolar soft sets in the two universes. Moreover, a detailed study of structural properties has been conducted in order to explore this concept. The key characteristics of the traditional MGRS model are completely preserved in this new approach. Following that, we suggest two decision-making algorithms with respect to aftersets and foresets of the soft binary relations over dual universes. This approach appears to be better suited and more adaptable than other available methods, making it a favorable option for addressing decision-making problems. Finally, we provide a practical application of the suggested approach to a real-world problem.

Optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and its application

<abstract><p>A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roughness, which has been researched by several researchers over dual universes. In light of this, we proposed a novel optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and established two types of approximations of a fuzzy set with respect to forsets and aftersets of the finite number of soft binary relations in this article. We obtain two sets of fuzzy soft sets in this way, referred to as the lower approximation and upper approximation with respect to the aftersets and the foresets, respectively. Next, we look into some of the lower and higher approximations of the newly multigranulation rough set model's algebraic properties. Both the roughness and accuracy measurements were defined. In order to show our suggested model, we first develop a decision-making algorithm. Then, we give an example from a variety of applications.</p></abstract>

Attribute reduction in inconsistent grey decision systems based on variable precision grey multigranulation rough set model

This paper mainly deals with attribute reduction of inconsistent grey decision systems (IGDSs) based on the variable precision grey multigranulation rough set (VP-GMGRS). Firstly, we present two transformation models to transform IGDS into consistent decision confidence system. One is the consistent decision system transformation model, based on which, an IGDS can be transformed into a VP-GMGRS approximate distribution consistent decision system. The other is the decision confidence system transformation model, which can be degenerated to a classical group decision system. Meanwhile, we educe related judgement theorems of approximation distribution consistent set in IGDS. Following that, a theoretical attribute reduction approach is presented by employing discernibility attribute sets and function based on VP-GMGRS approximate distributions. In addition, algorithms and illustrative examples with IGDS are employed and assisted to understand and explain the mechanism of attribute reduction theoretical approaches. Finally, comparison experiments are organized to verify the validity and feasibility of the proposed reduction method.

Cost-Sensitive Multigranulation Approximation in Decision-Making Applications

A multigranulation rough set (MGRS) model is an expansion of the Pawlak rough set, in which the uncertain concept is characterized by optimistic and pessimistic upper/lower approximate boundaries, respectively. However, there is a lack of approximate descriptions of uncertain concepts by existing information granules in MGRS. The approximation sets of rough sets presented by Zhang provide a way to approximately describe knowledge by using existing information granules. Based on the approximation set theory, this paper proposes the cost-sensitive multigranulation approximation of rough sets, i.e., optimistic approximation and pessimistic approximation. Their related properties were further analyzed. Furthermore, a cost-sensitive selection algorithm to optimize the multigranulation approximation was performed. The experimental results show that when multigranulation approximation sets and upper/lower approximation sets are applied to decision-making environments, multigranulation approximation produces the least misclassification costs on each dataset. In particular, misclassification costs are reduced by more than 50% at each granularity on some datasets.

Variable precision multi-granulation composite rough sets with multi-decision and their applications to medical diagnosis

Rough set theory has become an effective tool to address uncertain decision-making problems. Nevertheless, existing rough set-based decision-making methods cannot effectively deal with the management decision-making problems with heterogeneity, multi-decision, and diversified attributes simultaneously. Given this, the purpose of this paper is to explore an effective classification solution for solving decision-making problems with the above-described characteristics from the perspective of granular computing. First, we present the notion of heterogeneous diversified attribute multi-decision systems. Because attribute semantics is crucial to multi-attribute decision analysis, we then divide an attribute set into nine subsets according to attribute semantics. Further, a composite binary relation that fits the realistic attribute features is constructed. Subsequently, considering different decision scenarios, we establish four kinds of variable precision multi-decision multi-granulation rough set models. Meanwhile, the related properties and relationships of these models are explored. We find that the established models are extensions of the existing classical rough sets. In the end, we apply the established models to an illustrative example of medical diagnosis. The results of the case and comparative analyses demonstrate the models’ feasibility, effectiveness, and superiority. As a result, our work provides a kind of new decision thinking with reasonable semantic analysis for solving complex management decision-making problems in reality.

Multigranulation-Based Granularity Selection for Intuitionistic Fuzzy Weighted Neighborhood IoT Data

Granular computing is to represent, construct, and process information granules formalized in many different approaches, and different formal approaches emphasize the same fundamental facet in different ways. In this paper, we present the multigranulation rough set models in the intuitionistic fuzzy neighborhood information system generated by Internet of Things (IoT) data with weighted features and develop the basic properties of the proposed models. Moreover, the multigranulation-based optimal granularity selection approach is established by introducing the concept of granularity significance. The experimental results on eight IoT datasets demonstrate that the proposed methods exhibit better efficiency by comparing three classical methods under the intuitionistic fuzzy weighted neighborhood information system.

Rough set-based entropy measure with weighted density outlier detection method

Abstract The rough set theory is a powerful numerical model used to handle the impreciseness and ambiguity of data. Many existing multigranulation rough set models were derived from the multigranulation decision-theoretic rough set framework. The multigranulation rough set theory is very desirable in many practical applications such as high-dimensional knowledge discovery, distributional information systems, and multisource data processing. So far research works were carried out only for multigranulation rough sets in extraction, selection of features, reduction of data, decision rules, and pattern extraction. The proposed approach mainly focuses on anomaly detection in qualitative data with multiple granules. The approximations of the dataset will be derived through multiequivalence relation, and then, the rough set-based entropy measure with weighted density method is applied on every object and attribute. For detecting outliers, threshold value fixation is performed based on the estimated weight. The performance of the algorithm is evaluated and compared with existing outlier detection algorithms. Datasets such as breast cancer, chess, and car evaluation have been taken from the UCI repository to prove its efficiency and performance.

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.

Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application

The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.

Multi-granulation-based optimal scale selection in multi-scale information systems

The notions of multi-granulation and multi-scale are two important issues for the granular computing, both of which can describe the granular structure in certain ways. In this paper, we investigate the belief structure and the plausibility structure by defining belief and plausibility functions from the multi-granulation viewpoint, and discuss how to construct multi-granulation rough set (MGRS) models in multi-scale information systems (MSISs). Based on the MGRS in MSISs, the optimal scale selection methods with various requirements are studied in two aspects of optimistic and pessimistic multi-granulation for a multi-scale decision information system (MSDIS). To interpret and understand the proposed theories, some important properties of optimistic and pessimistic multi-granulation optimal scale selection are analyzed for the MSDIS, which could indicate the inner relationships among the different selection methods of the optimal scales. Furthermore, an example is provided to illustrate and verify these investigated properties.

Multigranulation roughness based on soft relations

The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian et al, extended this model and defined multigranulation rough sets by using finite number of equivalence relations. This model provide new direction to the research. Recently, Shabir et al. proposed a rough set model which depends on a soft relation from an universe V to an universe W . In this paper we are present multigranulation roughness based on soft relations. Firstly we approximate a non-empty subset with respect to aftersets and foresets of finite number of soft binary relations. In this way we get two sets of soft sets called the lower approximation and upper approximation with respect to aftersets and with respect to foresets. Then we investigate some properties of lower and upper approximations of the new multigranulation rough set model. It can be found that the Pawlak rough set model, Qian et al. multigranulation rough set model, Shabir et al. rough set model are special cases of this new multigranulation rough set model. Finally, we added two examples to illustrate this multigranulation rough set model.

Matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation

Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation.

A multigranulation fuzzy rough approach to multisource information systems

Multigranulation rough set is one class of the important models in rough set community. However, both pessimistic and optimistic rough sets have disadvantages in describing target concept. In this paper, a novel model, called weighted multigranulation fuzzy decision rough sets, is proposed. Gaussian kernel is used to compute the similarity between objects, which induces a fuzzy equivalence relation. We employ the relation to fuzzily partition the universe and then obtain multiple fuzzy granulations from multisource fuzzy information system. Moreover, some interesting properties of the proposed model are discussed. A comparative study between the proposed multigranulation model and Sun’s multigranulation rough set model is carried out. An example is employed to illustrate the effectiveness of the proposed method, which may provide an effective approach for multisource data analysis in real applications.

Type-2 fuzzy multigranulation rough sets

Aiming at expanding the application range of the multigranulation rough set (MGRS) theory, a type-2 fuzzy multigranulation rough set (T2FMGRS) model is proposed by combining type-2 fuzzy sets with multigranulation rough sets (MGRSs) in this paper. At first, definitions and properties of optimistic and pessimistic type-2 fuzzy multigranulation rough sets (T2FMGRSs) are introduced. Then, the rough measure is proposed to measure the uncertainty of T2FMGRSs. Finally, T2FMGRSs over two universes are put forward and some examples of decision-making are given to illustrate the applicability of the newly proposed model. In summary, the establishment of T2FMGRSs is a meaningful generalization of the MGRS theory from both theoretical and practical aspects.

Multi-Granulation Picture Hesitant Fuzzy Rough Sets

We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimistic multi-granulation picture hesitant fuzzy rough sets. Further, we also investigate the relationships among these two concepts and picture hesitant fuzzy rough sets.

A general framework for multi-granulation rough decision-making method under q-rung dual hesitant fuzzy environment

In the realistic decision-making (DM) process, the DM results were provided by multiple DM experts, which are more accurate than those based on one DM expert. Therefore, the multi-granulation rough set (MGRS) model is more accurate in DM problems. It is imperative to apply the idea of multi-granulation to the complex fuzzy uncertain information. By combining q-rung dual hesitant fuzzy sets (q-DHFSs) with multi-granulation rough sets (MGRSs) over two universes, we propose a q-rung dual hesitant fuzzy multi-granulation rough set (q-RDHFMGRS) over two universes, and prove some of their basic properties. Then, based on this model, we propose a new multi-attribute DM algorithm. Finally, we validate the practicability and validity of the algorithm through an example of medical diagnosis.

Compromised multi-granulation rough sets based on an attribute-extension chain

The multi-granulation rough sets serve as important hierarchical models for intelligent systems. However, their mainstream optimistic and pessimistic models are respectively too loose and strict, and this defect becomes especially serious in hierarchical processing on an attribute-expansion sequence. Aiming at the attribute-addition chain, compromised multi-granulation rough set models are proposed to systematically complement and balance the optimistic and pessimistic models. According to the knowledge refinement and measure order induced by the attribute-enlargement sequence, the basic measurement positioning and corresponding pointer labeling based on equilibrium statistics are used, and thus we construct four types of compromised models at three levels of knowledge, approximation, and accuracy. At the knowledge level, the median positioning of ordered granulations derives Compromised-Model 1; at the approximation level, the average positioning of approximation cardinalities is performed, and thus the separation and integration of dual approximations respectively generate Compromised-Models 2 and 3; at the accuracy level, the average positioning of applied accuracies yields Compromised-Model 4. Compromised-Models 1–4 adopt distinctive cognitive levels and statistical perspectives to improve and perfect the multi-granulation rough sets, and their properties and effectiveness are finally verified by information systems and data experiments.

Generalized multi-granulation double-quantitative decision-theoretic rough set of multi-source information system

Traditionally, multi-source information system (MsIS) is typically integrated into a single information table for knowledge acquisition. Therefore, discovering knowledge directly from MsIS without information loss is a valuable research direction. In this paper, we propose the generalized multi-granulation double-quantitative decision-theoretic rough set of multi-source information system (MS-GMDQ-DTRS) to handle this issue. First, we propose a generalized multi-granulation rough set model for MsIS (MS-GMRS) as the basis of other models. In this model, each single information system is treated as a granular structure. Next, we combine MS-GMRS with double-quantitative decision-theoretic rough set to obtain two new models. They have better fault tolerance capability compared with MS-GMRS. Furthermore, we propose corresponding algorithms to calculate the approximation accuracy of the proposed models. Experiments are carried out on four datasets downloaded from UCI. Experimental results show that the two new models have better fault tolerance in directly acquiring knowledge from MsIS.