Optimistic Multigranulation Rough Set Research Articles

A novel multigranulation roughness of bipolar fuzzy set over dual universes and its applications

In the world, multigranulation rough sets and bipolar fuzzy sets are the practical tools for dealing with the uncertainty, vagueness, and imperfection that frequently arise in decision making problems. The goal of multigranulation rough sets is to characterize uncertain situations in various granularity spaces, whereas bipolar fuzzy sets (BFSs) have the capacity to handle uncertainty as well as informational bipolarity in a variety of contexts. This article examines the optimistic multigranulation rough approximation of a BFS in the light of multi-soft binary relations across two different universes. We investigate some algebraic properties of our newly constructed optimistic multigranulation rough set scheme. Measures of accuracy and roughness are also covered in this paper. Finally, two decision algorithms are designed with respect to aftersets and foresets that are applied to a decision making problem in disease diagnoses, and the applicability of the method is illustrated by a numerical example.

Multigranulation vague rough set over two universes and its application to group decision making

This article studies the rough approximation of a vague concept based on multiple granularity over two universes. With the description of the background of risk decision making problems in reality, we first present the optimistic multigranulation rough vague set, pessimistic multigranulation rough vague set and variable precision multigranulation rough vague set on the multigranulation approximation space over two universes. Then, under the multigranulation fuzzy approximate space over two universes, we establish the corresponding three types of multigranulation vague rough set over two universes. Subsequently, the interesting properties and results as well as the relationship between the multigranulation rough vague set models and multigranulation vague rough set model over two universes are investigated in detail. The results show that multigranulation vague rough set models are extensions of the existing generalized rough set models under the framework of two universes. At the same time, we construct a new approach to group decision making under uncertainty by using the theory of multigranulation vague rough set over two universes. The basic principal and the detailed steps of the decision making model given in this paper are presented in detail. Meanwhile, an example of handling a medical diagnosis group decision making problem illustrates this approach. The main contribution of this paper is twofold. One is to provide the theoretical model of multigranulation vague rough set over two universes. Another is to try making a new way to handle group decision making problems under uncertainty based on multigranulation vague rough set theory and methodologies over two universes.

Multi-Granulation Rough Set for Incomplete Interval-Valued Decision Information Systems Based on Multi-Threshold Tolerance Relation

A relation is viewed as a granularity from a granular computing perspective. A classic rough set contains only one granularity. A multi-granulation rough set contains multiple granularities, which promotes the applications of classical rough set. Firstly, this paper uses the incomplete interval-valued decision information system (IIVDIS) as research object and constructs two rough set models in the light of single granularity rough set model for applying the rough set theory to real life more widely, which are optimistic multi-granulation rough set (OMGRS) model and pessimistic multi-granulation rough set (PMGRS) model in the IIVDIS. Secondly, we design two algorithms to compute the roughness and the degree of dependence that are two tools for measuring uncertainty of rough set. Finally, several experiments are performed on six UCI data sets to verify the validity of the proposed theorems.

SDMGRS: Soft Dominance Based Multi Granulation Rough Sets and Their Applications in Conflict Analysis Problems

The classical rough set theory was presented by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In this paper, we initiate a multi attribute group decision making problems in the presence of multi attribute and multi decision in decision making with preferences. Then resolving the problem, using two different approximation strategies, i.e., seeking common reserving difference and seeking common rejecting difference, four kinds of soft dominance-based multi-granulation rough sets are presented, namely, soft dominance based optimistic multi-granulation rough sets and soft dominance based pessimistic multi-granulation rough sets and their applications in solving a multi agent conflict analysis decision problem. The proposed method addresses the limitations of the Pawlak model and Sun's conflict analysis model and thus improve these models. Finally, the results on labor management negotiation problems show that the proposed algorithms are more effective and efficient for feasible consensus strategy when compared with Sun's technique.

Cardiac arrhythmia classification using multi-granulation rough set approaches

Cardiovascular disease is a most important reason for human death in modern society. Electrocardiogram (ECG) signal deals with valuable information about functioning of the heart. For that reason, ECG investigation signifies an efficient way to identification and treat different types of cardiac arrhythmia diseases. Nowadays various pattern classification methods has been developed for the classification of ECG signals. These classification methods helps to physician for diseases diagnosis. A multi-granulation rough set (MGRS) has become a new direction of rough set theory, which is based on multiple binary relations on the universe of discourse. In this present study, Multi-granulation rough set based classification approaches (Pessimistic Multi-Granulation Rough Set (PMGRS) and Optimistic Multi-Granulation Rough Set (OMGRS)) are applied to mine appropriate rules to explore better decision making process. The experiments were conducted on the ECG data from the Physionet arrhythmia database to classify five kinds of normal and abnormal signals. In the classification process, Feature extraction played an important role. And we have used two kinds feature extraction methods (1) Pan Tomkins (PT) feature extraction method. This method used to extract the morphological features are P, Q, R, S, T peak intervals, which is also used to determine heart rate. (2) Wavelet transform (WT) feature extraction method. This method used to extract the wavelet coefficients. Both two methods are successfully applied to (ECG signal) classification. The proposed multi-granulation rough set rule based classification methods is validated using the first 24 channel of the ECG signal records of the MIT-BITH arrhythmia database, and achieves finding high accuracies. Experimental results show that the proposed classification techniques significantly outperforms other well-known techniques.

L -fuzzy multigranulation rough set based on residuated lattices

This paper studies L-fuzzy multigranulation rough set based on residuted lattices, which is considered as an extension of the classical L-fuzzy rough set. Two models of L-fuzzy optimistic multigrannulation rough set and L-fuzzy pessimistic multigrannulation rough set based on residuted latteices are suggested. Then, we mainly investigate some funda- mental properties of the L-fuzzy multigranulation rough set model. With regards to residuated lattices' topology, we study the topological and the lattice structure in the L-fuzzy optimistic multigranulation rough set model and L-fuzzy pessimistic multigranulation rough set model, respectively.

A comparative study of multigranulation rough sets and concept lattices via rule acquisition

Recently, by combining rough set theory with granular computing, pessimistic and optimistic multigranulation rough sets have been proposed to derive “AND” and “OR” decision rules from decision systems. At the same time, by integrating granular computing and formal concept analysis, Wille’s concept lattice and object-oriented concept lattice were used to obtain granular rules and disjunctive rules from formal decision contexts. So, the problem of rule acquisition can bring rough set theory, granular computing and formal concept analysis together. In this study, to shed some light on the comparison and combination of rough set theory, granular computing and formal concept analysis, we investigate the relationship between multigranulation rough sets and concept lattices via rule acquisition. Some interesting results are obtained in this paper: (1) “AND” decision rules in pessimistic multigranulation rough sets are proved to be granular rules in concept lattices, but the inverse may not be true; (2) the combination of the truth parts of an “OR” decision rule in optimistic multigranulation rough sets is an item of the decomposition of a disjunctive rule in concept lattices; (3) a non-redundant disjunctive rule in concept lattices is shown to be the multi-combination of the truth parts of “OR” decision rules in optimistic multigranulation rough sets; and (4) the same rule is defined with a same certainty factor but a different support factor in multigranulation rough sets and concept lattices. Moreover, algorithm complexity analysis is made for the acquisition of “AND” decision rules, “OR” decision rules, granular rules and disjunctive rules.

Optimistic Multi-granulation Rough Set Based Classification for Medical Diagnosis

Medical analysis has been approached by several machine learning methods for many years.Pattern recognition algorithms are capable of improving the quality of prediction, early diagnosis of diseases and disease classification. The classification complications in medical area are solved based on the outcome of medical analysis or report of medical treatment by the medical specialist. This research focuses on applying Rough set based data mining techniques for medical data to discover locally frequent diseases. This work applies Optimistic Multi-granulation rough set model (OMGRS) for medical data classification. Multi-granulation rough set provides efficient results than single granulation rough set model and soft rough set based classifier model. The results of applying the OMGRS methodology to medical diagnosis based upon selected information. The performance of the proposed optimistic multi granulation Rough set based classification is compared with other rough set based (RS), Kth Nearest Neighbor (KNN) and Back propagation neural network (BPN) approaches using various classification Measures.

Multigranulation rough set theory over two universes

Recently, a multigranulation rough set MGRS has become a new direction in rough set theory, which is based on multiple binary relations on the universe of discourse. The existing literature about multigranulation rough set is based on the assumption of the same universe. In reality, however, a good deal of practical decision making may relate to the possibility of two or more different universes. In this paper, we consider the rough approximation of a given concept over two different universes with respect to the multigranulation space formed by different mappings of the two universes, i.e., the multigranulation rough set model. We respectively define the optimistic multigranulation rough set, pessimistic multigranulation rough set and variable precision multigranulation rough set over two universes, each of which can be appropriate to a different real-world decision-making problem in management science. Then several important properties of these models are discussed in detail. Also, the relationship between the multigranulation rough set over two universes and the existing models in the literature is investigated. At last, the entropy and granularity of the binary mapping between two different universes are defined, and then we give an approach to uncertainty measurement based on the granularity of binary mapping for multigranulation rough set over two universes. The multigranulation rough set model over two universes provides a new, effective approach for practical decision problems in management science.

Incomplete Variable Multigranulation Rough Sets Decision

Recently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is different from the Pawlake's rough set since the former takes multiple granulations on the un iverse into account. In this paper, by analyzing the limitations of optimistic multigranulation rough set (OMGRS) and pessimistic multigranulation rough set (PMGRS) in incomplete information system, the incomplete variable multigranulation rough set (VMGRS) is proposed, and the relationships among VMGRS, OMGRS and PMGRS are deeply explored, From the properties, it can be found that OMGRS and PMGRS are the special cases compared to our VMGRS. Furthermore, several important measurements are introduced into the VMGRS; it is shown that the measurements of the VMGRS are between the measurements of OMGRS and PMGRS. Finally, som e numerical examples are employed to substantiate the conceptual arguments.

Multigranulation rough sets: From partition to covering

The classical multigranulation rough set (MGRS) theory offers a formal theoretical framework for solving the complex problem under multigranulation environment. However, it is noticeable that MGRS theory cannot be applied in multi-source information systems with a covering environment in the real world. To address this issue, we firstly present in this paper three types of covering based multigranulation rough sets, in which set approximations are defined by different covering approximation operators. Then, by using two different approximation strategies, i.e., seeking common reserving difference and seeking common rejecting difference, two kinds of covering based multigranulation rough set are presented, namely, a covering based optimistic multigranulation rough set and a covering based pessimistic multigranulation rough sets. Finally, we develop some properties and several uncertainty measures of the covering based multigranulation rough sets. These results will enrich the MGRS theory and enlarge its application scope.

Hierarchical Structures on Multigranulation Spaces

Though many hierarchical structures have been proposed to analyze the flner or coarser relationships between two granulation spaces, these structures can only be used to compare the single granulation spaces. However, it should be noticed that the concept of multigranulation plays a fundamental role in the development of granular computing. Therefore, the comparison between two multigranulation spaces has become a necessity. To solve such problem, two types of the multigranulation spaces are considered: one is the partition-based multigranulation space, the other is the covering-based multigranulation space. Three difierent hierarchical structures are then proposed on such two multigranulation spaces, respectively. Not only the properties about these hierarchical structures are discussed, but also the relationships between these hierarchical structures and the multigranulation rough sets are deeply investigated. It is shown that the flrst hierarchical structure is consistent with the monotonic varieties of optimistic multigranulation rough set, and the second hierarchical structure is consistent to the monotonic varieties of pessimistic multigranulation rough set, the third hierarchical structure is consistent to the monotonic varieties of both optimistic and pessimistic multigranulation rough sets.

On the structure of the multigranulation rough set model

The original rough set model, i.e., Pawlak’s single-granulation rough set model has been extended to a multigranulation rough set model, where two kinds of multigranulation approximations, i.e., the optimistic and pessimistic approximations were introduced. In this paper, we consider some fundamental properties of the multigranulation rough set model, and show that(i)Both the collection of lower definable sets and that of upper definable sets in the optimistic multigranulation rough set model can form a lattice, such lattices are not distributive, not complemented and pseudo-complemented in the general case. The collection of definable sets in the optimistic multigranulation rough set model does not even form a lattice in general conditions.(ii)The collection of (lower, upper) definable sets in the optimistic multigranulation rough set model forms a topology on the universe if and only the optimistic multigranulation rough set model is equivalent to Pawlak’s single-granulation rough set model.(iii)In the context of the pessimistic multigranulation rough set model, the collections of three different kinds of definable sets coincide with each other, and they determine a clopen topology on the universe, furthermore, they form a Boolean algebra under the usual set-theoretic operations.