scholarly journals On Some Types of Multigranulation Covering Based on Binary Relations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ashraf Nawar ◽  
E. A. Elsakhawy
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Equivalence Relations ◽  
Binary Relations ◽  
New Models ◽  
Covering Rough Set

Recently, the notions of right and left covering rough sets were constructed by right and left neighborhoods to propose four types of multigranulation covering rough set (MGCRS) models. These models were constructed using the granulations as equivalence relations. In this paper, we introduce four types of multigranulation covering rough set models under arbitrary relations using the q -minimal and q -maximal descriptors of objects in a given universe. We also study the properties of these new models. Thus, we explore the relationships between these models. Then, we put forward an algorithm to illustrate the method of reduction based on the presented model. Finally, we give an illustrative example to show its efficiency and importance.

Approximations in Rough Sets vs Granular Computing for Coverings

2012 ◽  
pp. 152-163
Author(s):  
Guilong Liu ◽  
William Zhu
Keyword(s):  
Knowledge Discovery ◽  
Binary Relation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Knowledge Discovery In Databases ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Covering Rough Set

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

Approximations in Rough Sets vs Granular Computing for Coverings

2010 ◽  
Vol 4 (2) ◽  
pp. 63-76 ◽  
Author(s):  
Guilong Liu ◽  
William Zhu
Keyword(s):  
Binary Relation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Knowledge Discovery In Databases ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Covering Rough Set

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

Covering Rough Clustering Approach for Unstructured Activity Analysis

2016 ◽  
Vol 12 (2) ◽  
pp. 1-11 ◽  
Author(s):  
Prabhavathy Panneer ◽  
B.K. Tripathy
Keyword(s):  
Rough Set ◽  
Human Activities ◽  
Rough Sets ◽  
Real Life ◽  
Activity Analysis ◽  
Equivalence Relations ◽  
Sequential Data ◽  
Clustering Approach ◽  
Covering Rough Set ◽  
Real World Problems

Several tasks under human activities need to be performed in a sequence of navigation and manipulation of objects. In several applications of human activities like robotics monitoring plays an important role. So, in these applications, processing of sequential data is of utmost importance. Because of the presence of imprecision intelligent clustering approaches using fuzzy or rough set techniques play a major role. The basic rough sets which are defined by using equivalence relations is less useful because of their scarcity in real life scenarios. As a result, covering based rough sets have been introduced which are more general and applicable to real world problems. In this paper, covering rough set based clustering approach is introduced and studied using refined first type of covering based rough sets. Through experimental analysis,illustrated the efficiency of proposed algorithm and provided a comparative analysis of this algorithm with other existing algorithms.

scholarly journals Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 462 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Multiple Criteria ◽  
Approximation Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Covering Rough Set

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

scholarly journals Two Different Views for Generalized Rough Sets with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2275
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Mostafa K. El-Bably ◽  
Kamel K. Fleifel
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Binary Relations ◽  
Medical Field ◽  
Good Decision ◽  
Heart Attacks ◽  
Generalized Rough Sets

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base; that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar
Keyword(s):  
Information System ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Granular Computing ◽  
Real Life ◽  
Equivalence Relations ◽  
Life Problems ◽  
Algebraic Properties ◽  
The Universe

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.

Uncertainty Measurement for Covering Rough Sets

2014 ◽  
Vol 22 (02) ◽  
pp. 217-233 ◽  
Author(s):  
Jianhua Dai ◽  
Debiao Huang ◽  
Huashi Su ◽  
Haowei Tian ◽  
Tian Yang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Accuracy Measure ◽  
Uncertainty Measurement ◽  
Covering Rough Set ◽  
Measure Entropy ◽  
Theoretical Results ◽  
Generalized Rough Sets

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

scholarly journals Pseudolabel Decision-Theoretic Rough Set

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Xun Wang ◽  
Wendong Zhang ◽  
Dun Liu ◽  
Hualong Yu ◽  
Xibei Yang ◽  
...  
Keyword(s):  
Data Analysis ◽  
Rough Set ◽  
Heuristic Algorithm ◽  
Rough Sets ◽  
Attribute Reduction ◽  
Experimental Results ◽  
Data Sets ◽  
Binary Relations ◽  
Sensitivity Problem ◽  
Neighborhood Relation

In decision-theoretic rough set (DTRS), the decision costs are used to generate the thresholds for characterizing the probabilistic approximations. Similar to other rough sets, many generalized DTRS can also be formed by using different binary relations. Nevertheless, it should be noticed that most of the processes for calculating binary relations do not take the labels of samples into account, which may lead to the lower discrimination; for example, samples with different labels are regarded as indistinguishable. To fill such gap, the main contribution of this paper is to propose a pseudolabel strategy for constructing new DTRS. Firstly, a pseudolabel neighborhood relation is presented, which can differentiate samples by not only the neighborhood technique but also the pseudolabels of samples. Immediately, the pseudolabel neighborhood decision-theoretic rough set (PLNDTRS) can be constructed. Secondly, the problem of attribute reduction is explored, which aims to further reduce the PLNDTRS related decision costs. A heuristic algorithm is also designed to find such reduct. Finally, the clustering technique is employed to generate the pseudolabels of samples; the experimental results over 15 UCI data sets tell us that PLNDTRS is superior to DTRS without using pseudolabels because the former can generate lower decision costs. Moreover, the proposed heuristic algorithm is also effective in providing satisfied reducts. This study suggests new trends concerning cost sensitivity problem in rough data analysis.

Research on the N-Reduction of Fuzzy Covering Rough Sets

2014 ◽  
Vol 556-562 ◽  
pp. 3682-3685
Author(s):  
Qiao Yan Li ◽  
Yan Yan Chen ◽  
Shao Yang Li
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Lower Approximation ◽  
Covering Rough Set

The granular reduction plays an important role in covering rough sets, and the aim of this paper is to explore the granular reduction of covering rough sets and fuzzy covering rough set Firstly, the covering rough sets based on neighborhood element and the N-reduction are introduced, and their properties are discussed; secondly, The definitions and properties of upper and lower approximation of fuzzy covering rough based on the neighborhood are given; Lastly, the N- reduction of fuzzy covering rough based on the neighborhood element is proposed, and we can get that covering rough sets remain the same upper and lower approximations for N-reduction.

Multigranulation roughness based on soft relations

2021 ◽  
pp. 1-16
Author(s):  
Muhammad Shabir ◽  
Jamalud Din ◽  
Irfan Ahmad Ganie
Keyword(s):  
Finite Number ◽  
Rough Set ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Soft Sets ◽  
Upper Approximation ◽  
Special Cases ◽  
Multigranulation Rough Set ◽  
Empty Subset ◽  
Lower And Upper Approximations

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.

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