Toward a Generalization of Rough Sets Based on Active and Passive Relations

2006 ◽  
Vol 10 (6) ◽  
pp. 939-945
Author(s):  
Masashi Emoto ◽  
◽  
Rolly Intan ◽  
Masao Mukaidono ◽  
Keyword(s):  
Conditional Probability ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Probability Relation ◽  
Data Elements ◽  
The Relationship

In the generalization of rough sets, many concepts use a relation weaker than the equivalence relation usually used in classical rough sets, e.g., induced by a conditional probability relation. The conditional probability relation is binary and assumes that the relationship between two data (elements or objects) resembles a relationship between two events in conditional probability. We use the asymmetric property of the conditional probability relation to propose active and passive relations, then discuss a generalization and properties of rough sets based on active and passive relations.

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Multi-Granular Computing through Rough Sets

2014 ◽  
pp. 1-34 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Intelligent Systems ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Point Of View ◽  
Information Granules ◽  
Computing Platform

Granular Computing has emerged as a framework in which information granules are represented and manipulated by intelligent systems. Granular Computing forms a unified conceptual and computing platform. Rough set theory put forth by Pawlak is based upon single equivalence relation taken at a time. Therefore, from a granular computing point of view, it is single granular computing. In 2006, Qiang et al. introduced a multi-granular computing using rough set, which was called optimistic multigranular rough sets after the introduction of another type of multigranular computing using rough sets called pessimistic multigranular rough sets being introduced by them in 2010. Since then, several properties of multigranulations have been studied. In addition, these basic notions on multigranular rough sets have been introduced. Some of these, called the Neighborhood-Based Multigranular Rough Sets (NMGRS) and the Covering-Based Multigranular Rough Sets (CBMGRS), have been added recently. In this chapter, the authors discuss all these topics on multigranular computing and suggest some problems for further study.

scholarly journals On the Lattice of Intervals and Rough Sets

2009 ◽  
Vol 17 (4) ◽  
pp. 237-244 ◽  
Author(s):  
Adam Grabowski ◽  
Magdalena Jastrzębska
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Algebraic Theory ◽  
Algebraic Models ◽  
Lower Approximation ◽  
Definable Sets

On the Lattice of Intervals and Rough Sets Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].

Model of Covering Rough Sets in the Machine Intelligence

2012 ◽  
Vol 548 ◽  
pp. 735-739
Author(s):  
Hong Mei Nie ◽  
Jia Qing Zhou
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Machine Intelligence ◽  
Upper Approximation ◽  
Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

The relationship among soft sets, soft rough sets and topologies

2013 ◽  
Vol 18 (4) ◽  
pp. 717-728 ◽  
Author(s):  
Zhaowen Li ◽  
Tusheng Xie
Keyword(s):  
Rough Sets ◽  
Soft Sets ◽  
The Relationship

scholarly journals ANALYSIS OF DESIGNING TRANSPORT ZONES BASED ON NETWORK MODELING

2020 ◽  
Vol 1 (14) ◽  
pp. 125-129
Author(s):  
Ol'ga Lebedeva
Keyword(s):  
Land Use ◽  
Network Modeling ◽  
Transport Modeling ◽  
Physical Conditions ◽  
Transportation Process ◽  
Systematic Methodology ◽  
The Russian Federation ◽  
Data Elements ◽  
The Relationship

The article discusses the existing classifications of land use in relation to freight transport. Research on the relationship between the physical conditions (points of departure and destination) of travel («land use») and the actual transportation process is practically not carried out in the Russian Federation. To conduct them, it is necessary to collect information about the points of departure / destination and justify a systematic methodology for collecting and classifying data elements. Analysis and classification of land use are the foundations of transport planning. As a result of the study, it can be concluded that there is no single system of classification of "land use" suitable for freight transport, and a new version needs to be developed with a choice of attributes important for transport modeling in our country.

Topological Approaches to the Second Type of Covering-Based Rough Sets

2011 ◽  
Vol 204-210 ◽  
pp. 1781-1784
Author(s):  
Bin Chen
Keyword(s):  
Data Mining ◽  
Information Systems ◽  
Rough Sets ◽  
Relative Interior ◽  
Upper Approximation ◽  
Definition Of ◽  
The Relationship

Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies covering-based rough sets from the topological view. We explore the relationship between the relative closure and the second type of covering upper approximation. The major contributions of this paper are that we use the definition of the relative closure and the relative interior to discuss the conditions under which the relative operators satisfy certain classical properties. The theorems we get generalize some of the results in Zhu’s paper.

Sign in / Sign up

Export Citation Format

Share Document