Similarity measure for multi-granularity rough approximations of vague sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1609-1621
Author(s):  
Jie Yang ◽  
Wei Zhou ◽  
Shuai Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Target Concept ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Vague Sets ◽  
Rough Approximation ◽  
Vague Concept

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

Fuzzy Miner

2011 ◽  
pp. 299-321 ◽  
Author(s):  
Nikos Pelekis ◽  
Babis Theodoulidis ◽  
Ioannis Kopanakis ◽  
Yannis Theodoridis
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Selection ◽  
Internet Routing ◽  
Data Mining Approach ◽  
New Information

QOSP Quality of Service Open Shortest Path First based on QoS routing has been recognized as a missing piece in the evolution of QoS-based services in the Internet. Data mining has emerged as a tool for data analysis, discovery of new information, and autonomous decision-making. This paper focuses on routing algorithms and their appli-cations for computing QoS routes in OSPF protocol. The proposed approach is based on a data mining approach using rough set theory, for which the attribute-value system about links of networks is created from network topology. Rough set theory offers a knowledge discovery approach to extracting routing-decisions from attribute set. The extracted rules can then be used to select significant routing-attributes and make routing-selections in routers. A case study is conducted to demonstrate that rough set theory is effective in finding the most significant attribute set. It is shown that the algorithm based on data mining and rough set offers a promising approach to the attribute-selection prob-lem in internet routing.

A survey on granular computing and its uncertainty measure from the perspective of rough set theory

2019 ◽  
Vol 6 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Yunlong Cheng ◽  
Fan Zhao ◽  
Qinghua Zhang ◽  
Guoyin Wang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Uncertainty Measure

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

Representations of Vague Approximation Operators

2011 ◽  
Vol 282-283 ◽  
pp. 287-290
Author(s):  
Hai Dong Zhang ◽  
Yan Ping He
Keyword(s):  
Artificial Intelligence ◽  
Mathematical Model ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Relation ◽  
Partial Knowledge ◽  
Data Bases ◽  
Approximation Operators ◽  
Rough Approximation

As a suitable mathematical model to handle partial knowledge in data bases, rough set theory is emerging as a powerful theory and has been found its successive applications in the fields of artificial intelligence such as pattern recognition, machine learning, etc. In the paper, a vague relation is first defined, which is the extension of fuzzy relation. Then a new pair of lower and upper generalized rough approximation operators based on the vague relation is first proposed by us. Finally, the representations of vague rough approximation operators are presented.

An approach to the analysis of design concepts using the rough set theory

2004 ◽  
Vol 18 (4) ◽  
pp. 343-355 ◽  
Author(s):  
D. ALISANTOSO ◽  
L.P. KHOO ◽  
I.B.H. LEE
Keyword(s):  
Information System ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Design Knowledge ◽  
Dynamic Design ◽  
Design Evolution ◽  
Design Concepts ◽  
Design Specifications

This paper describes an approach to the analysis of design concepts (DCs) using the rough set theory. The proposed approach attempts to extract design knowledge from past designs, and used the knowledge obtained to perform DC–capability mapping in a dynamic design evolution environment. The mapping enables designers to estimate the feasibility of a DC to meet stipulated design specifications. The proposed approach encompasses two algorithms, namely, the dissimilar objects algorithm and the attribute decomposition algorithm, to deal with an information system with unavailable information and multidecision attributes, respectively. The details of these algorithms are presented. A case study on the design of vacuum cleaners is used to illustrate the capability of the proposed approach.

scholarly journals Idealization of j-approximation spaces

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 287-301
Author(s):  
Mona Hosny
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Current Work ◽  
Core Concept ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Generalized Rough Set ◽  
The Ideal

The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

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