article

Grey sets and greyness

Authors:

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 185, Issue 1

Pages 249 - 264

https://doi.org/10.1016/j.ins.2011.09.029

Published: 01 February 2012 Publication History

Abstract

This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed.

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Wang LFang ZZhang QLiu S(2023)Generalized grey dynamic clustering models with preferencesJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-23081645:3(3555-3565)Online publication date: 1-Jan-2023
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Index Terms

Grey sets and greyness
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic

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Reviews

Reviewer: Alexei Botchkarev

Making decisions based on incomplete and uncertain information is a challenge that faces researchers and management at all levels. Fuzzy sets and rough sets are well-established methodologies for dealing with uncertainties. Grey systems, proposed 30 years ago by Julong Deng, are less familiar to the broad scientific community, but have proven to be a helpful tool. Recently, these systems have been receiving increased attention. A grey system is usually defined as a system involving uncertain information presented by partially known grey numbers. A "grey number is a number with [an] unknown position within a clear boundary [(interval)]. In this sense, ... a set of candidate numbers within that boundary [is called] a grey set" [1]. In a grey system, "the information is classified into three categories: white, with completely certain information; grey, with insufficient information; and black, with totally unknown information. Grey systems are concerned with, in particular, the information belonging to the grey category" [1]. A distinctive feature of this research paper is that it compares fuzzy sets, rough sets, and grey systems. The definitions and theorems are accompanied by simple quantitative examples. The authors conclude that fuzzy sets, rough sets, and grey systems are different models for representing uncertainty, although they have some overlapping areas. It is shown that grey sets can be used to specify uncertainties where interval-valued fuzzy sets or rough sets fail. Readers who are interested in grey systems can find additional information on the subject [2,3]. The paper will be interesting to scientists specializing in fuzzy sets and grey systems, and to a broader group of researchers working on methods and tools for representing uncertainty. Its high quality is evident in the accurate definitions and logical presentation of the material. Online Computing Reviews Service

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Published In

Information Sciences: an International Journal Volume 185, Issue 1

February, 2012

265 pages

ISSN:0020-0255

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Elsevier Science Inc.

United States

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Published: 01 February 2012

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Wang LFang ZZhang QLiu S(2023)Generalized grey dynamic clustering models with preferencesJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-23081645:3(3555-3565)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.3233/JIFS-230816
Schneider JKuchta DMichalski R(2023)A vector visualization of uncertainty complementing the traditional fuzzy approach with applications in project managementApplied Soft Computing10.1016/j.asoc.2023.110155137:COnline publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1016/j.asoc.2023.110155
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Wang FLi HLi YWu A(2021)A BWM-based approach for customer-oriented product development with insufficient information and its application to 5 G smartphone designJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21079940:6(12443-12458)Online publication date: 1-Jan-2021
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Fan YFang ZLiu SLiu J(2021)A grey approach to site selection for nursing homesJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20048040:5(8807-8818)Online publication date: 1-Jan-2021
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Recommendations

A comparative study of fuzzy sets and rough sets

Axiomatic systems for rough sets and fuzzy rough sets

A new extension of fuzzy sets using rough sets: R-fuzzy sets

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