Study on distance measuring and sorting method of general grey number

Jiang, Shi Quan; Liu, Sifeng; Fang, Zhigeng; Liu, Zhongxia

doi:10.1108/gs-07-2017-0019

Cited by 6 publications

(5 citation statements)

References 14 publications

(18 reference statements)

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“…Almost simultaneously, the general grey number and their operations were summarized in [21]. After that, the general grey number can be used in many fields [25]- [27] because of its adequate representation and arithmetic operation system.…”

Section: Introductionmentioning

confidence: 99%

Enhance the Uncertainty Modeling Ability of Fuzzy Grey Cognitive Maps by General Grey Number

2020

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In real-life systems, people cannot get precise data. The data are represented in the forms of interval or multiple intervals in many cases. Most intelligent algorithms are designed for precise data in algorithm research. People always use a real number contained in the interval or multiple intervals as the candidate for the precise data. However, such a measure will lose lots of information contained in the interval or multiple intervals. Fuzzy Cognitive Map (FCM) is one of the famous intelligent algorithms. The Fuzzy Grey Cognitive Map (FGCM) was proposed to enable FCM to do interval computation. But FGCM can only deal with a single interval, as for multiple intervals, the FGCM is powerless. Thus, this paper aims to enhance the FGCM to make it can cope with multiple intervals. The paper introduces the general grey number and deduces the new activation functions according to Grey System Theory (GST) and Taylor series. Finally, an industrial process control problem is applied to verify the new algorithm. The results show that the new algorithm is not only compatible with the original FGCM and FCM, but can process more uncertain knowledge and data. In general, the new algorithm inherits most of FGCM's characteristics and can cope with the data expressed by multiple intervals, which means it can be used in environments with more uncertain knowledge and data.INDEX TERMS Fuzzy grey cognitive map, fuzzy cognitive map, uncertainty modeling, general grey number, grey system theory.

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Section: Introductionmentioning

confidence: 99%

Enhance the Uncertainty Modeling Ability of Fuzzy Grey Cognitive Maps by General Grey Number

2020

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“…The degree of greyness, for convenience, will be called greyness later, is a indicator of how much uncertainty a grey number represents [44]. If a grey number is ⊗, and the domain is Ω, the greyness is [45]:…”

Section: A Fuzzy Grey Cognitive Mapsmentioning

confidence: 99%

“…The µ() is the function to calculates the measure or "length" of the grey number or the domain [45]. And 0 As a fuzzy number is a kind of special case of a grey number [46], the FGCM uses IGNs instead of fuzzy numbers.…”

Section: A Fuzzy Grey Cognitive Mapsmentioning

confidence: 99%

The Dynamic Extensions of Fuzzy Grey Cognitive Maps

et al. 2021

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Fuzzy Cognitive Map is recognized as an important model in soft computing. The Fuzzy Cognitive Map theory studies often treat uncertainty modeling and dynamic modeling separately. So far, there is no single Fuzzy Cognitive Map that can deal with uncertain data and dynamic environments simultaneously. This paper proposed an environment model to describe the link between changing weights and the dynamic environment. As the extensions of the classic Fuzzy Grey Cognitive Map, two dynamic models were designed and implemented in this work: Dynamic Fuzzy Grey Cognitive Map and Dynamic Fuzzy General Grey Map.In this work, we also analyze the characteristics of the two models and evaluate their performance using industrial control problems. The results showed that the proposed models could well handle uncertain data in dynamic environments.

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“…To depict the foundation of a value range, the grey numbers can be divided into various categories, and out of these, the interval grey number is the most common category. While analyzing the characteristics of interval grey numbers, Liu et al (Jiang et al , 2017) established a novel algorithm, and a series of definitions, which are introduced in the following sections.…”

Section: Basic Concepts Of Interval Grey Numbersmentioning

confidence: 99%

“…Later, Xie adequately discussed the arithmetic of grey number system, but his findings without any reasonable formulas (Xie and Xin, 2014). While such shortcomings were addressed by Liu et al (2010), who defined and formulated a system called “Kernel”, along-with subsequent degree of greyness, on which a new algorithm of interval grey numbers has been established (Jiang et al , 2017). Later on Yang et al , 2012 further studied and refined the general grey numbers to develop a more sophisticated algebraic system.…”

Section: Introductionmentioning

confidence: 99%

An enhanced algorithm for calculating the degree of greyness of interval grey numbers and its application

Geng

Feng

Dang

et al. 2019

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Purpose This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent. Design/methodology/approach The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness. Findings Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results. Originality/value The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.

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Study on distance measuring and sorting method of general grey number

Cited by 6 publications

References 14 publications

Enhance the Uncertainty Modeling Ability of Fuzzy Grey Cognitive Maps by General Grey Number

Enhance the Uncertainty Modeling Ability of Fuzzy Grey Cognitive Maps by General Grey Number

The Dynamic Extensions of Fuzzy Grey Cognitive Maps

An enhanced algorithm for calculating the degree of greyness of interval grey numbers and its application

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