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Uncertainty representation and information measurement of grey numbers

Uncertainty representation and information measurement of grey numbers The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.Design/methodology/approachThis paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.FindingsThe results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.Practical implicationsUncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.Originality/valueThe proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Grey Systems: Theory and Application Emerald Publishing

Uncertainty representation and information measurement of grey numbers

Grey Systems: Theory and Application , Volume 10 (4): 18 – Oct 16, 2020

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
2043-9377
DOI
10.1108/gs-01-2020-0009
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.Design/methodology/approachThis paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.FindingsThe results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.Practical implicationsUncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.Originality/valueThe proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.

Journal

Grey Systems: Theory and ApplicationEmerald Publishing

Published: Oct 16, 2020

Keywords: Grey number; Uncertainty; Information; Probability; Information elements

References