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.

This 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.

The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.

Uncertain 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.

The 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.