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The purpose of this paper is to propose a framework for data analytics where everything is grey in nature and the associated uncertainty is considered as an essential part in data collection, profiling, imputation, analysis and decision making.

A comparative study is conducted between the available uncertainty models and the feasibility of grey systems is highlighted. Furthermore, a general framework for the integration of grey systems and grey sets into data analytics is proposed.

Grey systems and grey sets are useful not only for small data, but also big data as well. It is complementary to other models and can play a significant role in data analytics.

The proposed framework brings a radical change in data analytics. It may bring a fundamental change in our way to deal with uncertainties.

The proposed model has the potential to avoid the mistake from a misleading data imputation.

The proposed model takes the philosophy of grey systems in recognising the limitation of our knowledge which has significant implications in our way to deal with our social life and relations.

This is the first time that the whole data analytics is considered from the point of view of grey systems.

Online health monitoring of large complex equipment has become a trend in the field of equipment diagnostics and prognostics due to the rapid development of sensing and computing technologies. The purpose of this paper is to construct a more accurate and stable grey model based on similar information fusion to predict the real-time remaining useful life (RUL) of aircraft engines.

First, a referential database is created by applying multiple linear regressions on historical samples. Then similarity matching is conducted between the monitored engine and historical samples. After that, an information fusion grey model is applied to predict the future degradation trajectory of the monitored engine considering the latest trend of monitored sensory data and long-term trends of several similar referential samples, and the real-time RUL is obtained correspondingly.

The results of comparative analysis reveal that the proposed model, which is called similarity-based information fusion grey model (SIFGM), could provide better RUL prediction from the early degradation stage. Furthermore, SIFGM is still able to predict system failures relatively accurately when only partial information of the referential samples is available, making the method a viable choice when the historical whole life cycle data are scarce.

The prediction of SIFGM method is based on a single monotonically changing health indicator (HI) synthesized from monitoring sensory signals, which is assumed to be highly relevant to the degradation processes of the engine.

The SIFGM can be used to predict the degradation trajectories and RULs of those online condition monitoring systems with similar irreversible degradation behaviors before failure occurs, such as aircraft engines and centrifugal pumps.

This paper introduces the similarity information into traditional GM(1,1) model to make it more suitable for long-term RUL prediction and also provide a solution of similarity-based RUL prediction with limited historical whole life cycle data.

The purpose of this paper is to present the terms of grey numbers and its operations.

The definitions of elementary terms about grey numbers and its operations are presented one by one.

The reader could know the basic explanation about the important terms about grey numbers and its operations from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

The purpose of this paper is to present the terms of grey incidence analysis models.

The definitions of basic terms about various grey incidence analysis models are presented one by one.

The reader could know the basic explanation about the important terms about various grey incidence analysis models from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

The purpose of this paper is to present the terms of grey forecasting models and techniques.

The definitions of basic terms about grey forecasting models and techniques are presented one by one.

The reader could know the basic explanation about the important terms about various grey forecasting models and techniques from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

The purpose of this paper is to present the terms of sequence operators and grey data mining.

The definitions of basic terms about sequence operators and grey data mining are presented one by one.

The reader could know the basic explanation about the important terms about sequence operators and grey data mining from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

The purpose of this paper is to present the terms of grey clustering evaluation models.

The definitions of basic terms about grey clustering evaluation models are presented one by one.

The reader could know the basic explanation about the important terms about various grey clustering evaluation models from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

The purpose of this paper is to present the terms of concepts and fundamental principles of grey systems.

The definitions of basic terms about concepts and fundamental principles of grey systems are presented one by one.

The reader could know the basic explanation about the important terms about concepts and fundamental principles of grey systems from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.