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The purpose of this paper is to solve the problem existing in the forecast of impact disturbance grey system.

Under the axiomatic system of buffer operator in grey system theory, a novel kind of buffer operators with variable weight λ based on the principle of average tempo of time sequence and using new information is proposed. The optimization solution for variable weight λ is obtained by using genetic algorithm. It is proved that the new buffer operators are effective.

The results show that the new buffer operators accord with the buffer operator's three axioms and the monotonicity non‐variable axiom. It is proved theoretically and in practice that the new buffer operators are more useful than other buffer operators in grey modeling for sequence with impact disturbance.

The novel buffer operators can reduce the randomness of grey sequence distorted by impact factors, and the forecast accuracy of a model which is built through the process with a novel buffer operator is significantly increased.

The paper succeeds in constructing two novel buffer operators with variable weight and the properties of novel operators are studied. The method to solve optimization value of weight is proposed. The method widens the scope of grey model application.

The paper attempts to design an efficient algorithm for bearing track correlation of multi‐sensor on the same platform using grey incidence analysis which is on the basis of the line segment Hausdorff distance.

Starting from the line segment, Hausdorff distance that has been extended to calculate the distance between line segment sets by many scholars has been used for face recognition achieving good results. The degree of grey incidence is defined based on the above distance and properties which include normality, symmetry and closeness, are proved. Furthermore, a grey incidence matrix is built. With only the azimuth information detected by bearing sensors track correlation is difficult to judge, however grey incidence analysis can quickly and accurately determine whether two tracks are from the same target, and so an algorithm is designed to solve this dilemma. In the last part of the paper simulation experiment is conducted.

The results are convincing: not only the algorithm proposed in the paper can solve the problem of track correlation of bearing‐only sensors, but also the algorithm can judge the correlation degree of both tracks even in the case of intensive targets.

The method exposed in the paper can be used to judge correlation degree of tracks detected by different sensors even for less information, and also be used to determine the similarity of two waveforms in the field of engineering.

The paper succeeds in introducing the line segment Hausdorff distance into grey incidence analysis and on the basis of that an algorithm is designed to solve the problem of track correlation.

The purpose of this paper is to find the reason which the results of grey variable weight clustering method do not correspond with the reality. It proposes reconstructing the whitenization weight function, outlining why and how inconsistency is avoided. The study aims to improve the model of grey clustering method based on the whitenization weight function and list the steps of the new clustering model so that analysis and application of innovation capacity in a broader range is normally found.

First the reason for the problem that the clustering results of grey variable weight clustering do not correspond with the reality is analyzed in two existing literature. And then a new whitenization weight function is reconstructed, two properties of the whitenization weight function are proved. The solution of the new grey variable weight clustering based on the whitenization weight function is built by following six steps.

The paper provides a new whitenization weight function which satisfies the normative and non-triplecrossing. It suggests that successful clustering results of innovation capacity act on two levels: integrating the elements of innovation capacity indexes, and following steps of grey variable weight clustering.

This paper improves the existing method of grey variable weight clustering and fulfills an identified need to study how cities’ innovation capacity can be clustered.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.