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Final Report Summary - GS-A-DM-DS (Grey Systems and Its Application to Data Mining and Decision Support)

In this project, the international incoming research fellow, Prof. Sifeng Liu, has spent two years at De Montfort University conducting the proposed research together with Prof. Yingjie Yang. They have published over 30 research papers in academic journals and conferences, and conducted more than 10 outreach activities and training programs, both in China and in Europe. As a result, an international association on grey systems and uncertainty analysis has been established with members from China, Europe and North American.

During the course of the scientific research, the proposed outcome of the project was fully realized as follows:

Through systematic research into grey model selection and calibration, a set of criteria for grey model selection and calibration has been formulated. The suitable sequences of different models were studied by simulation and analysis with homogeneous exponential sequences, nonhomogeneous exponential increasing sequences, and vibration sequences. The robustness of various models with different sequences were evaluated and recommendations given for the selection of grey models for these sequences. Furthermore, a multi-variable weakening buffer operator was put forward which makes use of the freshest data and its buffer effect for small data. We proved that the essence of the weakening buffer operator can reduce the effects of disturbance. The analytical expression of discrete fractional summation operator and difference operator were also put forward. The properties, such as exponential law and commutative law have been proved. Based on these operators, a fractional reverse accumulative discrete grey model is put forward to reduce the perturbation of the discrete grey forecasting models, so as to increase its stability and make full use of new information of the system. The specific calibration formula was also defined. There results make grey prediction and forecasting easily accessible to new users who have no background knowledge in Grey Systems. This will help to promote the application of Grey Systems to data mining in Europe.

Based on the investigation on the special characteristics of limited and poor data, a number of new grey models have been developed in this project. Firstly, a novel self-memory multi-variable model is proposed. The new model can describe the relationships among system variables uniformly and improve the accuracy of the model. Secondly, a novel nonlinear grey Bernoulli self-memory model is developed for data sequences featured with saturation or fluctuation. The NGBSM model combines the advantages of the self-memory principle of dynamic systems and the traditional nonlinear grey Bernoulli model through a coupling of the above two prediction methods. Thirdly, a grey model with a time varying weighted generating operator is put forward in order to fully extract information concealed in recent data. This model increases the weight of new data and reduces the influence of possible data fluctuations. Fourthly, a grey accumulating generation operator that can smooth the random interference of data is introduced into the double exponential smoothing method. Fifthly, a novel GM(1,N) model is proposed to improve the performance of the traditional GM(1,N) model by introducing a linear correction term and a grey action quantity term to the traditional GM(1,N) model. Finally, based on the fractional order grey accumulating generation operator and reducing generation operator, the fractional order grey prediction model is also proposed. Our case studies demonstrate that these new models have significantly improved their prediction results.

In decision making, a number of new algorithms were also formulated in this project. Firstly, a grey target decision making method based on grey incidence analysis is proposed. This method integrates grey decision making together with intuitionistic fuzzy sets and achieves better results. Secondly, a novel two-stage decision making model with the weight vector of grey synthetic measures and the decision coefficient vectors is put forward to solve the clustering dilemma of “rule of maximum” in decision making. Thirdly, a new method of grey entropy-weight decision making is also proposed.

These new models have been validated by simulation and real application case studies, and their performance is superior to the counterparts in our research. Among these real world applications, of particular success is the performance evaluation of large commercial aircraft vendors for the ongoing Chinese large aircraft development. It demonstrates the feasibility of the proposed methodologies in real world R&D management of complex products.

These new prediction models will result in more accurate and reliable prediction and forecasting with small data and poor information. It will contribute to data mining operations requiring high speed and reliability and reduce data requirements. The new decision models will enable more realistic and reliable decision making and make the uncertainty representation more accessible for ordinary users.

All these research results have been published by leading international academic journals and conferences, and they are going to have significant impact in the development of grey systems and data mining both in China and Europe. As a developing subject, there are still gaps in grey systems both in theoretical and applied research, and they have restricted its further development in Europe. The progress made in this project has showcased the feasibility of grey systems in data mining and its great potential in limited and poor data. Given the big data oriented research in Europe, this project fills the gap for data mining with limited and poor data, and will contribute greatly to those areas with limited and poor data, such as social economic analysis, healthcare, new product development, etc. It is valuable especially for business decision makers, public policy makers and public system managers to obtain useful information from limited and poor information.

To promote the result of this research, the incoming fellow and the scientist in charge have made a number of outreach activities to deliver visits, seminars and training courses. For example, they have visited and delivered seminars at Napier University, South Bank University, Bucharest University of Economic Studies, Universidad Pablo de Olavide, Fuzhou University, Xiamen University, Lanzhou University, Shihezi University, Hebei University of Engineering, etc. They have also delivered a number of training courses at De Montfort University and Nanjing University of Aeronautics and Astronautics. Furthermore, they organized the 2015 IEEE International Conference on Grey Systems and Intelligent Services at De Montfort University. They have also initialized the establishment of the International Association of Grey Systems and Uncertainty Analysis in 2016. Obviously, the results of this project help to establish a new subject in Europe and complement the existing big data initiatives.

More details of this project is available at the project website (

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David Naylor, (Research & Innovation Officer)
Tel.: +44 116 257 7075


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