Novel models of grey relational analysis based on visual angle of similarity and nearness

Abstract

Purpose

The purpose of this paper is to solve the problems existing in traditional grey incidence models and advance several new grey incidence models based on visual angle of similarity and nearness.

Design/methodology/approach

Based on the definition of traditional grey incidence models, two novel grey incidence models, grey similar incidence model and grey close incidence model, are studied in this paper. The interrelations and influence can be measured by the new models with different visual angle of similarity and/or nearness, respectively. The grey similar incidence model is used mainly to measure the similitude degree of the geometric patterns of sequence curves. The grey close incidence model is used mainly to measure the nearness of the sequence curves in space. The properties of the new models are discussed. It is proved that the proposed models are simplified methods to calculate the similitude degree and the close degree of grey incidence models.

Findings

The results show that the two novel grey incidence models satisfy the grey incidence axiom properly. It is useful to calculate the similitude degree and the close degree of two different sequences, and the process of calculating is easier than with traditional grey incidence models.

Practical implications

The method exposed in the paper can be used to calculate every two sequences. The similitude degree and the close degree of two different sequences can be given out. The method can also be used to rank sequences of more than two.

Originality/value

The paper succeeds in constructing two novel grey incidence models. The properties of novel model are studied and it is undoubtedly a new development in grey systems theory.

Citation

Liu, S., Xie, N. and Forrest, J. (2011), "Novel models of grey relational analysis based on visual angle of similarity and nearness", Grey Systems: Theory and Application, Vol. 1 No. 1, pp. 8-18. https://doi.org/10.1108/20439371111106696