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

Abstract

PurposeThe 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/approachBased 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.FindingsThe 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 implicationsThe 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/valueThe 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.

Time-Aware and Grey Incidence Theory Based User Interest Modeling for Document Recommendation

“…We find that they are different geometric curves (i.e., more strictly, zigzagged lines) based on the geometric characteristics of the factor and reference sequences. Calculating the importance degree of user interest j I entails calculating the curve correlation between them, and grey incidence analysis theory can efficiently solve this kind of a problem [20,21].…”

“…Moreover, ζ Thus, it must be improved in practical specific applications. Given its development through many years, the grey incidence theory covers two incidence degrees: the Grey Closeness Incidence Degree (GCID) and the Grey Similarity Incidence Degree (GSID) [20,21,24], which have been improved by some scholars. We apply the two incidence degrees in analyzing and calculating the UICD.…”

“…The area in the three cases can be calculated using (9) according to the related mathematical knowledge. The proof of (9) is given in [21]. Thus, the final calculation formula of GCID is represented in line with Equations (8) and (9) and is given by …”

“…The similarity degree describes the geometric similarity between the user interest sequence zigzagged line and the interest degree sequence zigzagged line. According to [21], the formula of GSID is given by…”

A new grey relational model based on discrete Fourier transform and its application on Chinese marine economic

“…Xie and Liu (2011) proposed the grey geometric correlation model. Liu et al (2006Liu et al ( , 2011 constructed the grey absolute association model and the grey correlation degree of the similarity perspective based on the whole directed area of the broken line enclosed graph. Shi et al (2008Shi et al ( , 2010 constructed grey period correlation degree based on similarity vision and grey amplitude correlation degree.…”