Grey Relational Analysis and Its Application Based on the Angle Perspective in Time Series

Abstract

The research scope of grey relational analysis has not been developed in recent years, and the exiting GRA models are all based on three perspectives, including distance perspective, slope perspective, and area perspective. Under this situation, a novel model called grey relational analysis based on angle perspective (GRAAP) was developed in this paper for the first time, and this model can expand the research scope of GRA. Like other GRA models, GRAAP not only has the properties of symmetry, uniqueness, comparability, and so forth but also can be used to make predictions, assessments, classifications, and so on. Finally, this novel model was proved to be rational and effective through a comparative study on the similar degree of four time series.

A Comparative Study of EMG Indices in Muscle Fatigue Evaluation Based on Grey Relational Analysis during All-Out Cycling Exercise

“…Particularly, the decrease of maximal force or power output has been used as the valid criterion to evaluate the utility of other approaches (e.g., sEMG) in muscle fatigue assessment [ 8 , 9 ]. In previous researches, the proximity of researched indices changes and the decrease of maximal force or power output has been compared and adopted to evaluate the utility of indices [ 10 ], while grey relational analysis is a method to quantifying the proximity of changing trends between inspected sequences and standard sequence by grey relational grade [ 11 , 12 ]. Therefore, the utility of EMG indices in muscle fatigue can be evaluated by comparing their changing trends with maximum force or power output using grey relational analysis.…”

Tourism Competitiveness and Mobile Data: A Grey Relational Analysis for European Entrepreneurship Pre & During Pandemic

“…These data are the starting step for applying GRA. To apply the GRA method we respect the methodological steps and algorithm according to the international literature (Lusi et al, 2020;Nayakappa et al, 2019;Xu et al, 2014;Gerus -Gosciewska & Gosciewski, 2022;Wu & Zhan, 2017;Skrinjaric, 2021;Lusi et al, 2020;Ertugrul et al, 2018;Badi and Elghoul, 2023;Sarpkaya & Sabir, 2016;Fidan, 2020;Girish et al, 2019;Krstić et al, 2023) as follows (Figure 1) and mentioned in Appendix A.…”

“…The grey systems are an effective method for modelling and forecasting short-term time series that can be applied in all areas based on models with limited, incomplete, or uncertain data ranging from social sciences, through economy and economics, to technical sciences (Gerus -Gosciewska & Gosciewski, 2022). The Grey Relational Analysis (GRA), developed by Sunt & Dang (Xu et al, 2014), part of the grey system theory (Pakkar, 2016) can be applied to solve practical problems related to social participation (Gerus -Gosciewska & Gosciewski, 2022; as tourism enterprises development (Gerus -Gosciewska & Gosciewski, 2022) and for data that can be ranked as competitiveness indices and other indicators which can define the competitiveness. More, for data and/or studied with specified ranks, the GRA enables the determination of a significance sequence which indicates those characteristics/particularities that have the greatest influence on the phenomenon under study (Gerus -Gosciewska & Gosciewski, 2022).…”

A Novel Method for the Comprehensive Evaluation of Aerospace Components Based on GRAAP

“…Under these situations, a novel model called Grey Relational Analysis Based on the Angle Perspective (GRAAP) will be introduced in this section; this model not only can greatly improve the accuracy and validity of the research results by making more full use of the poor information in the research objects but has the properties of normativity, uniqueness, parallelism, and order-preserving; meanwhile, it can also expand the research scope of GRA and enrich GRT. Additionally, this novel model is mainly based on two mature models by Tang [19] and Sun and Dang [20] which have been widely accepted by academic and industry, and it can make more full use of the information existing in the research object [28]; therefore, this model will be a more reasonable model. And because of its advantages, it can usually be used to make prediction, assessment, classification and so on in the engineering.…”

“…The modeling thought of GRAAP is rooted in the traditional Grey System Theory (GST) [29]; its basic principle is to utilize the cointegrated similarity of angles to reveal the relationship between different research objects. Similar to other GRA models, GRAAP can also be used to make decisions, make predictions, and make classifications in grey system [28]. And in the system theory, one system can be divided into three categories according to their owned degree of system information; if the system information is fully known, this system will be called white system; if the information is wholly unknown, then it is called black system, and a system with partially known information is usually called a grey system [30][31][32].…”