Uncertainty representation of grey numbers and grey sets

In the literature there is a presumption that a grey set and an interval-valued fuzzy set are equivalent. This presumption ignores the existence of discrete components in a grey number. In this paper new measurements of uncertainties of grey numbers and grey sets, consisting of both absolute and relative uncertainties, are defined to give a comprehensive representation of uncertainties in a grey number and a grey set. Some simple examples are provided to illustrate that the proposed uncertainty measurement can give an effective representation of both absolute and relative uncertainties in a grey number and a grey set. The relationships between grey sets and interval-valued fuzzy sets are also analysed from the point of view of the proposed uncertainty representation. The analysis demonstrates that grey sets and intervalvalued fuzzy sets provide different but overlapping models for uncertainty representation in sets

A commentary on some of the intrinsic differences between grey systems and fuzzy systems

The aim of this paper is to distinguish between some of the more intrinsic differences that exist between grey system theory (GST) and fuzzy system theory (FST). There are several aspects of both paradigms that are closely related, it is precisely these close relations that will often result in a misunderstanding or misinterpretation. The subtly of the differences in some cases are difficult to perceive, hence why a definitive explanation is needed. This paper discusses the divergences and similarities between the interval-valued fuzzy set and grey set, interval and grey number; for both the standard and the generalised interpretation. A preference based analysis example is also put forward to demonstrate the alternative in perspectives that each approach adopts. It is believed that a better understanding of the differences will ultimately allow for a greater understanding of the ideology and mantras that the concepts themselves are built upon. By proxy, describing the divergences will also put forward the similarities. We believe that by providing an overview of the facets that each approach employs where confusion may arise, a thorough and more detailed explanation is the result. This paper places particular emphasis on grey system theory, describing the more intrinsic differences that sets it apart from the more established paradigm of fuzzy system theory

Investigation on soft computing techniques for airport environment evaluation systems

Spatial and temporal information exist widely in engineering fields, especially in airport environmental management systems. Airport environment is influenced by many different factors and uncertainty is a significant part of the system. Decision support considering this kind of spatial and temporal information and uncertainty is crucial for airport environment related engineering planning and operation. Geographical information systems and computer aided design are two powerful tools in supporting spatial and temporal information systems. However, the present geographical information systems and computer aided design software are still too general in considering the special features in airport environment, especially for uncertainty. In this thesis, a series of parameters and methods for neural network-based knowledge discovery and training improvement are put forward, such as the relative strength of effect, dynamic state space search strategy and compound architecture. [Continues.

Weight Analysis for Multiattribute Group Decision-Making with Interval Grey Numbers Based on Decision-Makers’ Psychological Criteria

open access articleTo address the problem of multiattribute group decision-making with interval grey numbers, decision matrices are adjusted using kernels of interval grey numbers to reduce the psychological effects of decision-makers. The comprehensive weights of attributes are obtained by aggregating the subjective weights with objective weights, which are calculated based on the accuracy and difference of attributes. Considering the consistent, best, and worst decision-making abilities of decision-makers, grey incidence models are established to obtain the consistency weights and individual bipolar weights of decision-makers; then, the comprehensive weights of decision-makers are determined. A clustering approach of interval grey numbers is presented, and overall evaluations are obtained. Finally, an example is provided and its validity is tested to verify the feasibility of the proposed method

Weld pool and keyhole dynamic analysis based on visual system and neural network during laser keyhole welding

In keyhole fiber laser welding processes, the weld pool behavior and keyhole dynamics are essential to determining welding quality. To observe and control the welding process, the accurate extraction of the weld pool boundary as well as the width is required. In addition, because of the cause-and-effect relationship between the welding defects and stability of the keyhole, which is primarily determined by keyhole geometry during the welding process, the stability of keyhole needs to be considered as well.^ The first part of this thesis presents a weld pool edge detection technique based on an off axial green illumination laser and a coaxial image capturing system that consists of a CMOS camera and optic filters. According to the difference of image quality, a complete developed edge detection algorithm is proposed based on the local maximum gradient of grayness searching approach and linear interpolation. The extracted weld pool geometry and the width are validated by the actual welding width measurement and predictions by a numerical multi-phase model.^ As for the keyhole dynamics, three essential attributes to describe the simplified three-dimensional keyhole shape include keyhole size, penetration depth and keyhole inclination angle. However, when using traditional measurement techniques, it is very challenging to take in-process measurements of penetration depth and inclination angle, even if the keyhole size can be detected by using a visual monitoring system. To realize the on-line estimation of keyhole dynamics and welding defects, a data-based radial basis function neural network state observer is adopted for estimating penetration depth and inclination angle in the transient state when welding parameters change suddenly. First, a static neural network is trained in advance to establish a correlation between the welding parameters and unobservable keyhole geometry. The dynamic state observer is trained based on the transient welding conditions predicted by a numerical model and then used to estimate the time-varying keyhole geometery. Meanwhile, the coaxial monitoring system is used to observe the keyhole shape from the top side in real time, which not only provides input to the neural network but also indicates the potential welding porosities. The predicted results are validated by experimental data performed by welding with stainless steel 304 and magnesium alloy AZ31B

Grey Critical Chain Project Scheduling Technique and Its Application

Based on the idea of Grey System and interval number coefficient notation, a Grey Critical Chain scheduling approach is studied. According to Grey system theory, the time of project or task completion can be considered as the object that extension is definite but intension is uncertain, which is coincident with the character of the project management. The Grey Critical Chain Scheduling Technique mainly aims at the single project time management, but the management idea can also be applied to the other knowledge areas of the project management. In this Technique, we improve the selection method of the buffer time in the Critical Chain, in order to obtain reasonable Feeding Buffer time and Project Buffer time. In this paper, we will use an example to discuss the Grey Critical Chain Scheduling Technique, compare Grey Critical Chain with Program Evaluation and Review Technique, Critical Chain and Fuzzy Critical Chain, analyze the advantages, disadvantages and applicable scope of their own. Key words: Critical Chain, Grey System, Interval Number, Schedule Management, Project Management Résumé: Sur la base de l’idée de Système Gris et la notation du coefficient de nombre d’intervalle, l’approche de pragrammtion d’une Chaîne Critique Grise est étudiée. Selon la théorie du Système Gris, le temps du projet ou de la tâche peut être considéré comme l’objet dont l’extention est définitive mais l’intention est incertaine, qui est conforme au caractère du management de projet. La Technique de Programmation de la Chaîne Critique Grise vise essentiellement le management du temps du projet simple, mais l’idée de management peut aussi être appliquée dans d’autres domaines du management de projet. Avec cette technique, nous améliorons la méthode de sélection du temps d’amortissement dans la Chaîne Critique afin d’obtenir le temps d’amortissement de l’alimentation raisonnable et le temps d’amortissement de projet. Dans l’article présent, nous allons utiliser un exemple pour discuter la Technique de Programmation de la Chaîne Critique Grise, comparer la Chaîne Critique Grise avec l’Evaluation du Programme et la Technique de révision, la Chaîne Critique et la Chaîne Critique Floue, et analyser leurs avantages, désavantages et champ d’application. Mots-Clés: Chaîne Critique, Système Gris, nombre d’intervalle, management de programme, management de proje

A greyness reduction framework for prediction of grey heterogeneous data

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modeling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness

Grey Models and Their Roles in Data Analytics

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper gives an introduction to the basic concepts of grey systems, grey numbers and grey models, and discusses their roles in data analysis of data science. The necessity of small data models is demonstrated, and their complementary functions to Big Data models are investigated. Based on these investigations, a novel framework for combining Big Data models with grey models is proposed

Grey Models and Their Roles in Data Analytics

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper gives an introduction to the basic concepts of grey systems, grey numbers and grey models, and discusses their roles in data analysis of data science. The necessity of small data models is demonstrated, and their complementary functions to Big Data models are investigated. Based on these investigations, a novel framework for combining Big Data models with grey models is proposed