Grey sets and greyness

This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed

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

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

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

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency

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

Evaluation of Smart City Logistics Solutions

The negative effects of goods flows realisation are most visible in urban areas as the places of the greatest concentration of economic and social activities. The main goals of this article were to identify the applicable Industry 4.0 technologies for performing various city logistics (CL) operations, establish smart sustainable CL solutions (SSCL) and rank them in order to identify those which will serve as the base points for future plans and strategies for the development of smart cities. This kind of problem requires involvement of multiple stakeholders with their opposing goals and interests, and thus multiple criteria. For solving it, this article proposed a novel hybrid multi-criteria decision-making (MCDM) model, based on BWM (Best-Worst Method) and CODAS (COmbinative Distance-based ASsessment) methods in grey environment. The results of the model application imply that the potentially best SSCL solution is based on the combination of the concepts of micro-consolidation centres and autonomous vehicles with the support of artificial intelligence and Internet of Things technologies. The main contributions of the article are the definition of original SSCLs, the creation of a framework and definition of criteria for their evaluation and the development of a novel hybrid MCDM model

Grey number based methodology for non-homogeneous preference elicitation in fuzzy risk analysis management

The significantly increase in the number of vehicles have become a major problem, that cause enormous problems such as congestion, pollution, wastage of money and time. Therefore, the simulating and optimizing traffic control algorithms are needed to accommodate the demand in order to solve traffic congestion problems. Predicting effective and optimal green time taken for the intersections will help minimizing the traffic congestion henceforth reducing the waiting time. In this study, fuzzy logic is used to find optimal traffic waiting time. The method determines the effective and optimal traffic signal timing that suits different traffic densities. In this case, the study has considered a four-way intersection. The results indicate that different road intersections require different effective and optimal of green time to reduce traffic congestion. The higher the number of cars at the intersection, the effective green time will be longer rather than the lesser number of cars. The flexibility feature of the fuzzy logic will provide suitable optimal green time for the intersection, which is cordially benefit the users. It is worth mentioning that fuzzy logic traffic lights controller performed better than the fixed-time controller due to its flexibility and the capability in reducing the waiting time

Dry Port Terminal Location Selection by Applying the Hybrid Grey MCDM Model

Globalization and decentralization of production generate the intensive growth of goods and transport flows, mostly performed by the maritime transport. Ports, as the main nodes in the global logistics networks, are becoming congested, space for their expansion limited, and traffic in their hinterland congested. As a solution to these and many other hinterland-transport-related problems stands out the development of dry port (DP) terminals. Selection of their location is one of the most important strategic decisions on which depends their competitiveness in the market and the functionality of the logistics network. Accordingly, the evaluation and selection of locations for the development of the DP in accordance with the requirements of various stakeholders is performed in this paper, as a prerequisite for the establishment of an ecological, economic, and socially sustainable logistics network in the observed area. To solve this problem, a new hybrid model of multi-criteria decision-making (MCDM) that combines Delphi, AHP (Analytical Hierarchy Process), and CODAS (Combinative Distance-based Assessment) methods in a grey environment is developed. The main contributions of this paper are the defined model, the problem-solving approach based on finding a compromise solution, simultaneous consideration of the environmental, economic, and social sustainability of the DP concept and its implementation in the regional international markets. The applicability of the approach and the defined MCDM model is demonstrated by solving a real-life case study of ranking the potential DP locations in the Western Balkans region. Based on the obtained results, it is concluded that in the current market conditions, it would be most realistic to open three DP terminals, in Zagreb, Ljubljana, and Belgrad