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• The new landscape in the longitudinal research of type-2 fuzzy sets (T2FS) domain are presented. • The multi-criteria decision making has gradually developed into moto theme. • The knowledge diffusion trajectory and thematic evolution of T2FS domain are presented. • The application of T2FSs in decision-making may the possible development directions. Nowadays, more scholars and practitioners are committed to improving and applying type-2 fuzzy sets (T2FSs) in various domains because of the stronger ability to handle the uncertainty of fuzzy complex systems. To explore the status and internal laws of development of this field, this paper presents the development overview based on the bibliometric analysis, then the dynamic evolution of main topics and the knowledge diffusion trajectory are also displayed on the basis of the strategy diagram and main path analysis (MPA). From 1997 to 2019, 1749 documents are retrieved from Web of Science (WoS) repository for the analysis. The results show that there are four stable collaborative communities existing in the countries/regions' collaborative network and the collaboration is affected by geographical factors to some degree. Three main evolution paths of hot topics are also presented in this paper and the multi-criteria decision-making (MCDM) has gradually developed into the moto theme. Furthermore, articles appearing on the main path mainly focus on the research of basic concept and framework, self-optimization and applications in various domains of T2FSs. In general, this paper provides a new landscape in the longitudinal research based on the development overview, thematic evolution and the knowledge diffusion trajectory. [ABSTRACT FROM AUTHOR]

The conceptual structures built with Formal Concept Analysis (FCA) and its extensions are appropriate constructs for supporting Exploratory Search (ES). FCA indeed classifies a set of objects described by Boolean attributes in a concept lattice which is prone to (intra-lattice) navigation. Relational Concept Analysis (RCA), for its part, classifies several sets of objects connected through multiple binary relationships by using logical operators (quantifiers) which can be approximate. The output is a set of interconnected concept lattices, thus adding inter-lattice navigation opportunities. In this paper, we describe the web platform RCAviz, which aims to support such intra- and inter-lattice navigation. The user can select a subset of objects and attributes as a starting point for navigation. Then RCAviz shows the associated concept and its close intra- and inter-lattice neighbors. The user can access to the objects and attributes introduced and inherited in a concept. They then can navigate, i.e. zoom and pan the current view, and move from one concept to another. Additional views show the previous and the next conceptual structures, as well as an history which allows the user to browse its navigation. A navigation example is shown on a real dataset to illustrate the potential of RCAviz for ES. [ABSTRACT FROM AUTHOR]

Topological relations are the predominant backbone of qualitative spatial reasoning, focusing to date mostly on objects that are embedded in R 2. With the advent of ball-shaped screen technologies and the growing importance of globally situated data, the digital sphere, known as T 2 , becomes a viable embedding. While topological relations have been investigated for a spherical embedding S 2 within a continuous framework, the lack of a full account of the relations in T 2 prevents more refined query systems on global discrete data. This paper extends the concept of spherical topological relations to the digital spherical embedding, building on the model of a planar digital region in Z 2 whose boundary comprises the pixels along the region's margin. With the 9-intersection and its detailed descendant, the 9+-intersection, 29 relations between two digital regions are derived. This set of binary digital spherical relations is jointly exhaustive and pairwise disjoint. The relations' conceptual neighborhood graph, capturing the similarity among the relations, further highlights that 18 of the 29 relations are refinements of those found in S 2. These topological relations between digital regions coincide with the binary relations found between broad-boundary regions when the broad boundaries are of uniform thickness, a scenario preventing the inclusion of an entire interior of one region within the boundary of the other. Five different rationales for coarsening are investigated, each leading to a different group of the relations along the conceptual neighborhood graph. [ABSTRACT FROM AUTHOR]

Abstract: The theory of Formal Concept Analysis is used as a knowledge representation mechanism and as a conceptual clustering method. Formal context is a basic notion in this theory. This paper proposes a kind of formal context, called n-Strong-Direct-Product-Formal-Context (n-SDPFC, for short), by the strong direct product of n formal contexts. It is found that the new context is closely related to the n original formal contexts in many aspects, for example, the concept lattices, and the implications between attributes, and so on. With the help of Kronecker product of boolean matrices, the main features of an n-SDPFC is given, and the method how to represent a formal context with such features by the strong direct product of some small formal contexts is brought forward. With this method, the workload for knowledge acquisition in formal context will be eased enormously. [Copyright &y& Elsevier]

Abstract: This paper addresses the important problem of efficiently mining numerical data with formal concept analysis (FCA). Classically, the only way to apply FCA is to binarize the data, thanks to a so-called scaling procedure. This may either involve loss of information, or produce large and dense binary data known as hard to process. In the context of gene expression data analysis, we propose and compare two FCA-based methods for mining numerical data and we show that they are equivalent. The first one relies on a particular scaling, encoding all possible intervals of attribute values, and uses standard FCA techniques. The second one relies on pattern structures without a priori transformation, and is shown to be more computationally efficient and to provide more readable results. Experiments with real-world gene expression data are discussed and give a practical basis for the comparison and evaluation of the methods. [Copyright &y& Elsevier]