Generalized concept lattices have been recently proposed to deal with uncertainty or incomplete information as a non-symmetric generalization of the theory of fuzzy formal concept analysis. On the other hand, concept lattices have been defined as well in the framework of fuzzy logics with noncommutative conjunctors. The contribution of this paper is to prove that any concept lattice for non-com...

Beginning with triangular fuzzy inputs representing fuzzy ratio judgments, we experiment with two procedures to obtain fuzzy relative priorities in the Analytic Hierarchy Process. We extend the simple geometric mean and simple normalized column sum methods with fuzzy arithmetic. When the pairwise comparisons are fully consistent the methods produce identical results, but they diverge in the pre...

This paper continuous the approach of developing an ordertheoretic structure theory of one-dimensional continuum structures as elaborated in [Wi07] (see also [Wi83],[Wi03]). The aim is to extend the order-theoretic structure theory by a meaningful algebraization; for this, we concentrate on the real linear continuum structure with its derived concept lattice which gives rise to the so-called “r...

Repertory grids are used widely in Personal Construct Psychology (PCP) research. An array of accepted techniques for analysing grid data is available to researchers. This paper revisits the use of formal concept analysis (FCA) in analysing repertory grids. It particular, this paper focuses on using FCA to explore hierarchical structures in grid data. A description of the technique is provided, ...

The provision of shared visual representations is considered to be an important facilitator for creative processes in group working and learning scenarios. Although reusability is an inherent feature of computerised representations in general, a comparative analysis of existing tools shows clear deficits in this respect. We are convinced that reusability and thus sustainability of the results o...

We suggest the Formal Concept Analysis (FCA) as theoretical backbone in technology-enhanced learning settings to support a students ́ learning process in two ways: i) by engaging with concept lattices, the structure of the knowledge domain and the interrelations of its concepts become explicit, and ii) by providing visual feedback in form of open learner modelling, the student ́s reflection on th...

Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most impor...