Adjoint pairs or adjoint triples defined on lattices have proven to be a useful tool when working in fuzzy formal concept analysis. This paper shows that adjoint pairs and triples can play as well an important role within the framework of multilattices, especially in order to form the Galois connections needed to build concept multilattices.

The most popular basis in Formal Concept Analysis is the Duquenne-Guigues basis, which ensure minimality in the number of dependencies and it is built with pseudo-intents, and some method to calculate these basis from an arbitrary set of implications have been introduced. We propose in this paper, an automated method to calculate a left-minimal direct basis from the set of all implications buil...

We provide a generalization of Formal Concept Analysis that works with different types of the values in a heterogeneous formal context. An appropriate counterpart of the basic theorem on concept lattices is formulated. We suggest the transformation of the heterogeneous formal context to Galois connectional approach. Illustration on an example is included. Moreover, we show that this approach is...

Within object oriented software, the minimal unit of development and testing is a class. So understanding how a class is defined and behaves is important. Considering that a class is composed of instance variables and methods, the process is not so easy to achieve because we must decide which different viewpoints can help us to detect features of a class. These viewpoints can include identifyin...

In [5], a representation of bounded lattices within so-called standard topological contexts has been developed. Based on the theory of formal concept analysis [14] it includes Stone’s representation of Boolean algebras by totally disconnected compact spaces [10], Priestley’s representation of bounded distributive lattices by totally order disconnected compact spaces [7] as well as Urquhardt’s r...

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the seq...

In Formal Concept Analysis the classical formal context is analized taking into account only the positive information, i.e. the presence of a property in an object. Nevertheless, the non presence of a property in an object also provides a significant knowledge which can only be partially considered with the classical approach. In this work we have modified the derivation operators to allow the ...

The main purpose of this paper is to show the use of FCA to support the building of ontology-based Traditional Chinese Medicine with herbal medicine serving as an example. This knowledge-sharing platform may make expert’s knowledge clearer, may connect with average people, and may provide patients with an opportunity to participate in and become knowledgeable of the whole prescription for his/h...

In formal concept analysis, the sets of attributes and objects are usually different, with different meaning and, hence, it might not make sense to evaluate them on the same carrier. In this context, the operators used to obtain the concept lattice could be defined by considering different lattices associated to attributes and objects. Anyway there exist several reasons for which we need to eva...

The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. All needed categorical properties like categorical product, tensor product and its bifunctor properties are presented and proved. Finally, the second order generalisation of FCA is represented by a category built up...