Cristina Alcalde

A constructive method for the definition of interval-valued fuzzy implication operators

In this paper, a new characterization for the interval-valued fuzzy implication operators is presented, which provides a simple way to construct interval valued fuzzy implication operators from a given fuzzy implication operator using aggregation operators. This method will be used for defining the interval-valued fuzzy R- and S-implications. Finally, some examples of the interval-valued fuzzy implications built by this constructive method and a comparative study among them are shown.

Treatment of L-Fuzzy contexts with absent values

This work shows how to extract the missing information from an interval-valued L-Fuzzy context with some unknown values. Absent values are replaced using implications between attributes with high levels of support and confidence. Three kinds of implications are defined and analyzed for this purpose. We apply these results to an electrical network simulation, where the estimated relations between faulty power lines and voltage measurements can be compared with their real values.

The use of linguistic variables and fuzzy propositions in the L-Fuzzy concept theory

The use of linguistic variables and fuzzy propositions in the interval-valued L-Fuzzy contexts can be an interesting tool to extract a more complete information from them. In this paper, we analyze three different situations. First, we obtain significant relations in order to study all the objects and attributes of the interval-valued L-Fuzzy context by means of the interval-valued L-Fuzzy concepts. After that, we show how to replace the erroneous values to be able to study in a suitable way the context. Finally, we use the linguistic labels to obtain a subcontext that represents our interest of study. We also show an experimental evaluation in the paper.

The use of two relations in L-fuzzy contexts

In the analysis of relations among the elements of two sets it is usual to obtain different values depending on the point of view from which these relations are measured. The main goal of the paper is the modelization of these situations by means of a generalization of the L-fuzzy concept analysis called L-fuzzy bicontext.We study the L-fuzzy concepts of these L-fuzzy bicontexts obtaining some interesting results. Specifically, we will be able to classify the biconcepts of the L-fuzzy bicontext.Finally, a practical case is developed using this new tool.

Application of the L-fuzzy concept analysis in the morphological image and signal processing

In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed result has also an interpretation for binary images or signals.

Evolution in time of L-fuzzy context sequences

In this work, we consider a complete lattice L and we study L-fuzzy context sequences which represent the evolution in time of an L-fuzzy context. To carry out this study, in the first part of the paper, we consider n-ary OWA operators in complete lattices, which enable us to make a general analysis and a temporal analysis at any moment in time of L-fuzzy context sequences. After that, evolution in time of the relationship between the objects and the attributes is considered. In particular, we analyze the concepts of Trend and Persistent formal contexts. Finally, we illustrate our results with an example where we consider the particular lattice L = J ( 0 , 1 ) .

ANALYSIS OF CERTAIN L-FUZZY RELATIONAL EQUATIONS AND THE STUDY OF ITS SOLUTIONS BY MEANS OF THE L-FUZZY CONCEPT THEORY

Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ LE×E which is reflexive and symmetric, certain fuzzy relations are characterized as solutions of X ⊲ R = X, proving that they play the role of the blocks in the context of crisp tolerance relations. Moreover, it is verified that these new fuzzy blocks can be determinated by means of the L-fuzzy concepts associated with the K-labeled L-fuzzy context (L,K,E,E,R).

Interval-valued linguistic variables: an application to the L-fuzzy contexts with absent values

The goal of this work is to extend the concept of the linguistic variable to the interval-valued case since there are some situations where their application would be justified, as can be seen in this paper. After a brief introduction on fuzzy numbers and linguistic variables in [0, 1], we define the interval-valued linguistic variables and we study their behaviour through three properties. In the second part of the paper, we show their utility for replacing the absent values in an L-fuzzy context.

The study of fuzzy context sequences

This is an accepted manuscript of an article published by Taylor & Francis in International Journal of Computational Intelligence Systems in 2013, available online: http://wwww.tandfonline.com/ 10.1080/18756891.2013.781337.

Fuzzy property-oriented concept lattices in morphological image and signal processing

Fuzzy property-oriented concept lattices are a formal tool for modeling and processing incomplete information in information systems. This paper relates this theory to fuzzy mathematical morphology, which scope, for instance, is to process and analyze images and signals. Consequently, the theory developed in the concept lattice framework can be used in these particular settings.