Ana Burusco

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.

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.

Upper bounding overlaps by groupings

The notions of overlapping and grouping arise from the problem how to assign an object to exactly one class among several available. In this respect, overlaps and groupings are connected with t-norms and t-conorms. However, there are some properties of t-norms and t-conorms that are not valid for overlaps and groupings, for example, that any t-norm is less than or equal than any t-conorm. This fact motivates the proposed research. Specifically, we determine conditions to ensure that an overlap is smaller than a certain grouping and methods to define operators satisfying such ordering. The relevance of this study is visible at the end of the paper by the inclusion of an illustrative example in the context of image processing.

Fuzzy concept lattices and fuzzy relation equations in the retrieval processing of images and signals

Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 25, Suppl. 1 (December 2017) 99-120

Linking Mathematical Morphology and L-Fuzzy Concepts

Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 25, Suppl. 1 (December 2017) 73–98

From Trillas’ Negations and Antonyms to a Set Representation of Contradiction Within Bipolar and Other Extensions of Fuzzy Sets

In 1979, Enric Trillas started to interest in in fuzzy connectives. His first paper on this topic was ”Funciones de negacin en la teora de subconjuntos difusos” ([9]) (Negation functions in the theory of fuzzy subsets), which appeared in Spanish in the Stochastica journal. This work, focused on the characterization of strong negations, has been so relevant for the development of fuzzy theory that it was translated into English and widely cited in the last 35 years.

The incidence relation of an L-Fuzzy Context as structuring element in Fuzzy Mathematical Morphology

The goal of this work is to prove a link between the Fuzzy Mathematical Morphology and the L-fuzzy Concept Analysis when we are using structuring relations which represent the effect that we want to produce over an initial fuzzy image or signal. In this case, we prove that the problem of obtaining the Lfuzzy concepts of an L-fuzzy context is equivalent to the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or closing.

Obtaining significant relations in L-fuzzy contexts

We use linguistic variables in order to obtain significant relations in L-Fuzzy contexts (L,X, Y,R) that allow us to extract complete information from the L-Fuzzy context.We analyze, in particular, the case of anomalous values in the relation R of the L-Fuzzy context, proposing a replacing method in the case where they are erroneous.