Eloísa Ramírez-Poussa

Attribute reduction in multi-adjoint concept lattices

Knowledge reduction is one of the key issues in formal concept analysis and there have been many studies on this topic. The irreducible elements in a lattice are also very important, since they form the basic information of a relational system. Moreover, they are also important from the viewpoint of attribute reduction.Both topics are notably more complicated in a fuzzy setting since not only the size of the sets of attributes and objects influence the size of the fuzzy concept lattice, but the truth-value sets, where the sets of objects, attributes and the relation are evaluated, are important.This paper presents, in the general fuzzy framework of multi-adjoint concept lattices, a characterization of the meet-irreducible elements, from which a classification of attributes and its application to attribute reduction is introduced.

Attribute and size reduction mechanisms in multi-adjoint concept lattices

Attribute reduction and size reduction in concept lattices are key research topics in Formal Concept Analysis (FCA). This paper combines both strategies in the multi-adjoint concept lattice framework in order to simplify the information provided by the original context. Specifically, we present three procedures which merge the attribute reduction and the size reduction by means of an irreducible α -cut concept lattice, analyzing the obtained properties.

On the use of irreducible elements for reducing multi-adjoint concept lattices

Looking for strategies to reduce the size of concept lattices is very important in formal concept analysis, when they preserve the main information of the relational database.This paper presents several properties of the useful fuzzy-attributes, in the general fuzzy case of multi-adjoint concept lattices and provides two mechanisms in order to reduce the size of concept lattices based on irreducible elements, without losing or modifying important information. Specifically, the reduced concept lattices are sublattices of the original one. Moreover, interesting properties of these mechanisms are studied and the relationship among both and other strategies is also introduced.

Adjoint negations, more than residuated negations

Negation operators are useful operators, which have extensively been studied and used in different fuzzy settings, such as in fuzzy logic. This paper introduces a new and flexible kind of negation operator, based on adjoint triples, and which is called adjoint negation relative to a fixed element.Besides proving several interesting properties, the comparison with weak negations, studied by Trillas, Esteva et al., and pairs of weak negations introduced by Georgescu and Popescu, is presented. Furthermore, adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor.

On the use of thresholds in multi-adjoint concept lattices

The size of the concept lattices increases exponentially from the number of objects and attributes. This situation is more complicated in the fuzzy case, in which the considered carriers to evaluate the objects and attributes, and for the relation, are also taken into account. Hence, it is very important to study mechanisms to reduce the size of fuzzy concept lattices maintaining the main information. One of the most important mechanisms to reduce the size of concept lattices is the use of thresholds in the concept-forming operators. This paper studies this mechanism in the general fuzzy framework of multi-adjoint concept lattices, obtaining interesting properties and consequences.

Fuzzy-Attributes and a Method to Reduce Concept Lattices

Reducing the size of the concept lattices is a fundamental problem in formal concept analysis. This paper presents several properties of useful fuzzy-attributes, in the general case of multi-adjoint concept lattices. Moreover, the use of these fuzzy-attributes provides a mechanism to reduce the size of concept lattices considering a subset of the original one and, therefore, without losing and modifying important information.

Bireducts with tolerance relations

Abstract Reducing the number of attributes by preventing the occurrence of incompatibilities and eliminating existing noise in the original data is an important goal in different frameworks, such as in those focused on modelling and processing incomplete information in information systems. Bireducts were introduced in Rough Set Theory (RST) as one of successful solutions for the problem aimed at achieving a balance between elimination of attributes and characterization of objects that the remaining attributes can still distinguish. This paper considers bireducts in a general framework in which attributes induce tolerance relations over the available objects. In order to compute the new reducts and bireducts a characterization based on a general discernibility function is given.

Attribute Reduction in Rough Set Theory and Formal Concept Analysis

Rough Set Theory (RST) and Formal Concept Analysis (FCA) are two mathematical tools for data analysis which, in spite of considering different philosophies, are closely related. In this paper, we study the relation between the attribute reduction mechanisms in FCA and in RST. Different properties will be introduced which provide a new size reduction mechanism in FCA based on the philosophy of RST.

General Negations for Residuated Fuzzy Logics

Involutive residuated negations are usually considered in residuated fuzzy logics and they are also based on continuous triangular norms. This paper introduces a generalization of these negations using flexible conjunctors, several properties of them and the corresponding disjunctive dual operators associated with the conjunctor.

Characterizing reducts in multi-adjoint concept lattices

Abstract The construction of reducts, that is, minimal sets of attributes containing the main information of a database, is a fundamental task in different frameworks, such as in Formal Concept Analysis (FCA) and Rough Set Theory (RST). This paper will be focused on a general fuzzy extension of FCA, called multi-adjoint concept lattice, and we present a study about the attributes generating meet-irreducible elements and on the reducts in this framework. From this study, we introduce interesting results on the cardinality of reducts and the consequences in the classical case.