# Eloisa Ramírez-PoussaUniversidad de Cádiz | UCA · Department of Mathematics

Eloisa Ramírez-Poussa

## About

55

Publications

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419

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Introduction

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February 2012 - January 2016

## Publications

Publications (55)

Managing and extracting information from databases is one of the main goals in several fields, as in Formal Concept Analysis (FCA). One-sided concept lattices and multi-adjoint concept lattices are two frameworks in FCA that have been developed in parallel. This paper shows that one-sided concept lattices are particular cases of multi-adjoint conce...

A fundamental issue about installation of photovoltaic solar power stations is the optimization of the energy generation and the fault detection, for which different techniques and methodologies have already been developed considering meteorological conditions. This fact implies the use of unstable and difficult predictable variables which may give...

This paper shows how fuzzy formal concept analysis can be applied to a real crimes dataset in order to extract patterns and knowledge from it. Different concepts and attribute implications have been selected and interpreted obtaining interesting consequences.

Attribute reduction is a topic of interest in data analysis. In particular, in formal concept analysis attribute reductions are associated with equivalence relations defined on concept lattices. In this paper, we study the equivalence relations induced by attribute reductions with the goal of characterizing when the equivalence classes are not conv...

Complex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, „mimicking” human reasoni...

This paper addresses the problem of attribute and size reduction of concept lattices in formal concept analysis. The reduction of the number of attributes in a formal context produces a partition on the set of concepts of the concept lattice. In this work, we introduce a weaker notion of congruence relation, called local congruence. This less restr...

In this paper, an alternative definition of implication between attributes in formal concept analysis, within the fuzzy environment of the multi-adjoint concept lattices, is presented. This novel definition establishes a relationship between crisp subsets of attributes, according to the information that these subsets provide. One of the main intere...

Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based on the notion of congruence on lattices, with the goal of losing as less information as possible and being su...

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper...

Implications pairs, adjoint pairs and adjoint triples provide general residuated structures considered in different mathematical theories. In this paper, we carry out a deep study on the operators involved in these structures, showing how they are characterized by means of the irreducible elements of a complete lattice. Moreover, the structure of e...

This paper considers an epistemic interpretation of formal contexts, interpreting blank entries in the context matrix as absence of information, which is in agreement with the usual focus on the extraction of implications between attributes. After recalling non-classical connections induced by rough sets and possibility theory in formal concept ana...

Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is called attribute reduction. Recently, the attribute reduction mechanism has been complemented with the use of...

This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on rough sets. The idea behind such a notion is to consider subsets of objects that characterize the different classes given by a decision system. Besides the formal definition of representative set of objec...

This paper presents a theoretical research about the relationship between weak negations and adjoint negations. Adjoint negations are a generalization of residuated negations built from the implications of an adjoint triple. Specifically, this work shows how to build adjoint triples on the unit interval such that their adjoint negations coincide wi...

In this work, we consider a special kind of equivalence relations, which are called local congruences. Specifically, local congruences are equivalence relations defined on lattices, whose equivalence classes are convex sublattices of the original lattices. In the present paper, we introduce an initial study about how the set of equivalence classes...

Formal concept analysis and rough set theory are two of the most important mathematical tools for the treatment of information collected on relational systems. In particular, the idea of reducing the size of a database is widely studied in both theories separately. There are some papers that studied the reduction of a formal context by means of red...

Local congruences are equivalence relations whose equivalence classes are convex sublattices of the original lattice. In this paper, we present a study that relates local congruences to attribute reduction in FCA. Specifically, we will analyze the impact in the context of the use of local congruences, when they are used for complementing an attribu...

Size reduction mechanisms are very important in several mathematical fields. In rough set theory, bireducts arose to reduce simultaneously the set of attributes and the set of objects of the considered dataset, providing subsystems with the minimal sets of attributes that connect the maximum number of objects preserving the information of the origi...

The problem of reducing information in databases is an important topic in Formal Concept Analysis, which has been studied in several papers. In this work, we consider the fuzzy environment of the multi-adjoint concept lattices, since it is a general fuzzy framework that allows us to easily establish degrees of preference on the elements of the cons...

Negations operators have been developed and applied in many fields such as image processing, decision making, mathematical morphology, fuzzy logic, etc. One of the most effective non-monotonic operators are weak negations. This paper studies the algebraic structure and the characterization of the adjoint triples and Galois implication pairs which p...

Adjoint triples are a general structure composed of operators satisfying weak properties, which are usefully used in important frameworks such as fuzzy logic programming, formal concept analysis and fuzzy relation equations. In this work, we will analyze how the exchange principle law should be defined on adjoint triples and what conditions the con...

In this paper we apply the philosophy of Rough Set Theory to reduce formal context in the environment of Formal Concept Analysis. Specifically, we propose a reduction mechanism based on the consideration of bireducts and we also study several properties of the reduced contexts.

This book combines computational intelligence and mathematics to solve theoretical and real-world problems. The real challenges of engineering and other applied sciences, e.g. economics and management, the social sciences, etc., and even everyday life, are increasingly raising complex problems – both in the usual sense, but also in the mathematical...

The reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems. Two remarkable formal tools for extracting such information are Rough Set Theory (RST) and Formal Concept Analysis (FCA), as well as their fuzzy generalizations. This work introduces a new method to reduce attributes i...

The reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems. Two remarkable formal tools for extracting such information are Rough Set Theory (RST) and Formal Concept Analysis (FCA). This work introduces a new method to reduce attributes in FCA considering the reduction philosop...

This paper introduces a procedure to apply Formal Concept Analysis (FCA) to a database obtained from a locate-base social network. In this way, we can know the interest of a target user and make recommendations according to these interests.

Attribute reduction is a fundamental part in different mathematical tools devoted to data analysis, such as, Rough Set Theory and Formal Concept Analysis. These last mathematical theories are closely related and, in this paper, we establish connections between attribute reduction in both frameworks. Mainly, we have introduced a sufficient and neces...

Due to real databases usually contain redundant information, reducing them preserving the main information is one of the most important branches of study within the theory of Formal Concept Analysis (FCA). Taking advantage of the close relationship between Rough Set Theory (RST) and FCA, in this work, we address the problem of attribute reduction i...

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 succes...

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 stu...

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 reductio...

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 a...

The computation of fuzzy concept lattices is really complex. Hence, looking for mechanisms in order to reduce this complexity is fundamental. This paper presents a new efficient mechanism which combines two procedures. First of all, an attribute reduction is given, which removes the unnecessary attributes, and then a reduction based on a truth degr...

The Dedekind–MacNeille completion of a poset P can be seen as the least complete lattice containing P. In this work, we analyze some results concerning the use of this completion within the framework of Formal Concept Analysis in terms of the poset of concepts associated with a Galois connection between posets. Specifically, we show an interesting...

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...

Adjoint triples and pairs are basic operators used in several domains, since they increase the flexibility in the framework in which they are considered. This paper introduces multi-adjoint algebras and several properties; also, we will show that an adjoint triple and its "dual" cannot be considered in the same framework. Moreover, a comparison amo...

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 red...

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...

Adjoint triples are an interesting generalization of t-norms and their residuated implications, since they increase the flexibility in the framework where they are used. Following the same motivation of adjoint triples, in order to reduce the mathematical requirements for the computation, extended-order algebras are studied. Extended-order algebras...

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 fu...

Involutive residuated negations are usually considered in resi\-duated 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.

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 o...

Several domains, such as fuzzy logic programming, formal concept analysis and fuzzy relation equations, consider basic operators which need to have associated residuated implications. Adjoint triples are formed by operators satisfying weak properties, usefully used in these domains. This paper presents the comparison of these triples with other gen...

The irreducible elements in a lattice are very important. For example, when the lattice is finite, which is the usual in the computational case, they form a base from which the complete lattice is obtained. These elements are also important in Formal Concept Analysis, since they are the basic information of a relational system. B. Ganter and R. Wil...

In formal concept analysis, attribute reduction is an important preprocessing in order to obtain concept lattices, which provides fundamental information of the attributes, as well. This importance is increased in the fuzzy case.
This paper presents, in the general fuzzy framework of multi-adjoint concept lattices, a classification of the fuzzy-att...

Adjoint triples are helpful as basic operators used in several domains. For example, adjoint triples play an important role in two important frameworks: multi-adjoint logic programming and multi-adjoint concept lattices. This paper shows that adjoint triples are an interesting generalization of t-norms and their residuated implications, since they...

Implication triples and adjoint triples are two of the more general residuated operators which have been applied independently
in manifold important fields. This paper presents diverse properties of adjoint triples in order to relate them to implication
triples. As a consequence of this relation, we obtain, for example, that a multi-adjoint lattice...

## Projects

Projects (2)

Digital forensics is a part of the Criminalistics Sciences which deals with digital evidence recovery and exploitation in the solution of criminal cases through the application of scientific principles. There are several and increasingly sophisticated methods for collecting digital evidence. As a matter of fact, the evolution of technology continuously pushes such kind of methods. Rough evidence must however be used to elicit hypotheses concerning events, actions and facts (or sequences of them) with the goal to obtain evidence to present in court. Evidence analysis involves examining fragmented incomplete knowledge, and reconstructing and aggregating complex scenarios involving time, uncertainty, causality, and alternative possibilities. No established methodology exists today for digital evidence analysis. The Scientific Investigation experts usually proceed by means of their experience and intuition.
The Challenge of the proposed COST Action consists in creating a Network for exploring the potential of the application of Artificial Intelligence and Automated Reasoning in the Digital Forensics field, and creating synergies between these fields. Specifically, the challenge is to address the Evidence Analysis phase, where evidence about possible crimes and crimes perpetrators collected from various electronic devices (by means of specialized software, and according to specific regulations) must be exploited so as to reconstruct possible events, event sequences and scenarios related to a crime. Evidence Analysis results are then made available to law enforcement, investigators, public prosecutors, lawyers and judges: it is therefore crucial that the adopted techniques guarantee reliability and verifiability, and that their result can be explained to the human actors.

Develop Multi-adjoint concept lattices and other useful Fuzzy Formal Concept Analysis frameworks.