Rough sets based on Galois connections

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately. different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

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 studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA's unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences

Characterizing One-Sided Formal Concept Analysis by Multi-Adjoint Concept Lattices

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 concept lattices. As a first consequence of this characterization, a new attribute reduction mechanism has been introduced in the one-side framework.This research was partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in Project PID2019-108991GB-I00 and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in Project FEDER-UCA18-108612 and by the European Cooperation in Science & Technology (COST) Action CA17124

Rough set decision algorithms for modeling with uncertainty

The use of decision rules allows to extract information and to infer conclusions from relational databases in a reliable way, thanks to some indicators like support and certainty. Moreover, decision algorithms collect a group of decision rules that satisfies desirable properties to describe the relational system. However, when a decision table is considered within a fuzzy environment, it is necessary to extend all notions related to decision algorithms to this framework. This paper presents a generalization of these notions, highlighting the new definitions of indicators of relevance to describe decision rules and decision algorithm

Value reducts and bireducts: A comparative study

In Rough Set Theory, the notion of bireduct allows to simultaneously reduce the sets of objects and attributes contained in a dataset. In addition, value reducts are used to remove some unnecessary values of certain attributes for a specific object. Therefore, the combination of both notions provides a higher reduction of unnecessary data. This paper is focused on the study of bireducts and value reducts of information and decision tables. We present theoretical results capturing different aspects about the relationship between bireducts and reducts, offering new insights at a conceptual level. We also analyze the relationship between bireducts and value reducts. The studied connections among these notions provide important profits for the efficient information analysis, as well as for the detection of unnecessary or redundant information

Multilattices and attribute reduction in multi-adjoint concept lattices

Since its introduction in the eighties by B. Ganter and R. Wille, Formal Concept Analysis has become an appealing research topic. It is a theory of data analysis which identifies conceptual structures among data sets. Specifically, it is a tool for extracting pieces of information from databases that contain a set of attributes A and a set of objects B together with a relationship between them. These pieces of information are called concepts and they can be hierarchized to obtain concept lattices. Attribute reduction is a very important part in Formal Concept Analysis because the difficulty in building the concept lattice increases exponentially when the number of objects and attributes increases. Therefore, one of the most important goals in this theory is the reduction of the context, removing the irrelevant information. Moreover, real databases usually give rise to complex concept lattices, from which extracting conclusions can be a really difficult task. Consequently, another important issue is the reduction of the size of the original concept lattice. This thesis has been focused on both these goals. Firstly, it introduces several results in order to classify the set of attributes. From this classification a mechanism to reduce the context on a fuzzy environment is obtained, which generalizes the current existing procedures. The most innovative aspect related to this contribution is that it maintains all the knowledge of the relational system. In addition, two procedures to reduce the size of a multi-adjoint concept lattice are presented. One of them considers thresholds in the concept-forming operators and this reduction method generalizes existing mechanisms based on this philosophy. Another procedure introduced shows a reduction from the irreducible elements of the lattice. This one provides an interesting property, that is, the reduced concept lattice is a sublattice of the original one and, consequently, the use of this mechanism does not involve the loss or modification of the original information. Lastly, the thesis concludes by demonstrating an extension of the theory of Formal Concept Analysis based on multilattices. As a consequence, the range of applications of Formal Concept Analysis has been increased

Interpreting and analyzing a location-based social network by fuzzy formal contexts

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.Formal Concept Analysis (FCA) is a mathematical tool for data analysis. In this work, we present a study on the application of FCA to databases obtained from location-base social networks. From FCA we can identify the schedule and the interest places, such as the working hours and days, eating hours, etc. As a consequence, using the user's timetable, we can recommend him/her the most probable interesting places in every moment

Disjunctive attribute dependencies in formal concept analysis under the epistemic view of formal contexts

International audienceThis 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 analysis (FCA), and the standard theory of attribute implications in FCA, this paper presents the notion of disjunctive attribute implications, which reflect additional information that can be extracted from an epistemic context. We show that they can be computed like standard attribute implications from the complementary context. The paper also recalls the logic of classical attribute implications, relying on works pertaining to functional dependencies in database theory, and proposes a dual logic for disjunctive attribute implications. A method for extracting the latter kind of rules from a formal context is proposed, using a counterpart of pseudo-intents. Lastly, the paper outlines a generalization of both conjunctive and disjunctive attribute implications under the form of rules, with a conjunction of conditions in the body and a disjunction of conditions in the head, that hold in a formal context under the epistemic view

Guía de la Pizarra Interactiva HitachiSoft StarBoard

Tutorial sobre la instalación y utilización de una pizarra interactiva para la realización de tutorías virtuales.35 página