Towards a Classification of Rough Set Bireducts

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 original dataset. This paper presents the main properties of bireducts and how they can be used for removing inconsistencies. © 2020, Springer Nature Switzerland AG

δ-information reducts and bireducts

Attribute reduction is an important step in order to decrease the computational complexity to derive information from databases. In this paper, we extend the notions of reducts and bireducts introduced in rough set theory for attribute reduction purposes and let them work with similarity relations defined on attribute values. Hence, the related mathematical concepts will be introduced and the characterizations of the new reducts and bireducts will be given in terms of the corresponding generalizations of the discernibility function.La reducción en atributos es un paso importante para disminuir la complejidad computacional para obtener información de una base de datos. En este trabajo, extendemos la noción de reductos y birredcutos introducidos en Teoría de Conjuntos Rugosos para reducción de atributos y trabajamos con relaciones de similaridad definidas en los valores de los atributos. Luego, los conceptos matemáticos relacionados se introducirán junto con las caracterizaciones de los nuevos reductos y birreductos en términos de la función de discernibilidad

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

Representative Set of Objects in Rough Sets Based on Galois Connections

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 objects of a decision class, we present different mathematical properties of such sets and a relationship with classification tasks based on rough sets. © 2020, Springer Nature Switzerland AG

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

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