Concept learning consistency under three‑way decision paradigm

Concept Mining is one of the main challenges both in Cognitive Computing and in Machine Learning. The ongoing improvement of solutions to address this issue raises the need to analyze whether the consistency of the learning process is preserved. This paper addresses a particular problem, namely, how the concept mining capability changes under the reconsideration of the hypothesis class. The issue will be raised from the point of view of the so-called Three-Way Decision (3WD) paradigm. The paradigm provides a sound framework to reconsider decision-making processes, including those assisted by Machine Learning. Thus, the paper aims to analyze the influence of 3WD techniques in the Concept Learning Process itself. For this purpose, we introduce new versions of the Vapnik-Chervonenkis dimension. Likewise, to illustrate how the formal approach can be instantiated in a particular model, the case of concept learning in (Fuzzy) Formal Concept Analysis is considered.This work is supported by State Investigation Agency (Agencia Estatal de Investigación), project PID2019-109152GB-100/AEI/10.13039/501100011033. We acknowledge the reviewers for their suggestions and guidance on additional references that have enriched our paper. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices

In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment

Attribute Classification and Reduct Computation in Multi-Adjoint Concept Lattices

The problem of reducing information in databases is an important topic in formal concept analysis, which has been studied in several articles. In this article, we consider the fuzzy en- vironment of the multi-adjoint concept lattices, since it is a general fuzzy framework that allows us to easily establish degrees of pref- erence on the elements of the considered database. We introduce algorithms to discover the information contained in the relational system. By means of these algorithms, we classify the attributes of a multi-adjoint context, and build a minimal subset of attributes preserving the information of the original knowledge system.The work of L. Antoni was supported in part by the Slovak Research and Development Agency under Contract APVV-15-0091. The work of M. E. Cornejo, J. Medina, and E. Ramírez-Poussa was supported in part by the Spanish Economy and Competitiveness Ministry (MINECO) under Project TIN2016-76653-P, in part by the Department of Economy, Knowl- edge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and in part by the European Cooperation in Science & Technology (COST) Action CA17124

Impact of Local Congruences in Attribute Reduction

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 attribute reduction

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

Impact of local congruences in variable selection from datasets

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 local congruences in order to obtain robust clusters of concepts, which form convex sublattices of the original concept lattice. Since the application of such local congruences modifies the quotient set associated with the attribute reduction, it is fundamental to know how the original context (attributes, objects and relationship) has been modified in order to understand the impact of the application of the local congruence in the attribute reduction.Partially supported by the the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project TIN2016-76653-P and 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

Conceptual Based Hidden Data Analytics and Reduction Method for System Interface Enhancement Through Handheld devices

With the increasing demand placed on online systems by users, many organizations and companies are seeking to enhance their online interfaces to facilitate the search process on their hidden databases. Usually, users issue queries to a hidden database by using the search template provided by the system. In this thesis, a new approach based mainly on hidden database reduction preserving functional dependencies is developed for enhancing the online system interface through a small screen device. The developed approach is applied to online market systems like eBay. Offline hidden data analysis is used to discover attributes and their domains and different functional dependencies. In this thesis, a comparative study between several methods for mining functional dependencies shows the advantage of conceptual methods for data reduction. In addition, by using online consecutive reductions on search results, we adopted a method of displaying results in order of decreasing relevance. The validation of the proposed designed and developed methods prove their generality and suitability for system interfacing through continuous data reductions.NPRP-07-794-1-145 grant from the Qatar National Research Fund (a member of Qatar foundation