Granular Partition and Concept Lattice Division Based on Quotient Space

In this paper, we investigate the relationship between the concept lattice and quotient space by granularity. A new framework of knowledge representation - granular quotient space - is constructed and it demonstrates that concept lattice classing is linked to quotient space. The covering of the formal context is firstly given based on this granule, then the granular concept lattice model and its construction are discussed on the sub-context which is formed by the granular classification set. We analyze knowledge reduction and give the description of granular entropy techniques, including some novel formulas. Lastly, a concept lattice constructing algorithm is proposed based on multi-granular feature selection in quotient space. Examples and experiments show that the algorithm can obtain a minimal reduct and is much more efficient than classical incremental concept formation methods

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

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