Removing redundancy for attribute implications in data with grades

Reasoning with if-then rules –in particular, with those taking from of implications between conjunctions of attributes– is crucial in many disciplines ranging from theoretical computer science to applications. One of the most important problems regarding the rules is to remove redundancies in order to obtain equivalent implicational sets with lower size.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Activating Generalized Fuzzy Implications from Galois Connections

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad

Attribute implications with unknown information based on weak Heyting algebras

Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we prove that it is possible to define a simplification logic on fuzzy sets in which the membership value structure is not necessarily distributive. For this purpose, we replace the structure of the complete dual Heyting algebra by the so-called weak complete dual Heyting algebra. We demonstrate the soundness and completeness of this simplification logic, and provide a characterisation of the operations defining weak complete dual Heyting algebras.Funding for open access charge: Universidad de Málaga/CBU

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

A conversational recommender system for diagnosis using fuzzy rules.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/4628Graded implications in the framework of Fuzzy Formal Concept Analysis are used as the knowledge guiding the recommendations. An automated engine based on fuzzy Simplification Logic is proposed to make the suggestions to the users. Conversational recommender systems have proven to be a good approach in telemedicine, building a dialogue between the user and the recommender based on user preferences provided at each step of the conversation. Here, we propose a conversational recommender system for medical diagnosis using fuzzy logic. Specifically, fuzzy implications in the framework of Formal Concept Analysis are used to store the knowledge about symptoms and diseases and Fuzzy Simplification Logic is selected as an appropriate engine to guide the conversation to a final diagnosis. The recommender system has been used to provide differential diagnosis between schizophrenia and schizoaffective and bipolar disorders. In addition, we have enriched the conversational strategy with two strategies (namely critiquing and elicitation mechanism) for a better understanding of the knowledge-driven conversation, allowing user’s feedback in each step of the conversation and improving the performance of the method.This work has been partially supported by the projects TIN2017- 89023-P and PGC2018-095869-B-I00 of the Science and Innovation Ministry of Spain, co-funded by the European Regional Develop- ment Fund (ERDF)

Attribute exploration with fuzzy attributes and background knowledge

Abstract. Attribute exploration is a formal concept analytical tool for knowledge discovery by interactive determination of the implications holding between a given set of attributes. The corresponding algorithm queries the user in an efficient way about the implications between the attributes. The result of the exploration process is a representative set of examples for the entire theory and a set of implications from which all implications that hold between the considered attributes can be deduced. The method was successfully applied in different real-life applications for discrete data. In many instances, the user may know some implications before the exploration starts. These are considered as background knowledge and their usage shortens the exploration process. In this paper we show that the handling of background information can be generalised to the fuzzy setting