May 2020
Conference papers accepted
12/05/20/10:16 Filed in: Conference papers
Inma P. Cabrera, P. Cordero, E. Muñoz and M. Ojeda-Aciego. Galois connections between unbalanced structures in a fuzzy framework. 18th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Lisboa, 2020.
ABSTRACT The construction of Galois connections between unbalanced structures has received considerable attention in the recent years.
In a nutshell, the problem is to find a right adjoint of a mapping defined between sets with unbalanced structure; in this paper we survey recent results obtained in this framework, focusing specially on the fuzzy structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.
F. Valverde, C. Peláez, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Exploratory Data Analysis of Multi-label Classification Tasks with Formal Context Analysis. Concept Lattices and their Applications (CLA), Tallinn, 2020.
ABSTRACT We introduce a new framework, Formal Context Analysis (FxA), for the exploratory analysis of data tasks cast in the guise of formal contexts. FxA gathers a number of results from Formal Concpt Analysis, Formal Independence Analysis and Formal Equivalence Analysis to enhance the establishment and processing of hypothesis about data. We apply this framework to the study of the Multi-label Classification (MLC) task and obtain a number of results of technical nature about how the induction mechanism for MLC classifiers should proceed. The application is based on an analysis of multilabel classification from the standpoint of FxA.
N. Madrid and M. Ojeda-Aciego. Inconsistency in fuzzy logic systems. International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2020.
ABSTRACT Different notions of consistency which are equivalent in the classical case are no longer equivalent in a fuzzy framework; this leads to different potential notions of consistency in a fuzzy setting. The underlying problem is to consider "consistency" as a crisp property; instead, we propose to consider a gradual notion of consistency, and different measures of consistency are introduced and analyzed.
N. Madrid. Towards the use of quantile fuzzy transforms for the construction of fuzzy association rules. IEEE Int Conf on Fuzzy Systems (FUZZ-IEEE), Glasgow, 2020.
ABSTRACT This paper analyzes the possibility of defining fuzzy association rules by means of direct quantiles F-transforms. The set of fuzzy association rules is used in a fuzzy inference system, defined by means of the inverse quantile F-transform. The obtained inference system reminds the Takagi-Sugeno one due to the use of a weighted sum to perform the inference. However, there is an important difference: the output is a fuzzy set and, as a result, we require the use of a defuzzification procedure. In addition, in this paper we prove experimentally that the fuzzy set obtained as the output of the proposed inference system is related to a probability distribution.
N. Madrid and E. Ramírez-Poussa. Representative Set of Objects in Rough Sets Based on Galois Connections. International Joint Conference on Rough Sets (IJCRS), La Habana, 2020.
ABSTRACT 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.
ABSTRACT The construction of Galois connections between unbalanced structures has received considerable attention in the recent years.
In a nutshell, the problem is to find a right adjoint of a mapping defined between sets with unbalanced structure; in this paper we survey recent results obtained in this framework, focusing specially on the fuzzy structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.
F. Valverde, C. Peláez, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Exploratory Data Analysis of Multi-label Classification Tasks with Formal Context Analysis. Concept Lattices and their Applications (CLA), Tallinn, 2020.
ABSTRACT We introduce a new framework, Formal Context Analysis (FxA), for the exploratory analysis of data tasks cast in the guise of formal contexts. FxA gathers a number of results from Formal Concpt Analysis, Formal Independence Analysis and Formal Equivalence Analysis to enhance the establishment and processing of hypothesis about data. We apply this framework to the study of the Multi-label Classification (MLC) task and obtain a number of results of technical nature about how the induction mechanism for MLC classifiers should proceed. The application is based on an analysis of multilabel classification from the standpoint of FxA.
N. Madrid and M. Ojeda-Aciego. Inconsistency in fuzzy logic systems. International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2020.
ABSTRACT Different notions of consistency which are equivalent in the classical case are no longer equivalent in a fuzzy framework; this leads to different potential notions of consistency in a fuzzy setting. The underlying problem is to consider "consistency" as a crisp property; instead, we propose to consider a gradual notion of consistency, and different measures of consistency are introduced and analyzed.
N. Madrid. Towards the use of quantile fuzzy transforms for the construction of fuzzy association rules. IEEE Int Conf on Fuzzy Systems (FUZZ-IEEE), Glasgow, 2020.
ABSTRACT This paper analyzes the possibility of defining fuzzy association rules by means of direct quantiles F-transforms. The set of fuzzy association rules is used in a fuzzy inference system, defined by means of the inverse quantile F-transform. The obtained inference system reminds the Takagi-Sugeno one due to the use of a weighted sum to perform the inference. However, there is an important difference: the output is a fuzzy set and, as a result, we require the use of a defuzzification procedure. In addition, in this paper we prove experimentally that the fuzzy set obtained as the output of the proposed inference system is related to a probability distribution.
N. Madrid and E. Ramírez-Poussa. Representative Set of Objects in Rough Sets Based on Galois Connections. International Joint Conference on Rough Sets (IJCRS), La Habana, 2020.
ABSTRACT 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.