Fuzzy closure systems: Motivation, definition and properties

The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved.The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved. Funding for open access charge: Universidad de Málaga / CBU

Lexicon-based sentiment analysis in texts using Formal Concept Analysis

In this paper, we present a novel approach for sentiment analysis that uses Formal Concept Analysis (FCA) to create dictionaries for classification. Unlike other methods that rely on pre-defined lexicons, our approach allows for the creation of customised dictionaries that are tailored to the specific data and tasks. By using a dataset of tweets categorised into positive and negative polarity, we show that our approach achieves a better performance than other standard dictionariesThis research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation, and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship and the research projects with reference PGC2018-095869-B-I00, TIN2017-89023-P, PID2021-127870OB-I00 (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE). Funding for open access charge: Universidad de Málaga / CBU

Fuzzy algebras of concepts

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.Partial funding for open access charge: Universidad de Málag

Fuzzy closure relations

The concept of closure operator is key in several branches of mathematics. In this paper, closure operators are extended to relational structures, more specifically to fuzzy relations in the framework of complete fuzzy lattices. The core of the work is the search for a suitable definition of (strong) fuzzy closure relation, that is, a fuzzy relation whose relation with fuzzy closure systems is one-to-one. The study of the properties of fuzzy closure systems and fuzzy relations helps narrow down this exploration until an appropriate definition is settled.This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship and the research projects with reference PGC2018-095869-B-I00, TIN2017-89023-P (MCIU/AEI/FEDER, UE) and UMA2018-FEDERJA-001 (JA/UMA/FEDER, UE). Funding for open access charge: Universidad de Málaga

Retrospective health impact assessment for ozone pollution in Mexico City from 1991 to 2011

AbstractAir pollution is the main environmental issue in Mexico City, where ozone is one of the most damaging pollutants for human health. In this work we present a retrospective health impact assessment (HIA) study split up by age groups for evaluating the benefits of ozone regulatory strategies from 1991 to 2011 in Mexico City. Since people move from one place to another during the day, which may affect their potential exposure to pollutants, we consider time-dependant spatial population distributions during the day. Ozone data is made up of observations taken with hourly frequency from January 1, 1991 to December 31, 2011, at approximately 22 stations of the monitoring network of Mexico City. Interpolated values for unknown locations are also taken into account in the HIA. The Cressman objective analysis method is applied for interpolating the observed ozone concentrations from monitoring stations to grids of convenient resolution. We demonstrate that different age groups present different spatial patterns of exposure, being the working-age people (between 18 and 64 years) the most benefited. We also confirm the hypothesis that, in general, people move to less polluted regions during the day

Quasi-closed elements in fuzzy posets

We generalize the notion of quasi-closed element to fuzzy posets in two stages: First, in the crisp style in which each element in a given universe either is quasi-closed or not. Second, in the graded style by defining degrees to which an element is quasi-closed. We discuss the different possible definitions and comparing them with each other. Finally, we show that the most general one has good properties to be used when we have a complete fuzzy lattice as a frame

Closure Structures as fixed points of some Galois connections.

The starting point of this work is a published paper where the fuzzy powerset of a fuzzy lattice A, the set of isotone mappings on A and the set of isotone total relations on A were proved to be related by three fuzzy Galois connections such that fuzzy closure systems, fuzzy closure operators and the so called strong fuzzy closure relations are fixed points. The final part of that paper studied the commutativity of the diagrams formed by these mappings.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Fuzzy Closure Structures as Formal Concepts II

This paper is the natural extension of Fuzzy Closure Structures as Formal Concepts. In this paper we take into consideration the concept of closure system which is not dealt with in the previous one. Hence, a connection must be found between fuzzy ordered sets and a crisp ordered set. This problem is two-fold, the core of the fuzzy orders can be considered in order to complete the ensemble, or the crisp order can be fuzzified. Both ways are studied in the paper. The most interesting result is, similarly to the previous paper, that closure systems are formal concepts of these Galois connections as well.Funding for open access charge: Universidad de Málaga / CBUA This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation, and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship, the project VALID (PID2022-140630NB-I00 funded by MCIN/ AEI/10.13039/501100011033) and the research projects with reference PGC2018-095869-B-I00, PID2021-127870OB-I00, (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE)

Fuzzy closure structures as formal concepts

Galois connections seem to be ubiquitous in mathematics. They have been used to model solutions for both pure and application-oriented problems. Throughout the paper, the general framework is a complete fuzzy lattice over a complete residuated lattice. The existence of three fuzzy Galois connections (two antitone and one isotone) between three specific ordered sets is proved in this paper. The most interesting part is that fuzzy closure systems, fuzzy closure operators and strong fuzzy closure relations are formal concepts of these fuzzy Galois connections.This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship and the research projects with reference PGC2018-095869-B-I00, TIN2017-89023-P, PID2021-127870OB-I00 (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE). Funding for open access charge: Universidad de Málaga / CBU

Neocortical tissue recovery in severe congenital obstructive hydrocephalus after intraventricular administration of bone marrow-derived mesenchymal stem cells

BACKGROUND: In obstructive congenital hydrocephalus, cerebrospinal fluid accumulation is associated with high intracranial pressure and the presence of periventricular edema, ischemia/hypoxia, damage of the white matter, and glial reactions in the neocortex. The viability and short time effects of a therapy based on bone marrow-derived mesenchymal stem cells (BM-MSC) have been evaluated in such pathological conditions in the hyh mouse model. METHODS: BM-MSC obtained from mice expressing fluorescent mRFP1 protein were injected into the lateral ventricle of hydrocephalic hyh mice at the moment they present a very severe form of the disease. The effect of transplantation in the neocortex was compared with hydrocephalic hyh mice injected with the vehicle and non-hydrocephalic littermates. Neural cell populations and the possibility of transdifferentiation were analyzed. The possibility of a tissue recovering was investigated using 1H High-Resolution Magic Angle Spinning Nuclear Magnetic Resonance (1H HR-MAS NMR) spectroscopy, thus allowing the detection of metabolites/osmolytes related with hydrocephalus severity and outcome in the neocortex. An in vitro assay to simulate the periventricular astrocyte reaction conditions was performed using BM-MSC under high TNFα level condition. The secretome in the culture medium was analyzed in this assay. RESULTS: Four days after transplantation, BM-MSC were found undifferentiated and scattered into the astrocyte reaction present in the damaged neocortex white matter. Tissue rejection to the integrated BM-MSC was not detected 4 days after transplantation. Hyh mice transplanted with BM-MSC showed a reduction in the apoptosis in the periventricular neocortex walls, suggesting a neuroprotector effect of the BM-MSC in these conditions. A decrease in the levels of metabolites/osmolytes in the neocortex, such as taurine and neuroexcytotoxic glutamate, also indicated a tissue recovering. Under high TNFα level condition in vitro, BM-MSC showed an upregulation of cytokine and protein secretion that may explain homing, immunomodulation, and vascular permeability, and therefore the tissue recovering. CONCLUSIONS: BM-MSC treatment in severe congenital hydrocephalus is viable and leads to the recovery of the severe neurodegenerative conditions in the neocortex. NMR spectroscopy allows to follow-up the effects of stem cell therapy in hydrocephalus.España Instituto Carlos III , PI15/00619 (to AJJ), PI19/00778 (to AJJ and PPG), PI15/00796, and PI18/01557España Ministerio de Educación, Cultura y Deporte FPU13/02906España, Ministerio de Economía y Competitividad RYC-2014-16980España, FEDER Andalucía y Universidad de Málaga UMA18-FEDERJA-27