Aggregating fuzzy subgroups and T-vague groups

Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations). In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft

On the relationship between fuzzy subgroups and indistinguishability operators

Fuzzy subgroups are revisited considering their close relationship with indistinguishability operators (fuzzy equivalences) invariant under translations. Different ways to obtain new fuzzy subgroups from a given one are provided and different ways to characterize normal fuzzy subgroups are obtained. The idea of double coset of two (crisp) subgroups allow us to relate them via their equivalence classes. This is generalized to the fuzzy framework. The conditions in which a fuzzy relation R on a group G can be considered a fuzzy subgroup of G × G are obtained.Peer ReviewedPostprint (author's final draft

Aggregation of L-probabilistic quasi-uniformities

[EN] The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen's functor iota which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.J. Rodriguez-Lopez acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion Proyecto PGC2018-095709-B-C21.Pedraza Aguilera, T.; Rodríguez López, J. (2020). Aggregation of L-probabilistic quasi-uniformities. Mathematics. 8(11):1-21. https://doi.org/10.3390/math8111980S12181

Fuzzy geometry

The concept of fuzzy space is due independently to Poincaré and Zeeman. (Poincaré used the term "physical continuum", Zeeman the term "tolerance space". I have reluctantly introduced a third expression since my attempts to generate a vocabulary from either of these have all proved impossibly unwieldy.) Both were led to it by the nature of our perception of space, and both adapted to it tools current in topology. Unfortunately, neither examined the application of these tools in complete detail, and as a result the argument from analogy was somewhat over-extended by both. The resemblances to topology are strong; the differences are sometimes glaring and sometimes subtle. In the latter case the difficulties produced by a topologically-conditioned intuition can be severe obstacles to progress. (Certainly, having been reared mathematically as a topologist I have found it necessary to distrust any conclusion whose proof is not painfully precise. ) For this reason many of the proofs in this paper are set out in somewhat more detail than would be natural in a more established field. For this reason also I have here not only set out the positive results I have so far obtained in the subject but, for the benefit of topologists, elaborated on the failures of analogy with topology where a more succinct exposition would have ignored them as dead ends (e.g., in Chap. I, §2)

Privacy-preserving human mobility and activity modelling

The exponential proliferation of digital trends and worldwide responses to the COVID-19 pandemic thrust the world into digitalization and interconnectedness, pushing increasingly new technologies/devices/applications into the market. More and more intimate data of users are collected for positive analysis purposes of improving living well-being but shared with/without the user's consent, emphasizing the importance of making human mobility and activity models inclusive, private, and fair. In this thesis, I develop and implement advanced methods/algorithms to model human mobility and activity in terms of temporal-context dynamics, multi-occupancy impacts, privacy protection, and fair analysis. The following research questions have been thoroughly investigated: i) whether the temporal information integrated into the deep learning networks can improve the prediction accuracy in both predicting the next activity and its timing; ii) how is the trade-off between cost and performance when optimizing the sensor network for multiple-occupancy smart homes; iii) whether the malicious purposes such as user re-identification in human mobility modelling could be mitigated by adversarial learning; iv) whether the fairness implications of mobility models and whether privacy-preserving techniques perform equally for different groups of users. To answer these research questions, I develop different architectures to model human activity and mobility. I first clarify the temporal-context dynamics in human activity modelling and achieve better prediction accuracy by appropriately using the temporal information. I then design a framework MoSen to simulate the interaction dynamics among residents and intelligent environments and generate an effective sensor network strategy. To relieve users' privacy concerns, I design Mo-PAE and show that the privacy of mobility traces attains decent protection at the marginal utility cost. Last but not least, I investigate the relations between fairness and privacy and conclude that while the privacy-aware model guarantees group fairness, it violates the individual fairness criteria.Open Acces

Some topics in fuzzy logic

2008-2009Si trattano diversi aspetti della logica fuzzy, in particolare: 1) le proprietà preservate da un modello fuzzy ogniqualvolta esso è sottoposto a qualche genere di modifica; 2) la programmazione logica fuzzy, la logica della similarità e la metaprogrammazione, considerando la relazione di sinonimia tra predicati; 3) la connessione tra logica fuzzy e teoria dei bireticoli per il trattamento sia della verità che del grado di informazione.VIII n.s

Ontological Investigations in the Quantum Domain: A deflationary approach on ontology of physics

The aim of this thesis is to propose a deflationary approach towards the ontological analysis of physical theories. Such an approach sustains that the development of ontologies for physical theories must be neutral relatively to the debate between realists and anti-realists in philosophy of physics. Mainly, our attention will be oriented towards what we called "quantum domain", which includes the non-relativistic Quantum Mechanics and variants of the Quantum Field Theory. This meta-ontological approach consists in an attempt to provide a methodology for the development of specific ontologies for physical theories. With this aim we suggest the separation between physical phenomena and physical theories on one side, and physical theories and ontologies on the other side. This separation intends to endorse the idea that physical theories can provide all the informative contents required for the development of the ontologies associated with them. The result is a defense of the idea that physical theories can positively contribute for the constitution of the ontologies in physics. Additionally, we present a critical analysis of four different ontological approaches to QM and QFT. Each one of these interpretations deals with a different ontological category (tropes, events and processes). At the end of the thesis we will analyze the concepts of interaction and commutation in QFT in order to exemplify the main lines of the deflationary approach suggested here

Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels

We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in quantum communication over adversarial channels. Our main application is an approximate quantum code over qubits which can efficiently correct from a number of (worst-case) erasure errors approaching the quantum Singleton bound. Our construction is based on the composition of a PMD code with a stabilizer code which is list-decodable from erasures. Our second application is a quantum authentication code for "qubit-wise" channels, which does not require a secret key. Remarkably, this gives an example of a task in quantum communication which is provably impossible classically. Our construction is based on a combination of PMD codes, stabilizer codes, and classical non-malleable codes (Dziembowski et al., 2009), and achieves "minimal redundancy" (rate $1-o(1)$)

Enhancing the ELECTRE decision support method with semantic data

Prendre una decisió quan les opcions es defineixen mitjançant un conjunt divers de criteris no és fàcil. Aqueta tesi es centra en ampliar la metodologia ELECTRE, que és el mètode del tipus "outranking" més utilitzat. En aquesta tesi ens centrem en problemes de decisió que involucren informació no numèrica, tal com els criteris semàntics multivaluats, que poden prendre com a valors els conceptes d'una ontologia de domini determinada. Primer proposo una nova manera de manipular els criteris semàntics per evitar l'agregació de les puntuacions numèriques abans del procediment de classificació. Aquest mètode, anomenat ELECTRE-SEM, segueix els mateixos principis que el clàssic ELECTRE però, en aquest cas, els índexs de concordança i discordança es defineixen en termes de la comparació per parelles de les puntuacions que indiquen l'interès de l'usuari sobre diferents conceptes de l'ontologia. En segon lloc, proposo crear un perfil d'usuari semàntic mitjançant el emmagatzemant de puntuacions de preferències a l'ontologia. Es vincula una puntuació d'interès numèrica als conceptes més específics, això permet distingir millor les preferències de l'usuari, i també s'incorpora un procediment d'agregació per inferir les preferències de l'usuari considerant les relacions taxonòmiques entre conceptes. La metodologia proposada s'ha aplicat en dos casos d’estudi: l'avaluació de plantes de generació d'energia i la recomanació d'activitats turístiques a Tarragona.Tomar una decisión cuando las opciones se definen sobre un conjunto diverso de criterios no es fácil. Esta tesis se centra en ampliar la metodología ELECTRE, que es el método del tipo "outranking" más utilizado. En esta tesis nos centramos en problemas de decisión que involucren información no numérica, tal como los criterios semánticos multi-valuados, que pueden tomar como valores los conceptos de una ontología de dominio determinada. Primero propongo una nueva forma de manejar los criterios semánticos para evitar la agregación de puntuaciones numéricas antes del procedimiento de clasificación. Este método, llamado ELECTRE-SEM, sigue los mismos principios que el clásico ELECTRE, pero en este caso los índices de concordancia y discordancia se definen en términos de la comparación por pares de unas puntuaciones que indican el interés del usuario sobre distintos conceptos de la ontología. En segundo lugar, propongo crear un perfil de usuario semántico mediante el almacenamiento de puntuaciones de preferencias en la ontología. Se asocian puntuaciones numéricas a los conceptos más específicos, lo cual permite distinguir mejor las preferencias del usuario, y se incorpora un proceso de agregación para inferir las preferencias del usuario mediante las relaciones taxonómicas entre conceptos. La metodología propuesta ha sido aplicada en dos casos de estudio: la evaluación de las plantas de generación de energía y la recomendación de actividades turísticas en Tarragona.Reach a decision when options are defined on a set of diverse criteria is not easy. This thesis is focused on improving the methodology ELECTRE, which is the most used outranking-based method. In this dissertation, we focus on decision problems involving non-numerical information, such as multi-valued semantic criteria, which may take as values the concepts of a given domain ontology. First, I propose a new way of handling semantic criteria to avoid the aggregation of the numerical scores before the ranking procedure. This method, called ELECTRE-SEM, follows the same principles than the classic ELECTRE but in this case the concordance and discordance indices are defined in terms of the pairwise comparison of the interest scores. Second, I also propose to create a semantic user profile by storing preference scores into the ontology. The numerical interest score attached to the most specific concepts permits to distinguish better the preferences of the user, improving the quality of the decision by the incorporation of an aggregation methodology to infer the user's preferences by considering taxonomic relations between concepts. The proposed methodology has been applied in two case studies: the assessment of power generation plants and the recommendation of touristic activities in Tarragona

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum