A map characterizing the fuzzy points and columns of a T-indistinguishability operator

A new map (ΛE) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of ΛE is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (φE and ψE) are also reviewed, in order to compare them with ΛE. Interesting properties of the fixed points of ΛE and Λ2 E are studied. Among others, the fixed points of ΛE (Fix(ΛE)) are proved to be the maximal fuzzy points of (X,E) and the fixed points of Λ2 E coincide with the Image of ΛE. An isometric embedding of X into Fix(ΛE) is established and studied

Extensionality with respect to indistinguishability operators

Extensionality is explored form different points of view. Extensional fuzzy subsets from a fuzzy equivalence relation E are considered as observable subsets with respect to the granularity generated by E. Interestingly, they are characterized as the fuzzy subsets that can be obtained as combinations of the fuzzy equivalence classes of E. Extensional mappings are characterized topologically and the set of extensional mappings between two universes are algebraically determined. Specifying the results to fuzzy mappings from a universe X onto [0, 1] an interpretation of type-2 fuzzy subsets of X as fuzzification of its type-1 fuzzy subsets is provided.Peer ReviewedPostprint (author's final draft

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

A finder and representation system for knowledge carriers based on granular computing

In one of his publications Aristotle states ”All human beings by their nature desire to know” [Kraut 1991]. This desire is initiated the day we are born and accompanies us for the rest of our life. While at a young age our parents serve as one of the principle sources for knowledge, this changes over the course of time. Technological advances and particularly the introduction of the Internet, have given us new possibilities to share and access knowledge from almost anywhere at any given time. Being able to access and share large collections of written down knowledge is only one part of the equation. Just as important is the internalization of it, which in many cases can prove to be difficult to accomplish. Hence, being able to request assistance from someone who holds the necessary knowledge is of great importance, as it can positively stimulate the internalization procedure. However, digitalization does not only provide a larger pool of knowledge sources to choose from but also more people that can be potentially activated, in a bid to receive personalized assistance with a given problem statement or question. While this is beneficial, it imposes the issue that it is hard to keep track of who knows what. For this task so-called Expert Finder Systems have been introduced, which are designed to identify and suggest the most suited candidates to provide assistance. Throughout this Ph.D. thesis a novel type of Expert Finder System will be introduced that is capable of capturing the knowledge users within a community hold, from explicit and implicit data sources. This is accomplished with the use of granular computing, natural language processing and a set of metrics that have been introduced to measure and compare the suitability of candidates. Furthermore, are the knowledge requirements of a problem statement or question being assessed, in order to ensure that only the most suited candidates are being recommended to provide assistance

Uncertainty and indistinguishability. Application to modelling with words.

El concepte d'igualtat és fonamental en qualsevol teoria donat que és una noció essencial a l'hora de discernir entre els elements objecte del seu estudi i possibilitar la definició de mecanismes de classificació.Quan totes les propietats són perfectament precises (absència d'incertesa), hom obtè la igualtat clàssica a on dos objectes són considerats iguals si i només si comparteixen el mateix conjunt de propietats. Però, què passa quan considerem l'aparició d'incertesa, com en el cas a on els objectes compleixen una determinada propietat només fins a un cert grau?. Llavors, donat que alguns objectes seran més similars entre si que d'altres, sorgeix la necessitat de una noció gradual del concepte d'igualtat.Aquestes consideracions refermen la idea de que certs contextos requereixen una definició més flexible, que superi la rigidesa de la noció clàssica d'igualtat. Els operadors de T-indistingibilitat semblen bons candidats per aquest nou tipus d'igualtat que cerquem.D'altra banda, La Teoria de l'Evidència de Dempster-Shafer, com a marc pel tractament d'evidències, defineix implícitament una noció d'indistingibilitat entre els elements del domini de discurs basada en la seva compatibilitat relativa amb l'evidència considerada. El capítol segon analitza diferents mètodes per definir l'operador de T-indistingibilitat associat a una evidència donada.En el capítol tercer, després de presentar un exhaustiu estat de l'art en mesures d'incertesa, ens centrem en la qüestió del còmput de l'entropia quan sobre els elements del domini s'ha definit una relació d'indistingibilitat. Llavors, l'entropia hauria de ser mesurada no en funció de l'ocurrència d'events diferents, sinó d'acord amb la variabilitat percebuda per un observador equipat amb la relació d'indistingibilitat considerada. Aquesta interpretació suggereix el "paradigma de l'observador" que ens porta a la introducció del concepte d'entropia observacional.La incertesa és un fenomen present al món real. El desenvolupament de tècniques que en permetin el tractament és doncs, una necessitat. La 'computació amb paraules' ('computing with words') pretén assolir aquest objectiu mitjançant un formalisme basat en etiquetes lingüístiques, en contrast amb els mètodes numèrics tradicionals. L'ús d'aquestes etiquetes millora la comprensibilitat del llenguatge de representació delconeixement, a l'hora que requereix una adaptació de les tècniques inductives tradicionals.En el quart capítol s'introdueix un nou tipus d'arbre de decisió que incorpora les indistingibilitats entre elements del domini a l'hora de calcular la impuresa dels nodes. Hem anomenat arbres de decisió observacionals a aquests nou tipus, donat que es basen en la incorporació de l'entropia observacional en la funció heurística de selecció d'atributs. A més, presentem un algorisme capaç d'induir regles lingüístiques mitjançant un tractament adient de la incertesa present a les etiquetes lingüístiques o a les dades mateixes. La definició de l'algorisme s'acompanya d'una comparació formal amb altres algorismes estàndards.The concept of equality is a fundamental notion in any theory since it is essential to the ability of discerning the objects to whom it concerns, ability which in turn is a requirement for any classification mechanism that might be defined. When all the properties involved are entirely precise, what we obtain is the classical equality, where two individuals are considered equal if and only if they share the same set of properties. What happens, however, when imprecision arises as in the case of properties which are fulfilled only up to a degree? Then, because certain individuals will be more similar than others, the need for a gradual notion of equality arises.These considerations show that certain contexts that are pervaded with uncertainty require a more flexible concept of equality that goes beyond the rigidity of the classic concept of equality. T-indistinguishability operators seem to be good candidates for this more flexible and general version of the concept of equality that we are searching for.On the other hand, Dempster-Shafer Theory of Evidence, as a framework for representing and managing general evidences, implicitly conveys the notion of indistinguishability between the elements of the domain of discourse based on their relative compatibility with the evidence at hand. In chapter two we are concerned with providing definitions for the T-indistinguishability operator associated to a given body of evidence.In chapter three, after providing a comprehensive summary of the state of the art on measures of uncertainty, we tackle the problem of computing entropy when an indistinguishability relation has been defined over the elements of the domain. Entropy should then be measured not according to the occurrence of different events, but according to the variability perceived by an observer equipped with indistinguishability abilities as defined by the indistinguishability relation considered. This idea naturally leads to the introduction of the concept of observational entropy.Real data is often pervaded with uncertainty so that devising techniques intended to induce knowledge in the presence of uncertainty seems entirely advisable.The paradigm of computing with words follows this line in order to provide a computation formalism based on linguistic labels in contrast to traditional numerical-based methods.The use of linguistic labels enriches the understandability of the representation language, although it also requires adapting the classical inductive learning procedures to cope with such labels.In chapter four, a novel approach to building decision trees is introduced, addressing the case when uncertainty arises as a consequence of considering a more realistic setting in which decision maker's discernment abilities are taken into account when computing node's impurity measures. This novel paradigm results in what have been called --observational decision trees' since the main idea stems from the notion of observational entropy in order to incorporate indistinguishability concerns. In addition, we present an algorithm intended to induce linguistic rules from data by properly managing the uncertainty present either in the set of describing labels or in the data itself. A formal comparison with standard algorithms is also provided

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

Cognitive Models and Computational Approaches for improving Situation Awareness Systems

2016 - 2017The world of Internet of Things is pervaded by complex environments with smart services available every time and everywhere. In such a context, a serious open issue is the capability of information systems to support adaptive and collaborative decision processes in perceiving and elaborating huge amounts of data. This requires the design and realization of novel socio-technical systems based on the “human-in-the-loop” paradigm. The presence of both humans and software in such systems demands for adequate levels of Situation Awareness (SA). To achieve and maintain proper levels of SA is a daunting task due to the intrinsic technical characteristics of systems and the limitations of human cognitive mechanisms. In the scientific literature, such issues hindering the SA formation process are defined as SA demons. The objective of this research is to contribute to the resolution of the SA demons by means of the identification of information processing paradigms for an original support to the SA and the definition of new theoretical and practical approaches based on cognitive models and computational techniques. The research work starts with an in-depth analysis and some preliminary verifications of methods, techniques, and systems of SA. A major outcome of this analysis is that there is only a limited use of the Granular Computing paradigm (GrC) in the SA field, despite the fact that SA and GrC share many concepts and principles. The research work continues with the definition of contributions and original results for the resolution of significant SA demons, exploiting some of the approaches identified in the analysis phase (i.e., ontologies, data mining, and GrC). The first contribution addresses the issues related to the bad perception of data by users. We propose a semantic approach for the quality-aware sensor data management which uses a data imputation technique based on association rule mining. The second contribution proposes an original ontological approach to situation management, namely the Adaptive Goal-driven Situation Management. The approach uses the ontological modeling of goals and situations and a mechanism that suggests the most relevant goals to the users at a given moment. Lastly, the adoption of the GrC paradigm allows the definition of a novel model for representing and reasoning on situations based on a set theoretical framework. This model has been instantiated using the rough sets theory. The proposed approaches and models have been implemented in prototypical systems. Their capabilities in improving SA in real applications have been evaluated with typical methodologies used for SA systems. [edited by Author]XXX cicl