The purpose of this thesis is to generalize Filippov's operation, and to get more useful results. It includes two main parts: The C-Filippov operation for the finite and countable cases and the Filippov operation with different measures. In the first chapter, we give brief information about the importance of Filippov's operation, our goal and the ideas behind our generalizations. In the second chapter, we give some sufficient background notes. In the third chapter, we introduce the Filippov operation, explain how to calculate the Filippov of a function and give some sufficient properties of it. In the fourth chapter, we introduce a generalization of the Filippov operation, the C-Filippov, and give some of its properties which we need for the next chapter. In the fifth chapter, in the first main part, we discuss some properties of the C-Filippov for special cases and observe the differences and common properties between the Filippov and C-Filippov operations. Finally, in the sixth chapter, we present the other generalization of the Filippov operation which is Filippov with different measures. We observe the properties of the corresponding Filippovs when we know the relationship between the measures. We finish the thesis by summarizing our work and discussing future work.

A multiple-valued function is a "function" that assumes two or more distinct values in its range for at least one point in its domain. While these "functions" are not functions in the normal sense of being single-valued, the usage is so common that there is no way to dislodge it. This thesis is devoted to a particular class of multiple-valued functions: Q-valued functions. A Q-valued function is essentially a rule assigning Q unordered and not necessarily distinct points of R^n to each element of R^m. This object is one of the key ingredients of Almgren's 1700 pages proof that the singular set of an m-dimensional mass minimizing integral current in R^n has dimension at most m-2. We start by developing a decomposition theory and show for instance when a continuous Q-valued function can or cannot be seen as Q "glued" continuous classical functions. Then, the decomposition theory is used to prove intrinsically a Rademacher type theorem for Lipschitz Q-valued functions. A couple of Lipschitz extension theorems are also obtained for partially defined Lipschitz Q-valued functions. The second part is devoted to a Peano type result for a particular class of nonconvex-valued differential inclusions. To the best of the author's knowledge this is the first theorem, in the nonconvex case, where the existence of a continuously differentiable solution is proved under a mere continuity assumption on the corresponding multifunction. An application to a particular class of nonlinear differential equations is included. The third part is devoted to the calculus of variations in the multiple-valued framework. We define two different notions of Dirichlet nearly minimizing Q-valued functions, generalizing Dirichlet energy minimizers studied by Almgren. Hölder regularity is obtained for these nearly minimizers and we give some examples showing that the branching phenomena can be much worse in this context.

Systems that utilise type-2 fuzzy sets to handle uncertainty have not been implemented in real world applications unlike the astonishing number of applications involving standard fuzzy sets. The main reason behind this is the complex mathematical nature of type-2 fuzzy sets which is the source of two major problems. On one hand, it is difficult to mathematically manipulate type-2 fuzzy sets, and on the other, the computational cost of processing and performing operations using these sets is very high. Most of the current research carried out on type-2 fuzzy logic concentrates on finding mathematical means to overcome these obstacles. One way of accomplishing the first task is to develop a meaningful mathematical representation of type-2 fuzzy sets that allows functions and operations to be extended from well known mathematical forms to type-2 fuzzy sets. To this end, this thesis presents a novel alpha-cut representation theorem to be this meaningful mathematical representation. It is the decomposition of a type-2 fuzzy set in to a number of classical sets. The alpha-cut representation theorem is the main contribution of this thesis. This dissertation also presents a methodology to allow functions and operations to be extended directly from classical sets to type-2 fuzzy sets. A novel alpha-cut extension principle is presented in this thesis and used to define uncertainty measures and arithmetic operations for type-2 fuzzy sets. Throughout this investigation, a plethora of concepts and definitions have been developed for the first time in order to make the manipulation of type-2 fuzzy sets a simple and straight forward task. Worked examples are used to demonstrate the usefulness of these theorems and methods. Finally, the crisp alpha-cuts of this fundamental decomposition theorem are by definition independent of each other. This dissertation shows that operations on type-2 fuzzy sets using the alpha-cut extension principle can be processed in parallel. This feature is found to be extremely powerful, especially if performing computation on the massively parallel graphical processing units. This thesis explores this capability and shows through different experiments the achievement of significant reduction in processing time.

In his paper introducing fuzzy sets, L.A. Zadeh describes the difficulty of assigning some real-world objects to a particular class when the notion of class membership is ambiguous. If exact classification is not obvious, most people approximate using intuition and may reach agreement by placing an object in more than one class. Numbers or ‘degrees of membership’ within these classes are used to provide an approximation that supports this intuitive process. This results in a ‘fuzzy set’. This fuzzy set consists any number of ordered pairs to represent both the class and the class’s degree of membership to provide a formal representation that can be used to model this process. Although the fuzzy approach to reasoning and classification makes sense, it does not comply with two of the basic principles of classical logic. These principles are the laws of contradiction and excluded middle. While they play a significant role in logic, it is the violation of these principles that gives fuzzy logic its useful characteristics. The problem of this representation within a database system, however, is that the class and its degree of membership are represented by two separate, but indivisible attributes. Further, this representation may contain any number of such pairs of attributes. While the data for class and membership are maintained in individual attributes, neither of these attributes may exist without the other without sacrificing meaning. And, to maintain a variable number of such pairs within the representation is problematic. C. J. Date suggested a relation valued attribute (RVA) which can not only encapsulate the attributes associated with the fuzzy set and impose constraints on their use, but also provide a relation which may contain any number of such pairs. The goal of this dissertation is to establish a context in which the relational database model can be extended through the implementation of an RVA to support of fuzzy data on an actual system. This goal represents an opportunity to study through application and observation, the use of fuzzy sets to support imprecise and uncertain data using database queries which appropriately adhere to the relational model. The intent is to create a pathway that may extend the support of database applications that need fuzzy logic and/or fuzzy data.

A primeira noção de topos, a de topos de Grothendieck, surgiu há cerca de 50 anos a partir de uma generalização do conceito de feixe na geometria algébrica. Poucos anos mais tarde, uma axiomatização categorial de algumas das propriedades de um topos de Grothendieck deu origem a uma segunda noção de topos, a de topos elementar; e essa descrição permitiu estabelecer ligações entre essas categorias e teoria dos conjuntos e lógica. Neste trabalho, estudamos a teoria de topos com um foco especial na construção da lógica interna dos topoi, e exploramos sua relação com modelos Heyting-valorados. / The first definition of a topos, that of a Grothendieck topos, emerged roughly 50 years ago from a generalization of the notion of sheaves in algebraic geometry. Few years later, a categorical axiomatization of some properties of Grothendieck topoi gave rise to a second notion of topoi, that of an elementary topos; and this description made it possible to establish connections between these categories and set theory and logic. In this work, we study topos theory with a particular focus on the construction of the internal logic of topoi, and explore its relation to Heyting-valued models.

Cette thèse est une contribution à la théorie des modèles des corps valués. Les principaux résultats de ce texte sont des résultats d’éliminations des quantificateurs et des imaginaires. Le premier chapitre contient une étude des imaginaires dans les extensions finies de Qp. On y démontre que ces corps ainsi que leurs ultraproduits éliminent les imaginaires dans le langage géométrique. On en déduit un résultat de rationalité uniforme pour les fonctions zêta associées aux familles de relations d’équivalences définissables dans les extensions finies de Qp. La motivation première du deuxième chapitre est l’étude de W(F_p^alg) en tant que corps valué analytique de différence. Plus généralement, on démontre un théorème d’élimination des quantificateurs de corps dans le langage RV pour les corps valués analytiques -Henséliens de caractéristique nulle. On donne aussi une axiomatisation de la théorie de W(F_p^alg) ainsi qu’une preuve qu’elle est NIP. Dans le troisième chapitre, on prouve la densité des types définissables dans certains enrichissements d’ACVF. On en déduit un critère pour l’élimination des imaginaires et la propriété d’extension invariante. Ce chapitre contient aussi des résultats abstraits sur les ensembles extérieurement définissables dans les théories NIP. Dans le dernier chapitre, les résultats du chapitre précédent sont appliqués à VDF, la modèle complétion des corps valués munis d’une dérivation qui préserve la valuation, pour obtenir l’élimination des imaginaires dans le langage géométrique ainsi que la densité des types définissables et la propriété d’extension invariante. Ce chapitre contient aussi des considérations sur les fonctions définissables, les types et les groupes définissables dans VDF. / This thesis is about the model theory of valued fields. The main results in this text are eliminationsof quantifiers and imaginaries. The first chapter is concerned with imaginaries in finite extensions of Qp. I show that these fields and their ultraproducts eliminate imaginaries in the geometric language. As a corollary, I obtain the uniform rationality of zeta functions associated to families of equivalence relations that aredefinable in finite extensions of Qp.The motivation for the second chapter is to study W(F_p^alg) as an analytic difference valued field. More generally, I show a field quantifier elimination theorem in the RV-language for -Henselian characteristic zero valued fields with an analytic structure. I also axiomatise the theory of W(F_p^alg) and I show that this theory is NIP.In the third chapter, I prove the density of definable types in certain enrichments of ACVF. From this result, I deduce a criterion for the elimination of imaginaries and the invariant property. This chapter also contains abstract results on externally definable sets in NIP theories. In the last chapter, the previous chapter is applied to VDF, the model completion of valued fields with a valuation preserving derivation, to obtain the elimination of imaginaries in the geometric language, as well as the density of definable types and the invariant extension property. This chapter also contains considerations about definable functions, types and definable groupes in VDF.

Utbredningen av sociala medier är markant och endast en minoritet av befolkningen finns inte med på sociala medier i någon form. Detta skapar värdefull information som bland annat används av organisationer och rekryterare för att skapa sig en bild om och riskminimera nästa rekrytering. Dock är detta ett förhållandevist nytt sätt att rekrytera och inhämta information och det saknas riktlinjer och förståelse för hur det kan användas på ett ansvarsfullt sätt. Ny lagstiftning som GDPR visar på att det finns ett behov av att säkerställa att informationen inte används felaktigt. Studiens syfte är att öka förståelsen för hur rekryteringsföretag använder information från sociala medier i rekryteringsprocessen utifrån ett ansvarsperspektiv. En kvalitativ studie utfördes med 10 informanter inom bemanningsbranschen. Metoden användes då studien ville fånga respondenternas uppfattning gällande sociala mediers användande i en rekryteringsprocess. Då bemanningsbranschen jobbar inriktat mot just rekrytering ansågs dessa var den målgrupp som erbjöd mest expertis och kunskap. Studien har kommit fram till att det finns en problematik med screening av sociala medier då det är ett oreglerat verktyg. Lagstiftningen är inte tillräcklig och det finns ingen tydlighet i vad för ansvarsroll som gäller. Rekryterare vill gärna använda sociala medier utan att vara oroliga för att de går över gränser och de befinner sig i en dialektal spänning där de anser det vara ett bra verktyg samtidigt som det riskerar att anses ansvarslöst att använda det. En ökad tydlighet om hur det kan och ska användas visar sig vara önskvärt från rekryterare för att ge dem möjlighet att vara transparenta med sitt arbete. / The prevalence of social media is significant and only a minority of the population is not on social media in any form. This creates valuable information that is used by organizations and recruiters, among other things, to create an image and risk minimize the next recruitment. However, this is a relatively new way of recruiting and collecting information and there are a lack of guidelines and understanding of how it can be used in a responsible manner. New legislation such as GDPR shows that there is a need to ensure that the information is not used incorrectly. The aim of the study is to increase understanding of how recruitment companies use information from social media in the recruitment process from a responsibility perspective. A qualitative study was conducted with 10 informants in the staffing industry. The method was used as the study wanted to capture the respondents' perception of social media use in a recruitment process. Since the staffing industry is focused on recruitment, these were considered the target group that offered the most expertise and knowledge. The study has concluded that there is a problem with screening of social media as it is an unregulated tool. Legislation is not sufficient and there is no clarity on what role of responsibility applies. Recruiters would like to use social media without being worried that they are crossing borders and they are in a dialectical tension where they consider it a good tool while at the same time risking being considered irresponsible to use it. Increased clarity on how it can and should be used proves desirable from recruiters to give them the opportunity to be transparent with their work.

La presente investigación tiene como objetivo principal determinar y analizar los beneficios valorados de los consumidores de cerveza artesanal que viven en Lima Moderna. Para la presente tesis se realizó una investigación cualitativa que consistió en 4 entrevistas en profundidad y un mini focus group y además se una investigación cuantitativa a través de 377 encuestas aplicadas a la población objetivo. En el capítulo 1 se presenta el marco teórico utilizado en la investigación, el cual incluye los antecedentes (estudios relacionados al mercado de cerveza artesanal en Perú y en el mundo), el marco conceptual e información del mercado de cerveza artesanal. En el capítulo 2, se plantea el problema de investigación, las hipótesis, los objetivos principales de la investigación y la justificación de la elección del tema. El capítulo 3 describe el público objetivo y las metodologías utilizada para realizar la investigación. En el capítulo 4 se presenta el análisis de la investigación, el cual está alineado a los objetivos y las hipótesis planteadas en el capítulo 2. Se pudo concluir que los beneficios valorados más importantes para a los consumidores de cerveza artesanal peruana en Lima Moderna son disfrutar de la experiencia sensorial y disfrutar de la experiencia de prueba. Además, el beneficio de autoexpresión surge como la principal variable para segmentar el mercado. En la última parte de la investigación se presentan las referencias bibliográficas utilizadas para la elaboración de la investigación así como los anexos. / The main objective of this research is to determine and analyze the valued benefits of craft beer consumers living in Modern Lima. For the present thesis, a qualitative research was carried out that consisted of 4 in-depth interviews and a mini focus group and also a quantitative research through 377 surveys applied to the target population. Chapter 1 presents the theoretical framework used in the research, which includes the background (studies related to the craft beer market in Peru and the world), the conceptual framework and the panorama of the craft beer industry in Latin America and in the world. In chapter 2, the research problem, the hypotheses, the main objectives of the research and the justification of the choice of topic are presented. Chapter 3 describes the target audience and the methodologies used to conduct the research. Chapter 4 presents the analysis of the research, which is aligned to the objectives and hypotheses set out in chapter 2. It was concluded that the most important valued benefits for consumers of Peruvian craft beer in Modern Lima are to enjoy the sensory experience and enjoy the test experience. In addition, the benefit of self-expression emerges as the main variable to segment the market. The findings coincide with the concepts and trends described in the theoretical framework. In the last part of the investigation, the bibliographic references and the annexes are presented. / Tesis

Les horizons sont des éléments indispensables à la création d’un modèle structural pour l’exploration d’hydrocarbures. Ces horizons peuvent avoir des formes complexes, les rendant difficiles voire impossibles à manipuler par les logiciels d’exploration. La gestion de ces horizons “multivalués” dans l’interprétation structural passe par deux axes de travail. Il faut premièrement trouver un modèle pour les représenter. Un état de l’art des modèles de données et un programme de comparaison automatique montrent ainsi comment les systèmes de patch et les surfaces triangulées sont les plus adaptés pour représenter les horizons avec failles inverses et les dômes de sel, respectivement. Dans un second temps, il faut pouvoir reconstruire les surfaces de ces horizons multivalués à partir de données d’interprétation, qui sont à la fois peu denses et non-uniformément distribuées. Nous proposons deux algorithmes de reconstruction, un pour chaque type d’horizon. Ces méthodes sont basées sur les approches classiques en géoscience, et forment donc une extension naturelle de l’état de l’art. Avec ces modèles et leurs méthodes de reconstruction, la gestion des horizons multivalués est désormais possible et pratique, permettant de considérer des champs plus complexes / Horizons are first-class elements of the structural models used for Oil & Gasexploration. When they have a complex shape, they become difficult or even outright impossibleto manage within typical software packages. Handling those so-called “multivalued”horizons indeed requires tackling two problems. First, data models must be found to representthem. A review of the state of the art, complemented by a benchmark, led us to promotethe use of patch systems and triangulated surfaces in order to represent reverse-faulted horizonsand salt domes, respectively. Second, multivalued surfaces must be reconstructed fromsparse and non-uniformly distributed interpretation data. We developed two reconstructionmethods, each targeting a multivalued horizon type. They are based on standard geoscienceinterpolation methods, making them both fast and natural extensions of the state of the art.Using the proposed models along with the reconstruction methods, it is now possible to efficientlytackle the more complex fields were they are typically found.

by Yan Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 78-80). / Abstract also in Chinese. / Chapter 1 --- Admissible Points of Convex Sets --- p.7 / Chapter 1.1 --- Introduction and Notations --- p.7 / Chapter 1.2 --- The Main Result --- p.7 / Chapter 1.2.1 --- The Proof of Theoreml.2.1 --- p.8 / Chapter 1.3 --- An Application --- p.10 / Chapter 2 --- A Generalization on The Theorems of Admissible Points --- p.12 / Chapter 2.1 --- Introduction and Notations --- p.12 / Chapter 2.2 --- Fundamental Lemmas --- p.14 / Chapter 2.3 --- The Main Result --- p.16 / Chapter 3 --- Introduction to Variational Inequalities --- p.21 / Chapter 3.1 --- Variational Inequalities in Finite Dimensional Space --- p.21 / Chapter 3.2 --- Problems Which Relate to Variational Inequalities --- p.25 / Chapter 3.3 --- Some Variations on Variational Inequality --- p.28 / Chapter 3.4 --- The Vector Variational Inequality Problem and Its Relation with The Vector Optimization Problem --- p.29 / Chapter 3.5 --- Variational Inequalities in Hilbert Space --- p.31 / Chapter 4 --- Vector Variational Inequalities --- p.36 / Chapter 4.1 --- Preliminaries --- p.36 / Chapter 4.2 --- Notations --- p.37 / Chapter 4.3 --- Existence Results of Vector Variational Inequality --- p.38 / Chapter 5 --- The Generalized Quasi-Variational Inequalities --- p.44 / Chapter 5.1 --- Introduction --- p.44 / Chapter 5.2 --- Properties of The Class F0 --- p.46 / Chapter 5.3 --- Main Theorem --- p.53 / Chapter 5.4 --- Remarks --- p.58 / Chapter 6 --- A set-valued open mapping theorem and related re- sults --- p.61 / Chapter 6.1 --- Introduction and Notations --- p.61 / Chapter 6.2 --- An Open Mapping Theorem --- p.62 / Chapter 6.3 --- Main Result --- p.63 / Chapter 6.4 --- An Application on Ordered Normed Spaces --- p.66 / Chapter 6.5 --- An Application on Open Decomposition --- p.70 / Chapter 6.6 --- An Application on Continuous Mappings from Order- infrabarreled Spaces --- p.72 / Bibliography