A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

A generalized 1D particle transport method for convection diffusion reaction model

This work is devoted to the development of numerical method to deal with convection diffusion dominated problem with reaction term, non - stiff chemical reaction and stiff chemical reaction. The technique is based on the unifying Eulerian - Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves created by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that, each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients (steep fronts) and discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that, the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consumer when compared with other classical technique e.g., method of lines. Apart from this advantage, the particle transport method can be used to simulate problems that involve movingsteep/smooth fronts such as separation of two or more elements in the system.

Generalized Differential Evolution for Global Multi-Objective Optimization with Constraints

The objective of this thesis work is to develop and study the Differential Evolution Algorithm for multi-objective optimization with constraints. Differential Evolution is an evolutionary algorithm that has gained in popularity because of its simplicity and good observed performance. Multi-objective evolutionary algorithms have become popular since they are able to produce a set of compromise solutions during the search process to approximate the Pareto-optimal front. The starting point for this thesis was an idea how Differential Evolution, with simple changes, could be extended for optimization with multiple constraints and objectives. This approach is implemented, experimentally studied, and further developed in the work. Development and study concentrates on the multi-objective optimization aspect. The main outcomes of the work are versions of a method called Generalized Differential Evolution. The versions aim to improve the performance of the method in multi-objective optimization. A diversity preservation technique that is effective and efficient compared to previous diversity preservation techniques is developed. The thesis also studies the influence of control parameters of Differential Evolution in multi-objective optimization. Proposals for initial control parameter value selection are given. Overall, the work contributes to the diversity preservation of solutions in multi-objective optimization.

Muon detector link system test set-up

CERNin tutkimuskeskuksen rakenteilla olevan hadronikiihdyttimen eräs tarkoitus on todistaa Higgsin bosonin olemassaolo. Higgsin bosonin löytyminen yhtenäistäisi nykyisen hiukkasfysiikan teorian ja antaisi selityksen sille kuinka hiukkaset saavat massansa. Kiihdyttimen CMS koeasema on tarkoitettu erityisesti myonien ilmaisuun. Tämä työ liittyy CMS koeaseman RPC-ilmaisintyypin linkkijärjestelmään, jonka tarkoituksena on käsitellä ilmaisimelta tulevia myonien aiheuttamia signaaleja ja lähettää tiedot tärkeäksi katsotuista törmäystapahtumista tallennettavaksi analysointia varten. Työssä on toteutettu linkkijärjestelmän ohjaus- ja linkkikorteille testiympäristö, jolla voidaan todeta järjestelmän eri osien keskinäinen yhteensopivuus ja toimivuus. Työn alkuosassa esitellään ilmaisimen linkkijärjestelmän eri osat ja niiden merkitykset. Työn loppuosassa käydään läpi eri testimenetelmiä ja analysoidaan niiden antamia tuloksia.

Modeling of non-isothermalvapor membrane separation with thermodynamic models and generalized mass transfer equations

A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

Level Set Methods in Image Processing

This thesis gives an overview of the use of the level set methods in the field of image science. The similar fast marching method is discussed for comparison, also the narrow band and the particle level set methods are introduced. The level set method is a numerical scheme for representing, deforming and recovering structures in an arbitrary dimensions. It approximates and tracks the moving interfaces, dynamic curves and surfaces. The level set method does not define how and why some boundary is advancing the way it is but simply represents and tracks the boundary. The principal idea of the level set method is to represent the N dimensional boundary in the N+l dimensions. This gives the generality to represent even the complex boundaries. The level set methods can be powerful tools to represent dynamic boundaries, but they can require lot of computing power. Specially the basic level set method have considerable computational burden. This burden can be alleviated with more sophisticated versions of the level set algorithm like the narrow band level set method or with the programmable hardware implementation. Also the parallel approach can be used in suitable applications. It is concluded that these methods can be used in a quite broad range of image applications, like computer vision and graphics, scientific visualization and also to solve problems in computational physics. Level set methods and methods derived and inspired by it will be in the front line of image processing also in the future.

A Dependency Parsing Approach to Biomedical Text Mining

Biomedical research is currently facing a new type of challenge: an excess of information, both in terms of raw data from experiments and in the number of scientific publications describing their results. Mirroring the focus on data mining techniques to address the issues of structured data, there has recently been great interest in the development and application of text mining techniques to make more effective use of the knowledge contained in biomedical scientific publications, accessible only in the form of natural human language. This thesis describes research done in the broader scope of projects aiming to develop methods, tools and techniques for text mining tasks in general and for the biomedical domain in particular. The work described here involves more specifically the goal of extracting information from statements concerning relations of biomedical entities, such as protein-protein interactions. The approach taken is one using full parsing—syntactic analysis of the entire structure of sentences—and machine learning, aiming to develop reliable methods that can further be generalized to apply also to other domains. The five papers at the core of this thesis describe research on a number of distinct but related topics in text mining. In the first of these studies, we assessed the applicability of two popular general English parsers to biomedical text mining and, finding their performance limited, identified several specific challenges to accurate parsing of domain text. In a follow-up study focusing on parsing issues related to specialized domain terminology, we evaluated three lexical adaptation methods. We found that the accurate resolution of unknown words can considerably improve parsing performance and introduced a domain-adapted parser that reduced the error rate of theoriginal by 10% while also roughly halving parsing time. To establish the relative merits of parsers that differ in the applied formalisms and the representation given to their syntactic analyses, we have also developed evaluation methodology, considering different approaches to establishing comparable dependency-based evaluation results. We introduced a methodology for creating highly accurate conversions between different parse representations, demonstrating the feasibility of unification of idiverse syntactic schemes under a shared, application-oriented representation. In addition to allowing formalism-neutral evaluation, we argue that such unification can also increase the value of parsers for domain text mining. As a further step in this direction, we analysed the characteristics of publicly available biomedical corpora annotated for protein-protein interactions and created tools for converting them into a shared form, thus contributing also to the unification of text mining resources. The introduced unified corpora allowed us to perform a task-oriented comparative evaluation of biomedical text mining corpora. This evaluation established clear limits on the comparability of results for text mining methods evaluated on different resources, prompting further efforts toward standardization. To support this and other research, we have also designed and annotated BioInfer, the first domain corpus of its size combining annotation of syntax and biomedical entities with a detailed annotation of their relationships. The corpus represents a major design and development effort of the research group, with manual annotation that identifies over 6000 entities, 2500 relationships and 28,000 syntactic dependencies in 1100 sentences. In addition to combining these key annotations for a single set of sentences, BioInfer was also the first domain resource to introduce a representation of entity relations that is supported by ontologies and able to capture complex, structured relationships. Part I of this thesis presents a summary of this research in the broader context of a text mining system, and Part II contains reprints of the five included publications.

Conditions for different autonomy regimes in the world : a fuzzy-set application

Avhandlingen behandlar temat territoriell autonomi ur ett globalt perspektiv. Syftet är dels att kartlägga de territoriella autonomierna i världen och dels att visa hur en ny metod som fuzzy-set kan användas inom ämnesområdet jämförande politik. Forskningsproblemet är att försöka finna de bakgrundsfaktorer som förklarar uppkomsten av territoriell autonomi som sådant. Territoriella autonomier ses som särlösningar inom stater. Dessa regioner har erhållit en specialställning i förhållande till andra regioner inom respektive stat och även i förhållande till centralmakten i övrigt. Regionerna kan därför ses som undantag inom det enhetliga federala, regionala eller decentraliserade systemet inom en viss stat ifråga. En kartläggning visar att det finns 65 specialregioner fördelade på 25 stater i världen. De flesta av dessa utgörs av öar. Resultaten visar att det finns två vägar vilka leder till territoriell autonomi i allmänhet. Den ena vägen är en kombination av etnisk särprägel och liten befolkningsmängd, medan den andra vägen utgörs av kombinationen av historiska orsaker och geografiskt avstånd. Båda vägar är lika giltiga och förutsättningen är en demokratisk miljö.

Social capital and health : variations, associations and challenges

Although social capital and health have been extensively studied during the last decade, there are still open issues in current empirical research. These concern for instance the measurement of the concept in different contexts, as well as the association between different types of social capital and different dimensions of health. The present thesis addressed these questions. The general aim was to promote the understanding of social capital and health by investigating the oldest old and the two major language groups in Finland, Swedish- and Finnish-speakers. Another aim was to contribute to the discussion on methodological issues in social capital and health research. The present thesis investigated two empirical data sets, Umeå 85+ and Health 2000. The Umeå 85+ study was a cross-sectional study of 163 individuals aged 85, 90, and 95 or older, living in the municipality of Umeå, Sweden, in the year of 2000. The Health 2000 survey was a national study of 8,028 persons aged 30 or above carried out in Finland in 2000-2001. Different indicators of structural (e.g. social contacts) and cognitive (e.g. trust) social capital, as well as health indicators were used as variables in the analyses. The Umeå 85+ data set was analyzed with factor analysis, as well as univariate and multivariate analysis of variance. The Health 2000 data was analyzed with logistic regression techniques. The results showed that the Swedish-speakers in the Finnish data set Health 2000 had consistently higher prevalence of social capital compared to the Finnish-speakers even after controlling for central sociodemographic variables. The results further showed that even if the language group differences in health were small, the Swedishspeakers experienced in general better self-reported health compared with the Finnish-speakers. Common sociodemographic variables could not explain these observed differences in health. The results imply that social capital is often, but not always, associated with health. This was clearly seen in the Umeå 85+ data set where only one health indicator (depressive symptoms) was associated with structural social capital among the oldest old. The results based on the analysis of the Health 2000 survey demonstrated that the cognitive component of social capital was associated with self-rated health and psychological health rather than with participation in social activities and social contacts. In addition, social capital statistically reduced the health advantage especially for Swedish-speaking men, indicating that high prevalence of social capital may promote health. Finally, the present thesis also discussed the issue of methodological challenges faced with when analyzing social capital and health. It was suggested that certain components of social capital such as bonding and bridging social capital may be more relevant than structural and cognitive components when investigating social capital among the two language groups in Finland. The results concerning the oldest old indicated that the structural aspects of social capital probably reflect current living conditions, whereas cognitive social capital reflects attitudes and traits often acquired decades earlier. This is interpreted as an indication of the fact that structural and cognitive social capital are closely related yet empirically two distinctive concepts. Taken together, some components of social capital may be more relevant to study than others depending on which population group and age group is under study. The results also implied that the choice of cut-off point of dichotomization of selfrated health has an impact on the estimated effects of the explanatory variables. When the whole age interval, 35-64 years, was analyzed with logistic regression techniques the choice of cut-off point did not matter for the estimated effects of marital status and educational level. The results changed, however, when the age interval was divided into three shorter intervals. If self-rated health is explored using wide age intervals that do not account for age-dependent covariates there is a risk of drawing misleading conclusions. In conclusion, the results presented in the thesis suggest that the uneven distribution of social capital observed between the two language groups in Finland are of importance when trying to further understand health inequalities that exist between Swedish- and Finnish-speakers in Finland. Although social capital seemed to be relevant to the understanding of health among the oldest old, the meaning of social capital is probably different compared to a less vulnerable age group. This should be noticed in future empirical research. In the present thesis, it was shown that the relationship between social capital and health is complex and multidimensional. Different aspects of social capital seem to be important for different aspects of health. This reduces the possibility to generalize the results and to recommend general policy implementations in this area. An increased methodological awareness regarding social capital as well as health are called for in order to further understand the cfomplex association between them. However, based on the present data and findings social capital is associated with health. To understand individual health one must also consider social aspects of the individuals’ environment such as social capital.