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.

Modelling non-industrial private forest landowners' strategic decision making by using logistic regression and neural networks: case of predicting the choice of forest taxation basis

Summary

Forecasting of wind speeds and directions with artificial neural networks

In this master’s thesis, wind speeds and directions were modeled with the aim of developing suitable models for hourly, daily, weekly and monthly forecasting. Artificial Neural Networks implemented in MATLAB software were used to perform the forecasts. Three main types of artificial neural network were built, namely: Feed forward neural networks, Jordan Elman neural networks and Cascade forward neural networks. Four sub models of each of these neural networks were also built, corresponding to the four forecast horizons, for both wind speeds and directions. A single neural network topology was used for each of the forecast horizons, regardless of the model type. All the models were then trained with real data of wind speeds and directions collected over a period of two years in the municipal region of Puumala in Finland. Only 70% of the data was used for training, validation and testing of the models, while the second last 15% of the data was presented to the trained models for verification. The model outputs were then compared to the last 15% of the original data, by measuring the mean square errors and sum square errors between them. Based on the results, the feed forward networks returned the lowest generalization errors for hourly, weekly and monthly forecasts of wind speeds; Jordan Elman networks returned the lowest errors when used for forecasting of daily wind speeds. Cascade forward networks gave the lowest errors when used for forecasting daily, weekly and monthly wind directions; Jordan Elman networks returned the lowest errors when used for hourly forecasting. The errors were relatively low during training of the models, but shot up upon simulation with new inputs. In addition, a combination of hyperbolic tangent transfer functions for both hidden and output layers returned better results compared to other combinations of transfer functions. In general, wind speeds were more predictable as compared to wind directions, opening up opportunities for further research into building better models for wind direction forecasting.

Use of neural networks in robot positioning of large flexible redundant manipulators

Deflection compensation of flexible boom structures in robot positioning is usually done using tables containing the magnitude of the deflection with inverse kinematics solutions of a rigid structure. The number of table values increases greatly if the working area of the boom is large and the required positioning accuracy is high. The inverse kinematics problems are very nonlinear, and if the structure is redundant, in some cases it cannot be solved in a closed form. If the structural flexibility of the manipulator arms is taken into account, the problem is almost impossible to solve using analytical methods. Neural networks offer a possibility to approximate any linear or nonlinear function. This study presents four different methods of using neural networks in the static deflection compensation and inverse kinematics solution of a flexible hydraulically driven manipulator. The training information required for training neural networks is obtained by employing a simulation model that includes elasticity characteristics. The functionality of the presented methods is tested based on the simulated and measured results of positioning accuracy. The simulated positioning accuracy is tested in 25 separate coordinate points. For each point, the positioning is tested with five different mass loads. The mean positioning error of a manipulator decreased from 31.9 mm to 4.1 mm in the test points. This accuracy enables the use of flexible manipulators in the positioning of larger objects. The measured positioning accuracy is tested in 9 separate points using three different mass loads. The mean positioning error decreased from 10.6 mm to 4.7 mm and the maximum error from 27.5 mm to 11.0 mm.

Pretraining Convolutional Neural Networks for Visual Recognition

Convolutional Neural Networks (CNN) have become the state-of-the-art methods on many large scale visual recognition tasks. For a lot of practical applications, CNN architectures have a restrictive requirement: A huge amount of labeled data are needed for training. The idea of generative pretraining is to obtain initial weights of the network by training the network in a completely unsupervised way and then fine-tune the weights for the task at hand using supervised learning. In this thesis, a general introduction to Deep Neural Networks and algorithms are given and these methods are applied to classification tasks of handwritten digits and natural images for developing unsupervised feature learning. The goal of this thesis is to find out if the effect of pretraining is damped by recent practical advances in optimization and regularization of CNN. The experimental results show that pretraining is still a substantial regularizer, however, not a necessary step in training Convolutional Neural Networks with rectified activations. On handwritten digits, the proposed pretraining model achieved a classification accuracy comparable to the state-of-the-art methods.

Deep convolutional neural networks for semantic video object segmentation

In this thesis, we propose to infer pixel-level labelling in video by utilising only object category information, exploiting the intrinsic structure of video data. Our motivation is the observation that image-level labels are much more easily to be acquired than pixel-level labels, and it is natural to find a link between the image level recognition and pixel level classification in video data, which would transfer learned recognition models from one domain to the other one. To this end, this thesis proposes two domain adaptation approaches to adapt the deep convolutional neural network (CNN) image recognition model trained from labelled image data to the target domain exploiting both semantic evidence learned from CNN, and the intrinsic structures of unlabelled video data. Our proposed approaches explicitly model and compensate for the domain adaptation from the source domain to the target domain which in turn underpins a robust semantic object segmentation method for natural videos. We demonstrate the superior performance of our methods by presenting extensive evaluations on challenging datasets comparing with the state-of-the-art methods.

Genetic Basis and Diagnostics of Extended-Spectrum Beta-Lactamases among Enterobacteriaceae in Finland

Since the introduction of antibiotic agents, the amount and prevalence of Beta-lactam resistant enterobacteria has become an increasing problem. Many enterobacteria are opportunistic pathogens that easily acquire resistance mechanisms and genes, which make the situation menacing. These bacteria have acquired resistance and can hydrolyse extended spectrum cephalosporins and penicillins by producing enzymes called extended-spectrum Beta-lactamases (ESBLs). ESBL-producing bacteria are most commonly found in the gastro-intestinal tract of colonised patients. These resistant strains can be found in both health-care associated and community-acquired isolates. The detection and treatment of infections caused by bacteria producing ESBLs are problematic. This study investigated the genetic basis of extended-spectrum Beta-lactamases in Enterobacteriaceae, especially in Escherichia coli and Klebsiella pneumoniae isolates. A total of 994 Finnish Enterobacteriaceae strains, collected at 26 hospital laboratories, during 2000 and 2007 were analysed. For the genetic basis studies, PCR, sequencing and pyrosequencing methods were optimised. In addition, international standard methods, the agar dilution and disk diffusion methods were performed for the resistance studies, and the susceptibility of these strains was tested for antimicrobial agents that are used for treating patients. The genetic analysis showed that bla_CTX-M was the most prevalent gene among the E. coli isolates, while blaS_HV-12 was the most common Beta-lactamase gene in K. pneumoniae. The susceptibility testing results showed that about 60% of the strains were multidrug resistant. The prevalence of ESBL-producing isolates in Finland has been increasing since 2000. However, the situation in Finland is still much better than in many other European countries.

Neural mechanisms underlying conscious and unconscious vision. Evidence from event-related potentials and transcranial magnetic stimulation

Vision affords us with the ability to consciously see, and use this information in our behavior. While research has produced a detailed account of the function of the visual system, the neural processes that underlie conscious vision are still debated. One of the aims of the present thesis was to examine the time-course of the neuroelectrical processes that correlate with conscious vision. The second aim was to study the neural basis of unconscious vision, that is, situations where a stimulus that is not consciously perceived nevertheless influences behavior. According to current prevalent models of conscious vision, the activation of visual cortical areas is not, as such, sufficient for consciousness to emerge, although it might be sufficient for unconscious vision. Conscious vision is assumed to require reciprocal communication between cortical areas, but views differ substantially on the extent of this recurrent communication. Visual consciousness has been proposed to emerge from recurrent neural interactions within the visual system, while other models claim that more widespread cortical activation is needed for consciousness. Studies I-III compared models of conscious vision by studying event-related potentials (ERP). ERPs represent the brain’s average electrical response to stimulation. The results support the model that associates conscious vision with activity localized in the ventral visual cortex. The timing of this activity corresponds to an intermediate stage in visual processing. Earlier stages of visual processing may influence what becomes conscious, although these processes do not directly enable visual consciousness. Late processing stages, when more widespread cortical areas are activated, reflect the access to and manipulation of contents of consciousness. Studies IV and V concentrated on unconscious vision. By using transcranial magnetic stimulation (TMS) we show that when early visual cortical processing is disturbed so that subjects fail to consciously perceive visual stimuli, they may nevertheless guess (above chance-level) the location where the visual stimuli were presented. However, the results also suggest that in a similar situation, early visual cortex is necessary for both conscious and unconscious perception of chromatic information (i.e. color). Chromatic information that remains unconscious may influence behavioral responses when activity in visual cortex is not disturbed by TMS. Our results support the view that early stimulus-driven (feedforward) activation may be sufficient for unconscious processing. In conclusion, the results of this thesis support the view that conscious vision is enabled by a series of processing stages. The processes that most closely correlate with conscious vision take place in the ventral visual cortex ~200 ms after stimulus presentation, although preceding time-periods and contributions from other cortical areas such as the parietal cortex are also indispensable. Unconscious vision relies on intact early visual activation, although the location of visual stimulus may be unconsciously resolved even when activity in the early visual cortex is interfered with.

Semantic and fuzzy modelling for human behaviour recognition in smart spaces : a case study on ambient assisted living.

Human activity recognition in everyday environments is a critical, but challenging task in Ambient Intelligence applications to achieve proper Ambient Assisted Living, and key challenges still remain to be dealt with to realize robust methods. One of the major limitations of the Ambient Intelligence systems today is the lack of semantic models of those activities on the environment, so that the system can recognize the speci c activity being performed by the user(s) and act accordingly. In this context, this thesis addresses the general problem of knowledge representation in Smart Spaces. The main objective is to develop knowledge-based models, equipped with semantics to learn, infer and monitor human behaviours in Smart Spaces. Moreover, it is easy to recognize that some aspects of this problem have a high degree of uncertainty, and therefore, the developed models must be equipped with mechanisms to manage this type of information. A fuzzy ontology and a semantic hybrid system are presented to allow modelling and recognition of a set of complex real-life scenarios where vagueness and uncertainty are inherent to the human nature of the users that perform it. The handling of uncertain, incomplete and vague data (i.e., missing sensor readings and activity execution variations, since human behaviour is non-deterministic) is approached for the rst time through a fuzzy ontology validated on real-time settings within a hybrid data-driven and knowledgebased architecture. The semantics of activities, sub-activities and real-time object interaction are taken into consideration. The proposed framework consists of two main modules: the low-level sub-activity recognizer and the high-level activity recognizer. The rst module detects sub-activities (i.e., actions or basic activities) that take input data directly from a depth sensor (Kinect). The main contribution of this thesis tackles the second component of the hybrid system, which lays on top of the previous one, in a superior level of abstraction, and acquires the input data from the rst module's output, and executes ontological inference to provide users, activities and their in uence in the environment, with semantics. This component is thus knowledge-based, and a fuzzy ontology was designed to model the high-level activities. Since activity recognition requires context-awareness and the ability to discriminate among activities in di erent environments, the semantic framework allows for modelling common-sense knowledge in the form of a rule-based system that supports expressions close to natural language in the form of fuzzy linguistic labels. The framework advantages have been evaluated with a challenging and new public dataset, CAD-120, achieving an accuracy of 90.1% and 91.1% respectively for low and high-level activities. This entails an improvement over both, entirely data-driven approaches, and merely ontology-based approaches. As an added value, for the system to be su ciently simple and exible to be managed by non-expert users, and thus, facilitate the transfer of research to industry, a development framework composed by a programming toolbox, a hybrid crisp and fuzzy architecture, and graphical models to represent and con gure human behaviour in Smart Spaces, were developed in order to provide the framework with more usability in the nal application. As a result, human behaviour recognition can help assisting people with special needs such as in healthcare, independent elderly living, in remote rehabilitation monitoring, industrial process guideline control, and many other cases. This thesis shows use cases in these areas.

Genetic diversity and phenotypic variability of phytoplankton populations in the Baltic Sea

En av naturens mest grundläggande aspekter är den enorma mängd av variation som existerar mellan arter. Denna variation har lett oss till att klassificera olika organismer på basis av morfologiska skillnader och på senare tid till att jämföra genetiska skillnader på individens nivå. Den marina kiselalgen Skeletonema marinoi är en av de vanligaste växtplanktonarter i Östersjön under vårblomningen och anses viktig för den årliga produktionen. En av mina främsta målsättningar var att beskriva den intra-specifika diversiteten hos denna art längs med miljögradienter i Östersjön. Ett annat mål var att klargöra de faktorer som eventuellt är involverade i konfigurationen av genetisk diversitet och differentiering. Med hjälp av genetiska markörer visade jag att den genetiska diversiteten hos S. marinoi populationer i Östersjön är lägre jämfört med populationer i östra delen av Nordsjön. Arten är genetiskt uppdelad så att en utpräglad population förekommer i Östersjön och en annan, genetiskt åtskild population förekommer norr om de Danska sunden. Resultaten visar att de genetiskt åtskilda populationerna är anpassade till lokala salinitetsförhållanden. Genflödet mellan populationerna korrelerade kraftigt med havströmmar i området. Mina studier avslöjade även omfattande variation av fenotypiska, ekologiskt vikitga särdrag hos olika kloner. Djurplankton som äter kiselalger kunde modifiera den klonala mångfalden av fenotypiskt variabla S. marinoi populationer. En ökad klonal mångfald ledde till högre prestationsförmåga i fråga om primär produktion och stabiliserade ekofysiologiska funktioner. Som visas i denna avhandling består en art allt som oftast av åtskilliga genetiska varianter med fenotypiska skillnader. Kunskap om sådana intra-specifika skillnader är en förutsättning för att vi skall kunna förstå var och varför arter förekommer. Denna kunskap utgör även en grund för prognoser som siktar på att förutspå huruvida arter kan anpassa sig till framtida miljöförhållanden. ------------------------------------------------------ Suunnaton määrä variaatioita eliölajien välillä on perustavanlaatuinen ominaisuus luonnossa. Perinteisesti tätä monimuotoisuutta on käytetty organismien luokittelemiseen eri lajeihin niiden morfologisten eroavaisuuksien perusteella. Hiljattain myös geneettisten erojen huomioimista yksilötasolla on hyödynnetty lajien luokittelemisessa. Merialueilla esiintyvä piilevä, Skeletonema marinoi on yksi Itämeren tavallisimmista kasviplanktonlajeista kevätkukinnan aikana. Tavoitteenani oli selventää geneettistä ja fenotyyppistä monimuotoisuutta pitkin Itämeren ympäristögradienttejä. Geneettisen monimuotoisuuteen ja erkaantumiseen vaikuttavien tekijöiden selvittäminen oli tärkeä aspekti väitöstutkimuksessani. Geneettisiä markkereita käyttämällä pystyin toteamaan, että S. marinoi levän geneettinen monimuotoisuus on Itämeressä merkittävästi alhaisempi kuin läheisessä Pohjanmeren itäosassa. Tutkittu laji jakautuu geneettisesti yhteen erilliseen populaatioon Itämeressä ja toiseen selvästi erottuvaan populaatioon Tanskan salmien pohjoispuolella. Kokeellisten tulosten perusteella nämä geneettisesti erilaistuneet populaatiot ovat kumpikin sopeutuneet paikalliseen veden suolapitoisuuteen. Populaatioiden välisen geenivirran ja merivirtojen luoman yhteyden välillä havaittiin vahva korrelaatio. Tutkimukseni paljastivat myös laajaa vaihtelua Skeletonema-kloonien ekologisesti tärkeissä ominaisuuksissa. Kokeellisten tutkimusteni perusteella laiduntajat pystyivät muuttamaan geneettisten kloonien lukumäärää monimuotoisissa S. marinoi populaatioissa. Lisääntynyt kloonien lukumäärä paransi perustuotantokykyä ja vakautti ekofysiologisia toimintoja. Kuten tässä väitöstutkimuksessa osoitetaan, lajit koostuvat useimmiten lukuisista geneettisistä muunnelmista, jotka eroavat usein fenotyypeiltään. Ymmärtääksemme missä tietyt lajit esiintyvät ja miksi, tarvitsemme tietoa lajien sisäisistä vaihteluista. Tämä tieto on tarpeellista, jotta voimme ennustaa lajien sopeutumista tuleviin ympäristönmuutoksiin.