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.

Fuzzy ontology for knowledge mobilisation and decision support

A growing concern for organisations is how they should deal with increasing amounts of collected data. With fierce competition and smaller margins, organisations that are able to fully realize the potential in the data they collect can gain an advantage over the competitors. It is almost impossible to avoid imprecision when processing large amounts of data. Still, many of the available information systems are not capable of handling imprecise data, even though it can offer various advantages. Expert knowledge stored as linguistic expressions is a good example of imprecise but valuable data, i.e. data that is hard to exactly pinpoint to a definitive value. There is an obvious concern among organisations on how this problem should be handled; finding new methods for processing and storing imprecise data are therefore a key issue. Additionally, it is equally important to show that tacit knowledge and imprecise data can be used with success, which encourages organisations to analyse their imprecise data. The objective of the research conducted was therefore to explore how fuzzy ontologies could facilitate the exploitation and mobilisation of tacit knowledge and imprecise data in organisational and operational decision making processes. The thesis introduces both practical and theoretical advances on how fuzzy logic, ontologies (fuzzy ontologies) and OWA operators can be utilized for different decision making problems. It is demonstrated how a fuzzy ontology can model tacit knowledge which was collected from wine connoisseurs. The approach can be generalised and applied also to other practically important problems, such as intrusion detection. Additionally, a fuzzy ontology is applied in a novel consensus model for group decision making. By combining the fuzzy ontology with Semantic Web affiliated techniques novel applications have been designed. These applications show how the mobilisation of knowledge can successfully utilize also imprecise data. An important part of decision making processes is undeniably aggregation, which in combination with a fuzzy ontology provides a promising basis for demonstrating the benefits that one can retrieve from handling imprecise data. The new aggregation operators defined in the thesis often provide new possibilities to handle imprecision and expert opinions. This is demonstrated through both theoretical examples and practical implementations. This thesis shows the benefits of utilizing all the available data one possess, including imprecise data. By combining the concept of fuzzy ontology with the Semantic Web movement, it aspires to show the corporate world and industry the benefits of embracing fuzzy ontologies and imprecision.

On the Condition Monitoring of Induction machines

The research of condition monitoring of electric motors has been wide for several decades. The research and development at universities and in industry has provided means for the predictive condition monitoring. Many different devices and systems are developed and are widely used in industry, transportation and in civil engineering. In addition, many methods are developed and reported in scientific arenas in order to improve existing methods for the automatic analysis of faults. The methods, however, are not widely used as a part of condition monitoring systems. The main reasons are, firstly, that many methods are presented in scientific papers but their performance in different conditions is not evaluated, secondly, the methods include parameters that are so case specific that the implementation of a systemusing such methods would be far from straightforward. In this thesis, some of these methods are evaluated theoretically and tested with simulations and with a drive in a laboratory. A new automatic analysis method for the bearing fault detection is introduced. In the first part of this work the generation of the bearing fault originating signal is explained and its influence into the stator current is concerned with qualitative and quantitative estimation. The verification of the feasibility of the stator current measurement as a bearing fault indicatoris experimentally tested with the running 15 kW induction motor. The second part of this work concentrates on the bearing fault analysis using the vibration measurement signal. The performance of the micromachined silicon accelerometer chip in conjunction with the envelope spectrum analysis of the cyclic bearing faultis experimentally tested. Furthermore, different methods for the creation of feature extractors for the bearing fault classification are researched and an automatic fault classifier using multivariate statistical discrimination and fuzzy logic is introduced. It is often important that the on-line condition monitoring system is integrated with the industrial communications infrastructure. Two types of a sensor solutions are tested in the thesis: the first one is a sensor withcalculation capacity for example for the production of the envelope spectra; the other one can collect the measurement data in memory and another device can read the data via field bus. The data communications requirements highly depend onthe type of the sensor solution selected. If the data is already analysed in the sensor the data communications are needed only for the results but in the other case, all measurement data need to be transferred. The complexity of the classification method can be great if the data is analysed at the management level computer, but if the analysis is made in sensor itself, the analyses must be simple due to the restricted calculation and memory capacity.

Artificially Intelligent and Adaptive Methods for Prediction and Analysis of Superheater Fireside Corrosion in Fluidized Bed Boilers

Superheater corrosion causes vast annual losses for the power companies. With a reliable corrosion prediction method, the plants can be designed accordingly, and knowledge of fuel selection and determination of process conditions may be utilized to minimize superheater corrosion. Growing interest to use recycled fuels creates additional demands for the prediction of corrosion potential. Models depending on corrosion theories will fail, if relations between the inputs and the output are poorly known. A prediction model based on fuzzy logic and an artificial neural network is able to improve its performance as the amount of data increases. The corrosion rate of a superheater material can most reliably be detected with a test done in a test combustor or in a commercial boiler. The steel samples can be located in a special, temperature-controlled probe, and exposed to the corrosive environment for a desired time. These tests give information about the average corrosion potential in that environment. Samples may also be cut from superheaters during shutdowns. The analysis ofsamples taken from probes or superheaters after exposure to corrosive environment is a demanding task: if the corrosive contaminants can be reliably analyzed, the corrosion chemistry can be determined, and an estimate of the material lifetime can be given. In cases where the reason for corrosion is not clear, the determination of the corrosion chemistry and the lifetime estimation is more demanding. In order to provide a laboratory tool for the analysis and prediction, a newapproach was chosen. During this study, the following tools were generated: · Amodel for the prediction of superheater fireside corrosion, based on fuzzy logic and an artificial neural network, build upon a corrosion database developed offuel and bed material analyses, and measured corrosion data. The developed model predicts superheater corrosion with high accuracy at the early stages of a project. · An adaptive corrosion analysis tool based on image analysis, constructedas an expert system. This system utilizes implementation of user-defined algorithms, which allows the development of an artificially intelligent system for thetask. According to the results of the analyses, several new rules were developed for the determination of the degree and type of corrosion. By combining these two tools, a user-friendly expert system for the prediction and analyses of superheater fireside corrosion was developed. This tool may also be used for the minimization of corrosion risks by the design of fluidized bed boilers.

Kiinteistön palautetiedon analysointi

Diplomityö käsittelee kiinteistön palautetiedon analysointia. Tässä diplomityössä palautetiedolla tarkoitetaan kiinteistön talotekniikkaan liittyviä teknisiä ja inhimillisiä tietoja, joiden perusteella rakennuksen ja sen tekniikan toimivuudesta voidaan tehdä päätelmiä. Tiedot kerätään järjestelmistä mittauspisteiden kautta etävalvomoon, josta niitä voidaan tarkastella ja edelleen analysoida. Valvomosta saatavan tiedon rinnalle pyritään suunnitteluvaiheessa kokoamaan valvottavasta kohteesta laskennallisia energiankulutusmalleja. Myös kiinteistön asukkaat, rakennuksen ominaisuudet ja ympäristö muodostavat osan palautetiedosta. Kiinteistön palautetieto voidaankin jakaa tekniseen ja inhimilliseen tietoon, ja edelleen analysoinnin kannalta staattiseen tai dynaamiseen tietoon. Tässä diplomityössä selvitettiin palautetiedon keruuta etävalvomolla yhdistämällä tähän rakentamisen laadunvalvonnan työkaluja ja sumeaa logiikkaa. Työn käytännön osio koostuu kiinteistön ja siihen yhdistetyn etävalvomon välillä kulkevan tiedon käsittelystä, mittauspisteiden määrittämisestä ja tietojen analysoinnista. Työssä esitellään kolme esimerkkikohdetta Helsingin seudulta. Työssä laadittiin arviointimalli, joka sisältää kaiken kiinteistön palautetietoon liittyvän aineiston ja sen analysointitavat, sekä erityisesti uutena asiana myös sumeaa logiikkaa. Tiedon analysointi etenee oletusarvojen muodostamisesta, simuloinnin laatimisesta ja sen vertaamisesta todellisiin tietoihin ja edelleen näistä tehtäviin päätelmiin. Tavanomaisten teknisten tietojen lisäksi sumean logiikan avulla tuotiin esille poikkeamia selittäviä tekijöitä mm. kiinteistön asukkaiden ominaisuuksista.

Advanced control methods for reducing nitrogen oxides in a fluidized bed boiler

Tämän työn tarkoituksena oli löytää keinoja erään leijukerroskattilan typenoksidipäästöjen vähentämiseksi. Koska päästöt olivat jo alunperin alhaiset leijukerrostekniikan ja hybridin SNCR/SCR –typenpoistolaitteiston ansiosta, päätettiin päästöjä lähteä vähentämään parantamalla ammoniakkiruiskutuksen säätöä. Alkuperäinen ammoniakkiruiskutuksen säätö oli liian hidas, jotta satunnaisten häiriöiden aiheuttamat typenoksidipiikit olisi pystytty poistamaan. Ammoniakkiruiskutusta parannettiin lisäämällä jokaiseen ammoniakkilinjaan mäntäpumput, joiden avulla ammoniakkia voidaan syöttää sinne, missä sitä eniten tarvitaan. Ammoniakkiruiskutuksen säätöön kehitettiin uusi sumeaan logiikkaan perustuva säätäjä. Myös muita kehittyneitä säätömenetelmiä kuten neuroverkkoa hyödynnettiin säätäjän kehityksessä. Ammoniakkiruiskutuksen säätäjää testattiin menestyksekkäästi Ruotsissa Brista Kraftin Märstassa sijaitsevalla voimalaitoksella

Asiantuntijajärjestelmä kattilakonseptin valintaan

Polttoaine asettaa puitteet kattilasuunnittelulle. Kiertoleijukattilakonseptin valinta kytkeytyy kiinteästi mitoitusarvoihin ja polttoaineen ominaisuuksiin. Asiakkaan vaatimuk-set kattilalle asettavat lähtökohdan kattilasuunnittelulle. Suorituskyky, kustannukset ja luotettavuus ovat asiakaslähtöisiä tekijöitä, joiden painotukset vaikuttavat kattilakonseptin valintaan. Korkeat lämpötilat tulistimien alueella tekevät tulistinjärjestelystä vaikean ja määräävän osan kattilakonseptin valintaa. Konvektiotulistimien altistuminen kuumille savukaasuille tekee niistä herkkiä likaantumiselle ja korroosiolle. Mitoitusarvojen ja tulistimien rakenteen oikeanlaisella valinnalla voidaan näitä polttoaineperäisiä ongelmia ehkäistä. Lisäksi kiertoleijukattiloissa käytetyt tulipesän ulkopuoliset tulistimet soveltuvat konvektiotulistimia korkeammille lämpötiloille huonolaatuisillakin polttoaineilla. Tässä työssä rakennettu asiantuntijajärjestelmä valitsee alustavan kattilakonseptin mitoitusta varten käyttäjän antamien vähäisten lähtötietojen pohjalta.

Spectral Color Appearance Modeling

Kuvien laatu on tutkituimpia ja käytetyimpiä aiheita. Tässä työssä tarkastellaan värin laatu ja spektrikuvia. Työssä annetaan yleiskuva olemassa olevista pakattujen ja erillisten kuvien laadunarviointimenetelmistä painottaen näiden menetelmien soveltaminen spektrikuviin. Tässä työssä esitellään spektriväriulkomuotomalli värikuvien laadunarvioinnille. Malli sovelletaan spektrikuvista jäljennettyihin värikuviin. Malli pohjautuu sekä tilastolliseen spektrikuvamalliin, joka muodostaa yhteyden spektrikuvien ja valokuvien parametrien välille, että kuvan yleiseen ulkomuotoon. Värikuvien tilastollisten spektriparametrien ja fyysisten parametrien välinen yhteys on varmennettu tietokone-pohjaisella kuvamallinnuksella. Mallin ominaisuuksien pohjalta on kehitetty koekäyttöön tarkoitettu menetelmä värikuvien laadunarvioinnille. On kehitetty asiantuntija-pohjainen kyselymenetelmä ja sumea päättelyjärjestelmä värikuvien laadunarvioinnille. Tutkimus osoittaa, että spektri-väri –yhteys ja sumea päättelyjärjestelmä soveltuvat tehokkaasti värikuvien laadunarviointiin.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

Rouhintasorvauksen säätöjärjestelmä

Tässä työssä kuvataan menetelmä, jonka avulla on mahdollista sorvausprosessista mitattujen signaalien perusteella muokata lastuamisprosessin parametreja siten, että prosessissa mahdollisesti esiintyvät ongelmatilanteet korjataan. Työ on tehty osana Feedchip-tutkimushanketta ja tukeutuu tutkimushankkeessa aiemmin tehtyyn työhön vaadittavien korjaustoimenpiteiden, signaaleja mittaavien antureiden instrumentoinnin sekä alustavan ongelmatilanteiden ominaispiirteiden signaaleista tunnistuksen osalta. Tämä työ keskittyy esittelemään toiminnot, joiden avulla aiemmat tulokset voidaan koota yhteen kokonaisuuteen. Järjestelmän toiminta edellyttää sen osien toiminnan korkean tason koordinointia. Lisäksi määritellään päättelyjärjestelmä, joka kykenee mitatuista arvoista tunnistettujen ongelmatilanteiden esiintymisasteiden perusteella määrittämään tarvittavat toimenpiteet ongelmatilanteiden poistamiseksi. Kandidaatintyön rinnalla toteutetaan ohjelmisto Lappeenrannan teknillisen yliopiston konepajatekniikan laboratorion sorvausjärjestelmän yhteyteen rakennetun prototyyppilaitteiston ohjaamiseksi.

Sumea suositin elokuville

Suositusmenetelmien tarkoituksena on auttaa käyttäjää löytämään häntä kiinnostavia asioita ja välttämään asioita, joista hän ei pitäisi. Suositusmenetelmät antavat suosituk- set yleensä terävinä lukuina. Tässä työssä kehitetään suositusmenetelmä, joka antaa suo- situkset arvosanojen sumeina jäsenyysasteina. Menetelmän antamat suositukset voidaan myös perustella käyttäjälle. Menetelmä kuuluu pääosin yhteisösuodatusmenetelmiin, jois- sa suositukset tehdään käyttäjien antamien arvosanojen perusteella, mutta myös tietoa elokuvien tyylilajeista hyödynnetään suositustarkkuuden parantamiseksi. Sumeiden suo- situsten suositeltavuusjärjestyksen laskemiseen esitetään myös menetelmä. Käyttäjien elokuville antamat arvosanat voidaan käsittää sumeana datana. Käyttäjä voi kuvata arvosanaa esimerkiksi ilmaisulla ”noin 4”. Tästä syystä on loogista esittää suo- situksetkin sumeina lukuina. Tällöin käyttäjälle voidaan antaa tietoa suosituksen tark- kuudesta ja mahdollisista ristiriidoista. Epävarmojen suositusten tapauksessa käyttäjä voi painottaa enemmän muita tietolähteitä. Kokeiden perusteella kehitetty menetelmä antaa joissa tapauksissa selvästi vertailtavia menetelmiä parempia suosituksia, kun taas toisissa tapauksissa suositukset ovat selvästi heikompia.

Adaptive Routing Approaches for Networked Many-Core Systems

Through advances in technology, System-on-Chip design is moving towards integrating tens to hundreds of intellectual property blocks into a single chip. In such a many-core system, on-chip communication becomes a performance bottleneck for high performance designs. Network-on-Chip (NoC) has emerged as a viable solution for the communication challenges in highly complex chips. The NoC architecture paradigm, based on a modular packet-switched mechanism, can address many of the on-chip communication challenges such as wiring complexity, communication latency, and bandwidth. Furthermore, the combined benefits of 3D IC and NoC schemes provide the possibility of designing a high performance system in a limited chip area. The major advantages of 3D NoCs are the considerable reductions in average latency and power consumption. There are several factors degrading the performance of NoCs. In this thesis, we investigate three main performance-limiting factors: network congestion, faults, and the lack of efficient multicast support. We address these issues by the means of routing algorithms. Congestion of data packets may lead to increased network latency and power consumption. Thus, we propose three different approaches for alleviating such congestion in the network. The first approach is based on measuring the congestion information in different regions of the network, distributing the information over the network, and utilizing this information when making a routing decision. The second approach employs a learning method to dynamically find the less congested routes according to the underlying traffic. The third approach is based on a fuzzy-logic technique to perform better routing decisions when traffic information of different routes is available. Faults affect performance significantly, as then packets should take longer paths in order to be routed around the faults, which in turn increases congestion around the faulty regions. We propose four methods to tolerate faults at the link and switch level by using only the shortest paths as long as such path exists. The unique characteristic among these methods is the toleration of faults while also maintaining the performance of NoCs. To the best of our knowledge, these algorithms are the first approaches to bypassing faults prior to reaching them while avoiding unnecessary misrouting of packets. Current implementations of multicast communication result in a significant performance loss for unicast traffic. This is due to the fact that the routing rules of multicast packets limit the adaptivity of unicast packets. We present an approach in which both unicast and multicast packets can be efficiently routed within the network. While suggesting a more efficient multicast support, the proposed approach does not affect the performance of unicast routing at all. In addition, in order to reduce the overall path length of multicast packets, we present several partitioning methods along with their analytical models for latency measurement. This approach is discussed in the context of 3D mesh networks.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Spatial modeling techniques for mapping and characterization of acid sulfate soils

Acid sulfate (a.s.) soils constitute a major environmental issue. Severe ecological damage results from the considerable amounts of acidity and metals leached by these soils in the recipient watercourses. As even small hot spots may affect large areas of coastal waters, mapping represents a fundamental step in the management and mitigation of a.s. soil environmental risks (i.e. to target strategic areas). Traditional mapping in the field is time-consuming and therefore expensive. Additional more cost-effective techniques have, thus, to be developed in order to narrow down and define in detail the areas of interest. The primary aim of this thesis was to assess different spatial modeling techniques for a.s. soil mapping, and the characterization of soil properties relevant for a.s. soil environmental risk management, using all available data: soil and water samples, as well as datalayers (e.g. geological and geophysical). Different spatial modeling techniques were applied at catchment or regional scale. Two artificial neural networks were assessed on the Sirppujoki River catchment (c. 440 km2) located in southwestern Finland, while fuzzy logic was assessed on several areas along the Finnish coast. Quaternary geology, aerogeophysics and slope data (derived from a digital elevation model) were utilized as evidential datalayers. The methods also required the use of point datasets (i.e. soil profiles corresponding to known a.s. or non-a.s. soil occurrences) for training and/or validation within the modeling processes. Applying these methods, various maps were generated: probability maps for a.s. soil occurrence, as well as predictive maps for different soil properties (sulfur content, organic matter content and critical sulfide depth). The two assessed artificial neural networks (ANNs) demonstrated good classification abilities for a.s. soil probability mapping at catchment scale. Slightly better results were achieved using a Radial Basis Function (RBF) -based ANN than a Radial Basis Functional Link Net (RBFLN) method, narrowing down more accurately the most probable areas for a.s. soil occurrence and defining more properly the least probable areas. The RBF-based ANN also demonstrated promising results for the characterization of different soil properties in the most probable a.s. soil areas at catchment scale. Since a.s. soil areas constitute highly productive lands for agricultural purpose, the combination of a probability map with more specific soil property predictive maps offers a valuable toolset to more precisely target strategic areas for subsequent environmental risk management. Notably, the use of laser scanning (i.e. Light Detection And Ranging, LiDAR) data enabled a more precise definition of a.s. soil probability areas, as well as the soil property modeling classes for sulfur content and the critical sulfide depth. Given suitable training/validation points, ANNs can be trained to yield a more precise modeling of the occurrence of a.s. soils and their properties. By contrast, fuzzy logic represents a simple, fast and objective alternative to carry out preliminary surveys, at catchment or regional scale, in areas offering a limited amount of data. This method enables delimiting and prioritizing the most probable areas for a.s soil occurrence, which can be particularly useful in the field. Being easily transferable from area to area, fuzzy logic modeling can be carried out at regional scale. Mapping at this scale would be extremely time-consuming through manual assessment. The use of spatial modeling techniques enables the creation of valid and comparable maps, which represents an important development within the a.s. soil mapping process. The a.s. soil mapping was also assessed using water chemistry data for 24 different catchments along the Finnish coast (in all, covering c. 21,300 km2) which were mapped with different methods (i.e. conventional mapping, fuzzy logic and an artificial neural network). Two a.s. soil related indicators measured in the river water (sulfate content and sulfate/chloride ratio) were compared to the extent of the most probable areas for a.s. soils in the surveyed catchments. High sulfate contents and sulfate/chloride ratios measured in most of the rivers demonstrated the presence of a.s. soils in the corresponding catchments. The calculated extent of the most probable a.s. soil areas is supported by independent data on water chemistry, suggesting that the a.s. soil probability maps created with different methods are reliable and comparable.