958 resultados para MIP Mathematical Programming Job Shop Scheduling


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Se estudia la programación de la producción en sistemas flow shop híbrido con tiempos depreparación dependientes de la secuencia de piezas a fabricar. Las piezas pueden pertenecer adiferentes familias y las máquinas requerirán un tiempo de preparación cada vez que se debacambiar de familia. Se han desarrollado procedimientos heurísticos para el caso monocriterio enel que el objetivo buscado en la programación de la producción es la minimización del retrasomedio, equivalente a minimizar la suma de retrasos de las piezas, y para el caso bicriterio en elque se tendrá en cuenta tanto la minimización de una función objetivo formada por la sumaponderada del retraso medio más la suma de los tiempos medios de proceso. Además se hanadaptado los métodos implementados para trabajar bajo la restricción nowait.

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Tutkimuksen päätavoite on arvioida, ovatko neljä ohjelmistovaihtoehtoa riittäviä tuotannon aikataulutuksen työkaluja ja mikä työkaluista sopii toimeksiantajayritykselle. Alatavoitteena on kuvata tuotannon aikataulutuksen nyky- ja tahtotila prosessimallinnuksen avulla, selvittää työkalun käyttäjätarpeet ja määritellä priorisoidut valintakriteerit työkalulle.Tutkimuksen teoriaosuudessa tutkitaan tuotannon aikataulutuksen logiikkaa ja haasteita. Työssä tarkastellaan aikataulutusohjelmiston valintaa rinnakkain prosessinmallinnuksen kanssa. Aikataulutusohjelmistovaihtoehdot ja metodit käyttäjätarpeiden selvittämiseksi käydään läpi. Empiriaosuudessa selvitetään tutkimuksen suhde toimeksiantajayrityksen strategiaan. Käyttäjätarpeet selvitetään haastattelujen avulla jaanalysoidaan QFD matriisin avulla. Toimeksiantajayrityksen tuotannon aikataulutuksen nyky- ja tahtotilaprosessit mallinnetaan, jotta ohjelmistojen sopivuutta, aikataulutusprosessia tukevana työkaluna voidaan arvioida.Tutkimustuloksena ovatpriorisoidut valintakriteerit aikataulutustyökalulle eli käyttäjätarpeista johdetut tärkeimmät toiminnalliset ominaisuudet, järjestelmätoimittaja-arvio sekä suositukset jatkotoimenpiteistä ja lisätutkimuksesta.

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Tämän työn tarkoituksena on käytännöllisen suositusjärjestelmäratkaisun kehittäminen verkkokauppaympäristöön olemassaolevaa teoriatietoa käyttäen. Työn ensimmäisessä osiossa tarkastellaan ensin tapoja lähdetiedon keräämiseksi järjestelmää varten. Tämän jälkeen käydään läpi eri menetelmiä suosituksen toteuttamiseksi. Lisäksi tutustutaan yleisiin ongelmiin eri menetelmien kanssa. Seuraavaksi tutkitaan miten järjestelmän käyttämään suositustietoa voidaan ryhmitellä. Tämänjälkeen arvioidaan esitettyjä menetelmiä yleisesti tunnettujen kriteerien perusteella. Suositusjärjestelmän toteutustyö on kuvattuna työn toisessa osiossa. Toteutettu ohjelmisto on asennettu kahteen erilliseen toimintaympäristöön.

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The Thesis gives a decision support framework that has significant impact on the economic performance and viability of a hydropower company. The studyaddresses the short-term hydropower planning problem in the Nordic deregulated electricity market. The basics of the Nordic electricity market, trading mechanisms, hydropower system characteristics and production planning are presented in the Thesis. The related modelling theory and optimization methods are covered aswell. The Thesis provides a mixed integer linear programming model applied in asuccessive linearization method for optimal bidding and scheduling decisions inthe hydropower system operation within short-term horizon. A scenario based deterministic approach is exploited for modelling uncertainty in market price and inflow. The Thesis proposes a calibration framework to examine the physical accuracy and economic optimality of the decisions suggested by the model. A calibration example is provided with data from a real hydropower system using a commercial modelling application with the mixed integer linear programming solver CPLEX.

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This paper analyses the effect of job accessibility by public and private transport on labour market outcomes in the metropolitan area of Barcelona. Beyond employment, we consider the effect of job accessibility on job-education mismatch, which represents a relevant aspect of job quality. We adopt a recursive system of equations that models car availability, employment and mismatch. Public transport accessibility appears as an exogenous variable in the three equations. Even though it may reflect endogenous residential sorting, falsification proofs suggest that the estimated effect of public transport accessibility is not entirely driven by the endogenous nature of residential decisions.

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This paper presents a programming environment for supporting learning in STEM, particularly mobile robotic learning. It was designed to maintain progressive learning for people with and without previous knowledge of programming and/or robotics. The environment was multi platform and built with open source tools. Perception, mobility, communication, navigation and collaborative behaviour functionalities can be programmed for different mobile robots. A learner is able to programme robots using different programming languages and editor interfaces: graphic programming interface (basic level), XML-based meta language (intermediate level) or ANSI C language (advanced level). The environment supports programme translation transparently into different languages for learners or explicitly on learners’ demand. Learners can access proposed challenges and learning interfaces by examples. The environment was designed to allow characteristics such as extensibility, adaptive interfaces, persistence and low software/hardware coupling. Functionality tests were performed to prove programming environment specifications. UV BOT mobile robots were used in these tests

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Teollisuuden tuotannon eri prosessien optimointi on hyvin ajankohtainen aihe. Monet ohjausjärjestelmät ovat ajalta, jolloin tietokoneiden laskentateho oli hyvin vaatimaton nykyisiin verrattuna. Työssä esitetään tuotantoprosessi, joka sisältää teräksen leikkaussuunnitelman muodostamisongelman. Valuprosessi on yksi teräksen valmistuksen välivaiheita. Siinä sopivaan laatuun saatettu sula teräs valetaan linjastoon, jossa se jähmettyy ja leikataan aihioiksi. Myöhemmissä vaiheissa teräsaihioista muokataan pienempiä kokonaisuuksia, tehtaan lopputuotteita. Jatkuvavaletut aihiot voidaan leikata tilauskannasta riippuen monella eri tavalla. Tätä varten tarvitaan leikkaussuunnitelma, jonka muodostamiseksi on ratkaistava sekalukuoptimointiongelma. Sekalukuoptimointiongelmat ovat optimoinnin haastavin muoto. Niitä on tutkittu yksinkertaisempiin optimointiongelmiin nähden vähän. Nykyisten tietokoneiden laskentateho on kuitenkin mahdollistanut raskaampien ja monimutkaisempien optimointialgoritmien käytön ja kehittämisen. Työssä on käytetty ja esitetty eräs stokastisen optimoinnin menetelmä, differentiaalievoluutioalgoritmi. Tässä työssä esitetään teräksen leikkausoptimointialgoritmi. Kehitetty optimointimenetelmä toimii dynaamisesti tehdasympäristössä käyttäjien määrittelemien parametrien mukaisesti. Työ on osa Syncron Tech Oy:n Ovako Bar Oy Ab:lle toimittamaa ohjausjärjestelmää.

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Diplomityön tavoitteena oli tehostaa venttiilipesien koneistuksessa käytettävän monitoimipystysorvin NC - ohjelmointia CAM - ohjelman käyttöönotolla. Tutkimus on osa laajempaa kokonaisuutta liittyen koneistusalihankinnan kehittämiseen ja yrityksen kilpailukyvyn ylläpitoon ja parantamiseen liiketoiminta-alueella, jolla on tällä hetkellä hyvät kasvunäkymät. Tavoite rajattiin yritykseen jo aiemmin hankitun WinCAM - ohjelman päivittämiseen ja hyödyntämiseen monitoimipystysorvin NC - ohjelmoinnissa. Tutkimuksen käytännön tavoitteena oli selvittää CAM - ohjelmoinnin käyttömahdollisuudet, sekä luoda CAM - ohjelmistoon pohjautuva, räätälöity NC - ohjelmointikonsepti pilottikohteeseen. Tutkimuksen kokeellisen osuuden muodostivat tällöin nykyisen tuotannon ongelmakohtien löytäminen, koneen ohjelmointitarpeiden kartoitus,sekä menetelmäkehitys. Tutkimuksen päämääränä oli tuotannon tasolla käytettävä järjestelmä, jolla koneen ohjelmointi olisi mahdollista myös vähemmällä konekohtaisella kokemuksella. Nykyisen toimintatavan ongelmina olivat yhtenäisen NC - ohjelmointikäytännön puute, niin valmiiden ohjelmien käytössä kuin uusienkin ohjelmien tekemisessä. Tähän olivat syynä NC - ohjauksen heikko käytettävyys erityisesti sorvauksen osalta. Nämä tekijät yhdistettynä monitoimityöstökoneessa tarvittavaan koordinaatiston hallintaan vaikeuttivat ohjelmointia. Työntekijäkohtaiset erot NC - ohjelmien käytössä, sekä laadultaan vaihtelevat valuaihiot aiheuttivat tuotannon läpäisyaikaan merkittävää vaihtelua. Siten myös koneen kuormituksen säätely oli vaikeaa. Uuden ohjelmointikonseptin toteutuksessa pidettiin etusijalla hyvää käytettävyyttä, sekä uuden menetelmän aukotonta liittymistä olemassa oleviin tuotantojärjestelmiin. Ohjelmointikonseptin toteutuksessa, osaperheestä haettiin selkeästi parametroitaviksi soveltuvat työvaiheet, jotka voitiin hallita yleiskäyttöisillä aliohjelmilla. Tuotteiden muidengeometrioiden hallintaan laadittiin geometriakirjasto, jota voitiin käyttää tavanomaisen graafisen ohjelmoinnin pohjana. Vanhaa toimintatapaa ja diplomityön aikana kehitettyä CAM - ohjelmointijärjestelmää vertailtiin perustuen NC - ohjelmien tehokkuuteen, jota tarkasteltiin saman työvaiheen työstöaikaan perustuen. Tämän lisäksi tärkeän tuloksen muodostavat myös kvalitatiivisetseikat, jotka liittyvät ohjelmointiympäristön käytettävyyteen. CAM - ohjelmoinnin kehittäminen ja käyttöönotto pilottikohteessa sujui pääosin hyvin ja laaditunsuunnitelman mukaisesti. Aiemmin hankalasti ohjelmoitavat työvaiheet, kuten erilaisten laippatasopintojen ja reikäpiirien ohjelmointi muutettiin makrokäyttöön soveltuviksi. Sorvauksessa ongelmia aiheuttaneen tiivistelilan koneistukseen sovellettiin graafista ohjelmointia. Koko tuotannon mittakaavassa NC - ohjelmoinninosuus oli kuitenkin vähäinen, mistä johtuen koneen tuottavuuteen ei tutkimuksenajanjaksolla voitu vaikuttaa. Sen sijaan tuotannon sujuvuuteen oleellisesti vaikuttavaa työtekijöiden 'hiljaisen tiedon' määrää voitiin vähentää vakioimalla ohjelmointia ja siirtämällä tehokkaiksi havaitut menetelmät ohjelmointijärjestelmään.

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Insults during the fetal period predispose the offspring to systemic cardiovascular disease, but little is known about the pulmonary circulation and the underlying mechanisms. Maternal undernutrition during pregnancy may represent a model to investigate underlying mechanisms, because it is associated with systemic vascular dysfunction in the offspring in animals and humans. In rats, restrictive diet during pregnancy (RDP) increases oxidative stress in the placenta. Oxygen species are known to induce epigenetic alterations and may cross the placental barrier. We hypothesized that RDP in mice induces pulmonary vascular dysfunction in the offspring that is related to an epigenetic mechanism. To test this hypothesis, we assessed pulmonary vascular function and lung DNA methylation in offspring of RDP and in control mice at the end of a 2-wk exposure to hypoxia. We found that endothelium-dependent pulmonary artery vasodilation in vitro was impaired and hypoxia-induced pulmonary hypertension and right ventricular hypertrophy in vivo were exaggerated in offspring of RDP. This pulmonary vascular dysfunction was associated with altered lung DNA methylation. Administration of the histone deacetylase inhibitors butyrate and trichostatin A to offspring of RDP normalized pulmonary DNA methylation and vascular function. Finally, administration of the nitroxide Tempol to the mother during RDP prevented vascular dysfunction and dysmethylation in the offspring. These findings demonstrate that in mice undernutrition during gestation induces pulmonary vascular dysfunction in the offspring by an epigenetic mechanism. A similar mechanism may be involved in the fetal programming of vascular dysfunction in humans.

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This paper presents a research concerning the conversion of non-accessible web pages containing mathematical formulae into accessible versions through an OCR (Optical Character Recognition) tool. The objective of this research is twofold. First, to establish criteria for evaluating the potential accessibility of mathematical web sites, i.e. the feasibility of converting non-accessible (non-MathML) math sites into accessible ones (Math-ML). Second, to propose a data model and a mechanism to publish evaluation results, making them available to the educational community who may use them as a quality measurement for selecting learning material.Results show that the conversion using OCR tools is not viable for math web pages mainly due to two reasons: many of these pages are designed to be interactive, making difficult, if not almost impossible, a correct conversion; formula (either images or text) have been written without taking into account standards of math writing, as a consequence OCR tools do not properly recognize math symbols and expressions. In spite of these results, we think the proposed methodology to create and publish evaluation reports may be rather useful in other accessibility assessment scenarios.

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Tämä kandidaatintyö tutkii tietotekniikan perusopetuksessa keskeisen aiheen,ohjelmoinnin, alkeisopetusta ja siihen liittyviä ongelmia. Työssä perehdytään ohjelmoinnin perusopetusmenetelmiin ja opetuksen lähestymistapoihin, sekä ratkaisuihin, joilla opetusta voidaan tehostaa. Näitä ratkaisuja työssä ovat mm. ohjelmointikielen valinta, käytettävän kehitysympäristön löytäminen sekä kurssia tukevien opetusapuvälineiden etsiminen. Lisäksi kurssin läpivientiin liittyvien toimintojen, kuten harjoitusten ja mahdollisten viikkotehtävien valinta kuuluu osaksitätä työtä. Työ itsessään lähestyy aihetta tutkimalla Pythonin soveltuvuutta ohjelmoinnin alkeisopetukseen mm. vertailemalla sitä muihin olemassa oleviin yleisiin opetuskieliin, kuten C, C++ tai Java. Se tarkastelee kielen hyviä ja huonoja puolia, sekä tutkii, voidaanko Pythonia hyödyntää luontevasti pääasiallisena opetuskielenä. Lisäksi työ perehtyy siihen, mitä kaikkea kurssilla tulisi opettaa, sekä siihen, kuinka kurssin läpivienti olisi tehokkainta toteuttaa ja minkälaiset tekniset puitteet kurssin toteuttamista varten olisi järkevää valita.

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The object of this project is to schedule a ctitious European basketball competition with many teams situated a long distances. The schedule must be fair, feasible and economical, which means that the total distance trav- eled by every team must be the minimal possible. First, we de ne the sport competition terminology and study di erent competition systems, focusing on the NBA and the Euroleague systems. Then we de ne concepts of graph theory and spherical distance that will be needed. Next we propose a com- petition system, explaining where will be allocated the teams and how will be the scheduling. Then there is a description of the programs that have been implemented, and, nally, the complete schedule is displayed, and some possible improvements are mentioned.

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The past few decades have seen a considerable increase in the number of parallel and distributed systems. With the development of more complex applications, the need for more powerful systems has emerged and various parallel and distributed environments have been designed and implemented. Each of the environments, including hardware and software, has unique strengths and weaknesses. There is no single parallel environment that can be identified as the best environment for all applications with respect to hardware and software properties. The main goal of this thesis is to provide a novel way of performing data-parallel computation in parallel and distributed environments by utilizing the best characteristics of difference aspects of parallel computing. For the purpose of this thesis, three aspects of parallel computing were identified and studied. First, three parallel environments (shared memory, distributed memory, and a network of workstations) are evaluated to quantify theirsuitability for different parallel applications. Due to the parallel and distributed nature of the environments, networks connecting the processors in these environments were investigated with respect to their performance characteristics. Second, scheduling algorithms are studied in order to make them more efficient and effective. A concept of application-specific information scheduling is introduced. The application- specific information is data about the workload extractedfrom an application, which is provided to a scheduling algorithm. Three scheduling algorithms are enhanced to utilize the application-specific information to further refine their scheduling properties. A more accurate description of the workload is especially important in cases where the workunits are heterogeneous and the parallel environment is heterogeneous and/or non-dedicated. The results obtained show that the additional information regarding the workload has a positive impact on the performance of applications. Third, a programming paradigm for networks of symmetric multiprocessor (SMP) workstations is introduced. The MPIT programming paradigm incorporates the Message Passing Interface (MPI) with threads to provide a methodology to write parallel applications that efficiently utilize the available resources and minimize the overhead. The MPIT allows for communication and computation to overlap by deploying a dedicated thread for communication. Furthermore, the programming paradigm implements an application-specific scheduling algorithm. The scheduling algorithm is executed by the communication thread. Thus, the scheduling does not affect the execution of the parallel application. Performance results achieved from the MPIT show that considerable improvements over conventional MPI applications are achieved.

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The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

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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.