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.

The Finnish Online University of Applied Sciences - from National to International

Julkaistu CD-ROM-levyllä

Tiedon jakaminen kolmen ammattikorkeakoulun strategisessa liittoumassa. Case: Federation of Universities of Applied Sciences.

Ammattikorkeakoulut ovat suurten rakenteellisten ja rahoituksellisten muutosten edessä. Rahoitus tulee jatkossa tutkintojen määrään painottuen nykyisen opiskelija-määrän sijaan ja tämä pakottaa ammattikorkeakoulut etsimään keinoja toiminnan tehostamiseksi, joista korkeakoulujen muodostamat liittoumat ovat yksi väline. Tämän tutkimuksen aiheena on tiedon jakaminen kolmen ammattikorkeakoulun muo-dostamassa strategisessa liittoumassa. Tutkimus toteutettiin kvantitatiivisena tutkimuksena, jonka empiirinen osuus toteutet-tiin kyselylomakkeella Hämeen, Lahden ja Laurea-ammattikorkeakoulujen toimijoilta keräten. Vastauksia saatiin 79, vastausprosentin ollessa 62,2 %. Tutkimustulosten perusteella FUASin johdon toimilla, organisaation rakenteella, organisaation kulttuu-rilla ja työilmapiirillä on positiivinen vaikutus tiedon jakamiseen. Lisäksi toimijoiden välinen luottamus ja avoimuus sekä motivaatio parantavat tiedon jakamista FUAS-ammattikorkeakoulujen välillä. Tiedon jakamisesta palkitseminen ja oman edun ta-voittelu eivät vaikuttaneet tilastollisesti merkittävästi FUASissa tapahtuvaan tiedon jakamiseen.

Open Repository Theseus – Success Story of 24 Finnish Universities of Applied Sciences

Poster at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Thick XML client and technology of its construction

Nykyään kolmeen kerrokseen perustuvat client-server –sovellukset ovat suuri kinnostuskohde sekä niiden kehittäjille etta käyttäjille. Tietotekniikan nopean kehityksen ansiosta näillä sovelluksilla on monipuolinen käyttö teollisuuden eri alueilla. Tällä hetkellä on olemassa paljon työkaluja client-server –sovellusten kehittämiseen, jotka myös tyydyttävät asiakkaiden asettamia vaatimuksia. Nämä työkalut eivät kuitenkaan mahdollista joustavaa toimintaa graafisen käyttöliittyman kanssa. Tämä diplomityö käsittelee client-server –sovellusten kehittamistä XML –kielen avulla. Tämä lähestymistapa mahdollistaa client-server –sovellusten rakentamista niin, että niiden graafinen käyttöliittymä ja ulkonäkö olisivat helposti muokattavissa ilman ohjelman ytimen uudelleenkääntämistä. Diplomityö koostuu kahdesta ostasta: teoreettisesta ja käytännöllisestä. Teoreettinen osa antaa yleisen tiedon client-server –arkkitehtuurista ja kuvailee ohjelmistotekniikan pääkohdat. Käytannöllinen osa esittää tulokset, client-server –sovellusten kehittämisteknologian kehittämislähestymistavan XML: ää käyttäen ja tuloksiin johtavat usecase– ja sekvenssidiagrammit. Käytännöllinen osa myos sisältää esimerkit toteutetuista XML-struktuureista, jotka kuvaavat client –sovellusten kuvaruutukaavakkeiden esintymisen ja serverikyselykaaviot.

The grammar of psychosis

This thesis is concerned with the philosophical grammar of certain psychiatric concepts, which play a central role in delineating the field of psychiatric work. The concepts studied are ‘psychosis’, ‘delusion’, ‘person’, ‘understanding’ and ‘incomprehensibility’. The purpose of this conceptual analysis is to provide a more perspicuous view of the logic of these concepts, how psychiatric work is constituted in relation to them, and what this tells us about the relationships between the conceptual and the empirical in psychiatric concepts. The method used in the thesis is indebted primarily to Ludwig Wittgenstein’s conception of philosophy, where we are urged to look at language uses in relation to practices in order to obtain a clearer overview of practices of interest; this will enable us to resolve the conceptual problems related to these practices. This questioning takes as its starting point the concept of psychosis, a central psychiatric concept during the twentieth century. The conceptual analysis of ‘psychosis’ shows that the concept is logically dependent on the concepts of ‘understanding’ and ‘person’. Following the lead found in this analysis, the logic of person-concepts in psychiatric discourse is analysed by a detailed textual analysis of a psychiatric journal article. The main finding is the ambiguous uses of ‘person’, enabling a specifically psychiatric form of concern in human affairs. The grammar of ‘understanding’ is then tackled from the opposite end, by exploring the logic of the concept of ‘incomprehensibility’. First, by studying the DSM-IV definition of delusion it is shown that its ambiguities boil down to the question of whether psychiatric practice is better accounted for in terms of the grammar of ‘incorrectness’ or ‘incomprehensibility’. Second, the grammar of ‘incomprehensibility’ is further focused on by introducing the distinction between positive and negative conceptions of ‘incomprehensibility’. The main finding is that this distinction has wide-ranging implications for our understanding of psychiatric concepts. Finally, some of the findings gained in these studies are ‘put into practice’ in studying the more practical question of the conceptual and ethical problems associated with the concept of ‘prodromal symptom of schizophrenia’ and the agenda of early detection and intervention in schizophrenia more generally.

Consistency of UML based designs using ontology reasoners

Software plays an important role in our society and economy. Software development is an intricate process, and it comprises many different tasks: gathering requirements, designing new solutions that fulfill these requirements, as well as implementing these designs using a programming language into a working system. As a consequence, the development of high quality software is a core problem in software engineering. This thesis focuses on the validation of software designs. The issue of the analysis of designs is of great importance, since errors originating from designs may appear in the final system. It is considered economical to rectify the problems as early in the software development process as possible. Practitioners often create and visualize designs using modeling languages, one of the more popular being the Uni ed Modeling Language (UML). The analysis of the designs can be done manually, but in case of large systems, the need of mechanisms that automatically analyze these designs arises. In this thesis, we propose an automatic approach to analyze UML based designs using logic reasoners. This approach firstly proposes the translations of the UML based designs into a language understandable by reasoners in the form of logic facts, and secondly shows how to use the logic reasoners to infer the logical consequences of these logic facts. We have implemented the proposed translations in the form of a tool that can be used with any standard compliant UML modeling tool. Moreover, we authenticate the proposed approach by automatically validating hundreds of UML based designs that consist of thousands of model elements available in an online model repository. The proposed approach is limited in scope, but is fully automatic and does not require any expertise of logic languages from the user. We exemplify the proposed approach with two applications, which include the validation of domain specific languages and the validation of web service interfaces.

Convergence and divergence in global economy and social development : global perspectives on the contents of economic and soical development policy and its effects on rich and poor countries

The study of convergence and divergence in global economy and social development utilises comparative indicators to investigate the contents of economic and social development policy and their effects on the global samples that represent the rich industrial, semi-industrial and the poor developing nations. The study searchesfor answers to questions such as "what are the objectives of economic growth policies in globalisation under the imperatives of convergence and divergence, and how do these affect human well-being in consideration to the objectives of social policy in various nations?" The empirical verification of data utilises the concepts of the `logic of industrialism´ for comparative analysis that focuses mainly on identifying the levels of well-being in world nations after the Second World War. The perspectives of convergence and divergence in global economy and social development critically examine the stages of early development processes in global economy, distinguish the differences between economy and social development, illustrate the contents of economic and social development policies, their effects on rich and poor countries, and the nature of convergence and divergence in propelling economic growth and unequal social development in world nations. The measurement of convergence and divergence in global economy and social development utilised both economic and social data that were combined into an index that measures the precise levels of the effects of economic and social development policies on human well-being in the rich and poor nations. The task of finding policy solutions to resolve the controversies are reviewed through empirical investigations and the analyses of trends indicated within economic and social indicators and data. These revealed how the adoption of social policy measures in translating the gains from economic growth, towards promoting education, public health, and equity, generate social progress and longer life expectancy, higher economic growth, and sustain more stable macro economy for the nations. Social policy is concerned with the translation of benefits from objectives of global economic growth policies, to objectives of social development policy in nation states. Social policy, therefore, represents an open door whereby benefits of economic growth policies are linked with the broader objectives of social development policy, thereby enhancing the possibility of extending benefits from economic growth to all human being in every nation.