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.

Preservation and Management of Added Value in Networked R&D environment

Tämä tutkielma käsittelee lisäarvon syntymistä, ylläpitämistä ja hallintaa verkostoi-tuneessa tuotekehitysympäristössä. Teemahaastattelu-menetelmää käyttäen, tavoitteena on tunnistaa ja kuvata ne prosessit, käytännöt ja toimintatavat, joissa kohdeyritys on onnistunut ja joissa lisäarvoa on syntynyt. Toinen keskeinen tavoite on löytää ongelmalliset alueet lisäarvon tuottamisessa ja analysoida, miksi nämä alueet ovat ongelmallisia. Käsitteiden arvo, arvoketju ja arvoverkosto, sekä viitekirjallisuuden esimerkkien perusteella muodostetaan teoreettinen viitekehys ja kuvataan niitä hyödyllisiä toimintatapoja ja käytäntöjä, joihin panostamalla lisäarvoa syntyy. Erityisesti informaatioteknologian alalla verkostoituminen ja arvoverkosto ovat yhä merkittävämpiä tuotekehityksen toimintatapoja, mihin horisontaalisen yhteistyön kehittyminen, globalisoituminen ja informaatioteknologian nopea kehitys on johtanut. Keskeisiä tuloksia ovat tarve yhtenäisempään, prosessinomaisempaan toimintatapaan ja liiketoimintaprosessien muokkaamiseen verkostoituneen T&K ympäristön vaatimusten mukaisesti. Myös tarve paremman näkyvyyden luomiseen sekä aktiviteettien hallintaan uudentyyppisen arvoverkoston vaatimusten mukaisesti korostui tuloksissa.

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.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Costs and Benefits of a Shared Digital Long-Term Preservation System

Paper presented at the 40th Annual Conference of LIBER (Ligue des Bibliothèques Européennes de Recherche - Association of European Research Libraries) on July 1st, 2011; with the slides used at the presentation.

Costs and Benefits of a Shared Digital Long-Term Preservation System

This paper describes the cost-benefit analysis of digital long-term preservation (LTP) that was carried out in the context of the Finnish National Digital Library Project (NDL) in 2010. The analysis was based on the assumption that as many as 200 archives, libraries, and museums will share an LTP system. The term ‘system’ shall be understood as encompassing not only information technology, but also human resources, organizational structures, policies and funding mechanisms. The cost analysis shows that an LTP system will incur, over the first 12 years, cumulative costs of €42 million, i.e. an average of €3.5 million per annum. Human resources and investments in information technology are the major cost factors. After the initial stages, the analysis predicts annual costs of circa €4 million. The analysis compared scenarios with and without a shared LTP system. The results indicate that a shared system will have remarkable benefits. At the development and implementation stages, a shared system shows an advantage of €30 million against the alternative scenario consisting of five independent LTP solutions. During the later stages, the advantage is estimated at €10 million per annum. The cumulative cost benefit over the first 12 years would amount to circa €100 million.

Practical Experiences with Ingesting Materials for Long-Term Preservation

The National Library of Finland is responsible for the collection, preservation and accessibility of Finland’s published national heritage, and for its other unique collections. This presentation will give a general overview of the several processes employed in the digitization and handling of electronic legal deposit. METS format has been chosen as the container format for digitized materials, and considerable amount of effort has been put into creating adequate METS profiles. As METS will be heavily relied as a container format, the practicalities are discussed in some depth. Regarding electronic legal deposit, the National Library has concentrated on large-scale web harvesting. Depositing of e-books is being tested with publishers. The future plans concerning digital preservation will be presented, especially the National Digital Library initiative.

Usable Privacy Preservation in Mobile Electronic Personality

Personalised ubiquitous services have rapidly proliferated due technological advancements in sensing, ubiquitous and mobile computing. Evolving societal trends, business and the economic potential of Personal Information (PI) have overlapped the service niches. At the same time, the societal thirst for more personalised services has increased and are met by soliciting deeper and more privacy invasive PI from customers. Consequentially, reinforcing traditional privacy challenges and unearthed new risks that render classical safeguards ine ective. The absence of solutions to criticise personalised ubiquitous services from privacy perspectives, aggravates the situation. This thesis presents a solution permitting users' PI, stored in their mobile terminals to be disclosed to services in privacy preserving manner for personalisation needs. The approach termed, Mobile Electronic Personality Version 2 (ME2.0), is compared to alternative mechanisms. Within ME2.0, PI handling vulnerabilities of ubiquitous services are identi ed and sensitised on their practices and privacy implications. Vulnerability where PI may leak through covert solicits, excessive acquisitions and legitimate data re-purposing to erode users privacy are also considered. In this thesis, the design, components, internal structures, architectures, scenarios and evaluations of ME2.0 are detailed. The design addresses implications and challenges leveraged by mobile terminals. ME2.0 components and internal structures discusses the functions related to how PI pieces are stored and handled by terminals and services. The architecture focusses on di erent components and their exchanges with services. Scenarios where ME2.0 is used are presented from di erent environment views, before evaluating for performance, privacy and usability.

Comprehensive digital preservation repositories: gaps, and what do we mean by “repository” anyway?

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

Open Preservation: Community Approaches to Ensuring Long-Term Access to Digital Collections

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

Audio and Video Repositories at Scale: Indiana University’s Media Digitization and Preservation Initiative

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

Ingest into the Digital Preservation Network: Standard Pipelines

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

Recommendations for Preservation Data Policies

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