Reducing grain damage in naked oat through gentle harvesting

Selostus: Paljasjyväisen kauran hellävarainen sadonkorjuu

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 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.

The intrinsic mechanisms of softwood fiber damage in brown stock fiber line unit operations Lappeenranta 2010

The effects of pulp processing on softwood fiber properties strongly influence the properties of wet and dry paper webs. Pulp strength delivery studies have provided observations that much of the strength potential of long fibered pulp is lost during brown stock fiber line operations where the pulp is merely washed and transferred to the subsequent processing stages. The objective of this work was to study the intrinsic mechanisms which maycause fiber damage in the different unit operations of modern softwood brown stock processing. The work was conducted by studying the effects of industrial machinery on pulp properties with some actions of unit operations simulated in laboratory scale devices under controlled conditions. An optical imaging system was created and used to study the orientation of fibers in the internal flows during pulp fluidization in mixers and the passage of fibers through the screen openings during screening. The qualitative changes in fibers were evaluated with existing and standardized techniques. The results showed that each process stage has its characteristic effects on fiber properties: Pulp washing and mat formation in displacement washers introduced fiber deformations especially if the fibers entering the stage were intact, but it did not decrease the pulp strength properties. However, storage chests and pulp transfer after displacement washers contributed to strength deterioration. Pulp screening proved to be quite gentle, having the potential of slightly evening out fiber deformations from very deformed pulps and vice versa inflicting a marginal increase in the deformation indices if the fibers were previously intact. Pulp mixing in fluidizing industrial mixers did not have detrimental effects on pulp strength and had the potential of slightly evening out the deformations, provided that the intensity of fluidization was high enough to allow fiber orientation with the flow and that the time of mixing was short. The chemical and mechanical actions of oxygen delignification had two distinct effects on pulp properties: chemical treatment clearly reduced pulp strength with and without mechanical treatment, and the mechanical actions of process machinery introduced more conformability to pulp fibers, but did not clearly contribute to a further decrease in pulp strength. The chemical composition of fibers entering the oxygen stage was also found to affect the susceptibility of fibers to damage during oxygen delignification. Fibers with the smallest content of xylan were found to be more prone to irreversibledeformations accompanied with a lower tensile strength of the pulp. Fibers poor in glucomannan exhibited a lower fiber strength while wet after oxygen delignification as compared to the reference pulp. Pulps with the smallest lignin content on the other hand exhibited improved strength properties as compared to the references.