Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

This paper focuses on the issue of how generalizations of continuous and left-continuous t-norms over linearly ordered sets should be from a logical point of view. Taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation, we advocate linearly ordered BL-algebras and MTL-algebras as adequate generalizations of continuous and left-continuous t-norms respectively. In both cases, the underlying basic structure is that of linearly ordered residuated lattices. Although the residuation property is equivalent to left-continuity in t-norms, continuous t-norms have received much more attention due to their simpler structure. We review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to BL-chains. In particular we show the good behavior of BL-algebras over a finite or complete chain, and discuss the partial knowledge of rational BL-chains. Then we move to the general non-continuous case corresponding to left-continuous t-norms and MTL-chains. The unsolved problem of describing the structure of left-continuous t-norms is presented together with a fistful of construction-decomposition techniques that apply to some distinguished families of t-norms and, finally, we discuss the situation in the general study of MTL-chains as a natural generalization of left-continuous t-norms

Contributions to unsupervised and supervised learning with applications in digital image processing

311 p. : il.[EN]This Thesis covers a broad period of research activities with a commonthread: learning processes and its application to image processing. The twomain categories of learning algorithms, supervised and unsupervised, have beentouched across these years. The main body of initial works was devoted tounsupervised learning neural architectures, specially the Self Organizing Map.Our aim was to study its convergence properties from empirical and analyticalviewpoints.From the digital image processing point of view, we have focused on twobasic problems: Color Quantization and filter design. Both problems have beenaddressed from the context of Vector Quantization performed by CompetitiveNeural Networks. Processing of non-stationary data is an interesting paradigmthat has not been explored with Competitive Neural Networks. We have statesthe problem of Non-stationary Clustering and related Adaptive Vector Quantizationin the context of image sequence processing, where we naturally havea Frame Based Adaptive Vector Quantization. This approach deals with theproblem as a sequence of stationary almost-independent Clustering problems.We have also developed some new computational algorithms for Vector Quantizationdesign.The works on supervised learning have been sparsely distributed in time anddirection. First we worked on the use of Self Organizing Map for the independentmodeling of skin and no-skin color distributions for color based face localization. Second, we have collaborated in the realization of a supervised learning systemfor tissue segmentation in Magnetic Resonance Imaging data. Third, we haveworked on the development, implementation and experimentation with HighOrder Boltzmann Machines, which are a very different learning architecture.Finally, we have been working on the application of Sparse Bayesian Learningto a new kind of classification systems based on Dendritic Computing. This lastresearch line is an open research track at the time of writing this Thesis

The Translocal Event and the Polyrhythmic Diagram

This thesis identifies and analyses the key creative protocols in translocal performance practice, and ends with suggestions for new forms of transversal live and mediated performance practice, informed by theory. It argues that ontologies of emergence in dynamic systems nourish contemporary practice in the digital arts. Feedback in self-organised, recursive systems and organisms elicit change, and change transforms. The arguments trace concepts from chaos and complexity theory to virtual multiplicity, relationality, intuition and individuation (in the work of Bergson, Deleuze, Guattari, Simondon, Massumi, and other process theorists). It then examines the intersection of methodologies in philosophy, science and art and the radical contingencies implicit in the technicity of real-time, collaborative composition. Simultaneous forces or tendencies such as perception/memory, content/ expression and instinct/intellect produce composites (experience, meaning, and intuition- respectively) that affect the sensation of interplay. The translocal event is itself a diagram - an interstice between the forces of the local and the global, between the tendencies of the individual and the collective. The translocal is a point of reference for exploring the distribution of affect, parameters of control and emergent aesthetics. Translocal interplay, enabled by digital technologies and network protocols, is ontogenetic and autopoietic; diagrammatic and synaesthetic; intuitive and transductive. KeyWorx is a software application developed for realtime, distributed, multimodal media processing. As a technological tool created by artists, KeyWorx supports this intuitive type of creative experience: a real-time, translocal “jamming” that transduces the lived experience of a “biogram,” a synaesthetic hinge-dimension. The emerging aesthetics are processual – intuitive, diagrammatic and transversal