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Information in vague data sources

Milan Mareš, Radko Mesiar (2013)

Kybernetika

This paper deals with the concept of the “size“ or “extent“ of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.

Information Measure for Vague Symbols

Milan Mareš (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.

Information measures and uncertainty of particular symbols

Milan Mareš (2011)

Kybernetika

The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced...

Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.

Information-type divergence when the likelihood ratios are bounded

Andrew Rukhin (1997)

Applicationes Mathematicae

The so-called ϕ-divergence is an important characteristic describing "dissimilarity" of two probability distributions. Many traditional measures of separation used in mathematical statistics and information theory, some of which are mentioned in the note, correspond to particular choices of this divergence. An upper bound on a ϕ-divergence between two probability distributions is derived when the likelihood ratio is bounded. The usefulness of this sharp bound is illustrated by several examples of...

Informazione relativa in uno spazio con legge d'indipendenza qualsiasi.

Carla Poggi (1982)

Stochastica

The notion of relative measure of information in an abstract information space with generalized independence law is studied. The axiomatic definition is given and the form of dependence on the absolute measures is determined, as a solution of a system of functional equations.

Instruments and mutual entropies in quantum information

Alberto Barchielli, Giancarlo Lupieri (2006)

Banach Center Publications

General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize...

Integrated region-based segmentation using color components and texture features with prior shape knowledge

Mehryar Emambakhsh, Hossein Ebrahimnezhad, Mohammad Hossein Sedaaghi (2010)

International Journal of Applied Mathematics and Computer Science

Segmentation is the art of partitioning an image into different regions where each one has some degree of uniformity in its feature space. A number of methods have been proposed and blind segmentation is one of them. It uses intrinsic image features, such as pixel intensity, color components and texture. However, some virtues, like poor contrast, noise and occlusion, can weaken the procedure. To overcome them, prior knowledge of the object of interest has to be incorporated in a top-down procedure...

Interpretability of linguistic variables: a formal account

Ulrich Bodenhofer, Peter Bauer (2005)

Kybernetika

This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what “interpretability” actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, we attempt to approach this problem from a more general...

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