AGGREGATION AND COMPLETION OF RANDOM SETS WITH DISTRIBUTIONAL FUZZY MEASURES

1996 ◽  
Vol 04 (04) ◽  
pp. 307-329 ◽  
Author(s):  
CLIFF JOSLYN
Keyword(s):  
Information Theory ◽  
Possibility Theory ◽  
Random Sets ◽  
Random Set ◽  
Topological Structures ◽  
Fuzzy Measures ◽  
New Information ◽  
Set Intersection

The two known information theories, probability and possibility theory, are based on t-conorm decomposable fuzzy measures, so that bijective mappings exist between their set-valued measures and their point-valued distributions. Further, their random set (Dempster-Shafer evidence theoretical) interpretations have simple topological structures, with bijective mappings between the subset focal elements and the point singletons. We introduce the concepts of distributional and aggregable random sets and random set completion, and first use them as a model in which to cast probability and possibility measures and distributions. Then, towards the goal of deriving new forms of information theory, general Sugeno conorm decomposable fuzzy measures and ring-like aggregable random sets with set-intersection structural aggregation are examined, but it is shown that in these two cases no new information theories are forthcoming.

Art as Information Ecology

2021 ◽  
Author(s):  
Jason A. Hoelscher
Keyword(s):  
Information Theory ◽  
Aesthetic Experience ◽  
American Art ◽  
Aesthetic Theory ◽  
Information Ecology ◽  
Robert Morris ◽  
New Information ◽  
Theory Of Information ◽  
Gilbert Simondon

In Art as Information Ecology, Jason A. Hoelscher offers not only an information theory of art but an aesthetic theory of information. Applying close readings of the information theories of Claude Shannon and Gilbert Simondon to 1960s American art, Hoelscher proposes that art is information in its aesthetic or indeterminate mode—information oriented less toward answers and resolvability than toward questions, irresolvability, and sustained difference. These irresolvable differences, Hoelscher demonstrates, fuel the richness of aesthetic experience by which viewers glean new information and insight from each encounter with an artwork. In this way, art constitutes information that remains in formation---a difference that makes a difference that keeps on differencing. Considering the works of Frank Stella, Robert Morris, Adrian Piper, the Drop City commune, Eva Hesse, and others, Hoelscher finds that art exists within an information ecology of complex feedback between artwork and artworld that is driven by the unfolding of difference. By charting how information in its aesthetic mode can exist beyond today's strictly quantifiable and monetizable forms, Hoelscher reconceives our understanding of how artworks work and how information operates.

scholarly journals A New Information Inequality and Its Application in Establishing Relation Among Various f-Divergence Measures

2012 ◽  
Vol 8 (1) ◽  
pp. 17-32 ◽  
Author(s):  
K. Jain ◽  
Ram Saraswat
Keyword(s):  
Information Theory ◽  
Jensen Inequality ◽  
Chi Square ◽  
Information Inequality ◽  
Divergence Measures ◽  
New Information

A New Information Inequality and Its Application in Establishing Relation Among Various f-Divergence MeasuresAn Information inequality by using convexity arguments and Jensen inequality is established in terms of Csiszar f-divergence measures. This inequality is applied in comparing particular divergences which play a fundamental role in Information theory, such as Kullback-Leibler distance, Hellinger discrimination, Chi-square distance, J-divergences and others.

scholarly journals The Relationship between Autopoiesis Theory and Biosemiotics: On Philosophical Suppositions as Bases for a New Information Theory

2011 ◽  
Vol 9 (2) ◽  
pp. 424-433
Author(s):  
Yohei Nishida
Keyword(s):  
Information Theory ◽  
Systems Theory ◽  
Unified Theory ◽  
Methodological Issues ◽  
Basic Principles ◽  
New Information ◽  
Theory Of Information ◽  
The Relationship

This paper discusses methodological issues related to a possible framework for a unified theory of information. We concentrate on the relationship between systems theory and semiotics, or to put it more concretely, the relationship between autopoiesis theory and biosemiotics. These theories give rise to two decisive viewpoints on life that seem poten- tially contradictory and consequently provoke a fruitful controversy, which is conducive for the consideration of philosophical suppositions vital for a new information theory. The following three points are derived in the context of basic principles: epistemology rather than ontology, constructivism rather than metaphysics, meta-theoretical recursiveness rather than linear consistency.

Estimating the reduced moments of a random measure

1996 ◽  
Vol 28 (02) ◽  
pp. 335-336
Author(s):  
Kiên Kiêu ◽  
Marianne Mora
Keyword(s):  
Transformation Group ◽  
Smooth Boundary ◽  
Random Measure ◽  
Random Sets ◽  
Random Set ◽  
Counting Measure ◽  
Geometrical Properties ◽  
Measure Decomposition ◽  
Moment Measures ◽  
Curvature Measures

Random measures are commonly used to describe geometrical properties of random sets. Examples are given by the counting measure associated with a point process, and the curvature measures associated with a random set with a smooth boundary. We consider a random measure with an invariant distribution under the action of a standard transformation group (translatioris, rigid motions, translations along a given direction and so on). In the framework of the theory of invariant measure decomposition, the reduced moments of the random measure are obtained by decomposing the related moment measures.

MULTIVARIATE MODELS AND VARIABILITY INTERVALS: A LOCAL RANDOM SET APPROACH

2011 ◽  
Vol 19 (05) ◽  
pp. 799-823 ◽  
Author(s):  
THOMAS FETZ
Keyword(s):  
Confidence Level ◽  
Structural Mechanics ◽  
Random Sets ◽  
Confidence Limits ◽  
Random Set ◽  
Multivariate Functions ◽  
Multivariate Models ◽  
Multivariate Case ◽  
Fréchet Bounds

This article is devoted to the propagation of families of variability intervals through multivariate functions comprising the semantics of confidence limits. At fixed confidence level, local random sets are defined whose aggregation admits the calculation of upper probabilities of events. In the multivariate case, a number of ways of combination is highlighted to encompass independence and unknown interaction using random set independence and Fréchet bounds. For all cases we derive formulas for the corresponding upper probabilities and elaborate how they relate. An example from structural mechanics is used to exemplify the method.

scholarly journals Stationary countable dense random sets

2000 ◽  
Vol 32 (01) ◽  
pp. 86-100 ◽  
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Probability Theory ◽  
Polish Space ◽  
Measurable Subset ◽  
Locally Compact Group ◽  
Random Sets ◽  
Random Set ◽  
Locally Compact ◽  
Polish Spaces ◽  
Probability Zero ◽  
Group Of Symmetries

We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-stationarity (null-events stay null under the group action). In passing, it is noted that the property of being countable does not correspond to a measurable subset of the space of subsets of an uncountably infinite Polish space.

Law of small numbers as concentration inequalities for sums of independent random setsand random set valued mappings

2012 ◽  
Author(s):  
Vladimir I. Norkin ◽  
Roger J-B Wets
Keyword(s):  
Hilbert Space ◽  
Discrete Distributions ◽  
Random Sets ◽  
Concentration Inequalities ◽  
Random Set ◽  
Infinite Dimensional ◽  
Random Functions ◽  
The Monte Carlo Method ◽  
Exponential Bounds ◽  
Set Valued Mappings

In the paper we study concentration of sample averages (Minkowski's sums) of independent bounded random sets and set valued mappings around their expectations. Sets and mappings are considered in a Hilbert space. Concentration is formulated in the form of exponential bounds on probabilities of normalized large deviations. In a sense, concentration phenomenon reflects the law of small numbers, describing non-asymptotic behavior of the sample averages. We sequentially consider concentration inequalities for bounded random variables, functions, vectors, sets and mappings, deriving next inequalities from preceding cases. Thus we derive concentration inequalities with explicit constants for random sets and mappings from the sharpest available (Talagrand type) inequalities for random functions and vectors. The most explicit inequalities are obtained in case of discrete distributions. The obtained results contribute to substantiation of the Monte Carlo method in infinite dimensional spaces.

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