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172
VARIABLE SETS OVER AN ALGEBRA OF LIFETIMES: A CONTRIBUTION OF LATTICE THEORY TO THE STUDY OF COMPUTATIONAL TOPOLOGY
"... Abstract. A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines the structure of data through topology. The basic ..."
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Abstract. A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines the structure of data through topology. The basic
IFSAEUSFLAT 2009 Fuzzy concept lattice is made by protofuzzy concepts.
"... Abstract — An Lfuzzy context is a triple consisting of a set of objects, a set of attributes and an Lfuzzy binary relation between them. An lcut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater or equa ..."
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Abstract — An Lfuzzy context is a triple consisting of a set of objects, a set of attributes and an Lfuzzy binary relation between them. An lcut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater
A NOVEL APPROACH: FUZZY TOPOLOGICAL CONCEPTS
"... In this present paper, we study some fuzzy topological concepts and introduce fuzzy open, fuzzy semiopen sets and related notions in a different manner by assigning a topological structure to the universe set.X We construct a fuzzy topology and a fuzzy semi topology over.X Also we investigate some ..."
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In this present paper, we study some fuzzy topological concepts and introduce fuzzy open, fuzzy semiopen sets and related notions in a different manner by assigning a topological structure to the universe set.X We construct a fuzzy topology and a fuzzy semi topology over.X Also we investigate some
CATEGORICALLYALGEBRAIC TOPOLOGY AND ITS APPLICATIONS
, 2015
"... Abstract. This paper introduces a new approach to topology, based on category theory and universal algebra, and called categoricallyalgebraic (catalg) topology. It incorporates the most important settings of latticevalued topology, including poslat topology of S. E. Rodabaugh, (L, M )fuzzy topol ..."
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topology of T. Kubiak and A.Šostak, and M fuzzy topology on Lfuzzy sets of C. Guido. Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of topological system of S. Vickers (and its numerous many
A Decision Procedure for Rough Set Equalities
"... We use the notion of the rough set diagram introduced by Wasilewska and Vigneron [8] to present a general decision procedure for validity of equations in rough boolean algebra. First, we establish equivalence of validity in rough boolean algebra to validity in so called simple rough boolean algebra. ..."
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that there are 2 S (n) \Gamma 1 topologically different simplified rough diagrams over n sets, where S (n) is the number of different simple rough diagram configurations, which is equal to the number of essential cases of models of simple rough boolean algebra for n set variables (S (1) = 3, S (2) = 15, S (3
Rough Sets, Kernel Set and SpatioTemporal Outlier Detection
"... Abstract Nowadays, the high availability of data gathered from wireless sensor networks and telecommunication systems, has drawn the attention of researchers on the problem of extracting knowledge from spatiotemporal data. Detecting outliers which are grossly different from or inconsistent with th ..."
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is able to describe the original dataset both in terms of data structure and of obtained results. Experimental results on real world datasets demonstrate the superiority of ROSE, both in terms of some quantitative indices and outliers detected, over those obtained by various rough fuzzy clustering
Rough set, kernel set and spatiotemporal outlier detection
 IEEE Trans. Knowledge and Data Engineering
"... Abstract—Nowadays, the high availability of data gathered from wireless sensor networks and telecommunication systems has drawn the attention of researchers on the problem of extracting knowledge from spatiotemporal data. Detecting outliers which are grossly different from or inconsistent with the r ..."
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is able to describe the original data set both in terms of data structure and of obtained results. Experimental results on realworld data sets demonstrate the superiority of ROSE, both in terms of some quantitative indices and outliers detected, over those obtained by various rough fuzzy clustering
Fuzzy Rough Approach To Handling Imprecision In Semantic Web Ontologies
"... Abstract Mining and discovering ontological structures plays a major role in the Semantic Web. As long as many domains in the Semantic Web involve different sorts of imprecision, ontologies must be expressive enough to deal with imperfect information. Most of approaches to manage imprecision in ont ..."
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in ontologies deal either with probability or employ Fuzzy Set and Fuzzy Logic techniques for representing ontologies for intrinsically vague domains. The aim of this paper is to show how they can be complemented by Rough Set methods to capture another type of imprecision caused by approximation spaces
Roughness Method to Estimate Fractal Dimension
, 2009
"... A method based on the pattern roughness was introduced for determination of the fractal dimension and tested for fractals like the Sierpiński carpet, the Sierpiński triangle, standard Cantor set, the Menger sponge and the Sierpiński tetrahedron. It was tested for nonfractal pattern like two and fo ..."
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for patterns being composed of the hierarchy of structures having the same topological dimension as the space embedding them. It is applicable to “fuzzy ” patterns with overlapping structures, where other methods are useless. It is designed for pixelized structures, the latter structures resulting as typical
Computational Analysis of Canny & Binary Fuzzy Rough Set Model Based on Triangle Modulus Edge Detectors
"... Abstract—In this work we present a formal comparative over the computational complexity of two edge detectors, in one hand the Canny Edges Detector and on the other an edges detector based on Rough Sets Theory which has been proved as very efficient from the results point of view, so we are now inte ..."
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Abstract—In this work we present a formal comparative over the computational complexity of two edge detectors, in one hand the Canny Edges Detector and on the other an edges detector based on Rough Sets Theory which has been proved as very efficient from the results point of view, so we are now
Results 11  20
of
172