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A Geometry of ApproximationObservations, Noumena and Phenomena

A Geometry of Approximation: Observations, Noumena and Phenomena Chapter 1 Observations, Noumena and Phenomena 1.1 Foreword Despite the name, Rough Set Theory relies on a well defined mathemat- ical ground. This, of course, is what one would like to obtain from any sort of formal and analytic approach to “cognitive” problems. But, sur- prisingly enough, besides the required rigour, Rough Set Theory shares a number of common features with old and new theories belonging to widely different traditions and fields. And “surprise” is not just a rhetoric if one thinks of the peculiar “practical” problem this theory is originated from. At times, this theory appears as a particular case of more comprehensive approaches, while in other cases it appears as a generalization of well established theories. The latter case will be evident in the logico-algebraic analysis of Rough Set Theory (see Part II). The former case may be observed when dealing with the very beginning of Rough Set Theory which is based on the concept of a classification of entities by means of their observed properties. From this point of view Rough Set Theory happens to arise from a particular data analysis approach. Its peculiarity is synthesized as follows: • Data are analysed statically at a given http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Geometry of ApproximationObservations, Noumena and Phenomena

Part of the Trends in Logic Book Series (volume 27)
Editors: Pagliani, Piero; Chakraborty, Mihir
Springer Journals — Jan 1, 2008
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Publisher
Springer Netherlands
Copyright
© Springer Netherlands 2008
ISBN
978-1-4020-8621-2
Pages
3 –42
DOI
10.1007/978-1-4020-8622-9_1
Publisher site
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Abstract

Chapter 1 Observations, Noumena and Phenomena 1.1 Foreword Despite the name, Rough Set Theory relies on a well defined mathemat- ical ground. This, of course, is what one would like to obtain from any sort of formal and analytic approach to “cognitive” problems. But, sur- prisingly enough, besides the required rigour, Rough Set Theory shares a number of common features with old and new theories belonging to widely different traditions and fields. And “surprise” is not just a rhetoric if one thinks of the peculiar “practical” problem this theory is originated from. At times, this theory appears as a particular case of more comprehensive approaches, while in other cases it appears as a generalization of well established theories. The latter case will be evident in the logico-algebraic analysis of Rough Set Theory (see Part II). The former case may be observed when dealing with the very beginning of Rough Set Theory which is based on the concept of a classification of entities by means of their observed properties. From this point of view Rough Set Theory happens to arise from a particular data analysis approach. Its peculiarity is synthesized as follows: • Data are analysed statically at a given

Published: Jan 1, 2008

Keywords: Closure Operator; Complete Lattice; Observable Property; Follow Diagram Commute; Galois Connection

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