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A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)October 2008
Publisher:
  • Springer Publishing Company, Incorporated
ISBN:978-1-4020-8621-2
Published:24 October 2008
Pages:
706
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Abstract

'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost. Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields. 'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.

Cited By

  1. Diker M (2015). A category approach to relation preserving functions in rough set theory, International Journal of Approximate Reasoning, 56:PA, (71-86), Online publication date: 1-Jan-2015.
  2. Tan A, Li J and Lin G (2015). Connections between covering-based rough sets and concept lattices, International Journal of Approximate Reasoning, 56:PA, (43-58), Online publication date: 1-Jan-2015.
  3. Bianchi M (2014). A temporal semantics for Nilpotent Minimum logic, International Journal of Approximate Reasoning, 55:1, (391-401), Online publication date: 1-Jan-2014.
  4. Restrepo M, Cornelis C and Gómez J (2014). Duality, conjugacy and adjointness of approximation operators in covering-based rough sets, International Journal of Approximate Reasoning, 55:1, (469-485), Online publication date: 1-Jan-2014.
  5. Chakraborty M (2014). Membership function based rough set, International Journal of Approximate Reasoning, 55:1, (402-411), Online publication date: 1-Jan-2014.
  6. Csajbók Z Approximation of sets based on partial covering Transactions on Rough Sets XVI, (144-220)
  7. She Y and He X (2012). Uncertainty measures for rough formulae in rough logic, Computers & Mathematics with Applications, 63:1, (83-93), Online publication date: 1-Jan-2012.
  8. Mani A Dialectics of counting and the mathematics of vagueness Transactions on Rough Sets XV, (122-180)
  9. She Y, He X and Wang G (2011). Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic, Fundamenta Informaticae, 107:1, (67-83), Online publication date: 1-Jan-2011.
  10. She Y, He X and Wang G (2011). Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic, Fundamenta Informaticae, 111:2, (223-239), Online publication date: 1-Apr-2011.
  11. Bhowmik S IC-topological spaces and applications in soft computing Proceedings of the 4th international conference on Pattern recognition and machine intelligence, (311-317)
  12. Ghosh S and Velázquez-Quesada F A qualitative approach to uncertainty Proceedings of the 4th Indian conference on Logic and its applications, (90-104)
  13. Nagarajan E and Umadevi D New approach in defining rough approximations Transactions on rough sets XIV, (119-138)
  14. Samanta P and Chakraborty M Generalized rough sets and implication lattices Transactions on rough sets XIV, (183-201)
  15. Stell J Relational granularity for hypergraphs Proceedings of the 7th international conference on Rough sets and current trends in computing, (267-276)
Contributors
  • Indraprastha Institute of Information Technology, Delhi

Index Terms

  1. A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)
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