Overview
- Shows how to apply fuzzy geometry to solve basic multi-objective optimization problems
- Focuses on two-dimensional analytical fuzzy geometry
- Includes several diagrams and numerical illustrations
Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 381)
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Table of contents (8 chapters)
Keywords
About this book
This book offers a rigorous mathematical analysis of fuzzy geometrical ideas. It demonstrates the use of fuzzy points for interpreting an imprecise location and for representing an imprecise line by a fuzzy line. Further, it shows that a fuzzy circle can be used to represent a circle when its description is not known precisely, and that fuzzy conic sections can be used to describe imprecise conic sections. Moreover, it discusses fundamental notions on fuzzy geometry, including the concepts of fuzzy line segment and fuzzy distance, as well as key fuzzy operations, and includes several diagrams and numerical illustrations to make the topic more understandable. The book fills an important gap in the literature, providing the first comprehensive reference guide on the fuzzy mathematics of imprecise image subsets and imprecise geometrical objects. Mainly intended for researchers active in fuzzy optimization, it also includes chapters relevant for those working on fuzzy image processing and pattern recognition. Furthermore, it is a valuable resource for beginners interested in basic operations on fuzzy numbers, and can be used in university courses on fuzzy geometry, dealing with imprecise locations, imprecise lines, imprecise circles, and imprecise conic sections.
Authors and Affiliations
Bibliographic Information
Book Title: An Introduction to Analytical Fuzzy Plane Geometry
Authors: Debdas Ghosh, Debjani Chakraborty
Series Title: Studies in Fuzziness and Soft Computing
DOI: https://doi.org/10.1007/978-3-030-15722-7
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-15721-0Published: 22 May 2019
Softcover ISBN: 978-3-030-15724-1Published: 14 August 2020
eBook ISBN: 978-3-030-15722-7Published: 13 May 2019
Series ISSN: 1434-9922
Series E-ISSN: 1860-0808
Edition Number: 1
Number of Pages: XIII, 206
Number of Illustrations: 53 b/w illustrations
Topics: Computational Intelligence, Optimization, Computer Imaging, Vision, Pattern Recognition and Graphics, Signal, Image and Speech Processing
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