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An introduction to analytical fuzzy plane geometry

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An introduction to analytical fuzzy plane geometry/ by Debdas Ghosh, Debjani Chakraborty.
Author:	Ghosh, Debdas.
other author:	Chakraborty, Debjani.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xiii, 206 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Fuzzy mathematics. -
Online resource:	https://doi.org/10.1007/978-3-030-15722-7
ISBN:	9783030157227

An introduction to analytical fuzzy plane geometry
Ghosh, Debdas.

An introduction to analytical fuzzy plane geometry[electronic resource] /by Debdas Ghosh, Debjani Chakraborty. - Cham :Springer International Publishing :2019. - xiii, 206 p. :ill., digital ;24 cm. - Studies in fuzziness and soft computing,v.3811434-9922 ;. - Studies in fuzziness and soft computing ;vol. 45..

Introduction -- Basic ideas on fuzzy plane geometry I -- Fuzzy line -- Fuzzy triangle and fuzzy trigonometry -- Fuzzy Circle -- Fuzzy Parabola -- Fuzzy Pareto-optimality -- Concluding Remarks and Future Directions.

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.

ISBN: 9783030157227

Standard No.: 10.1007/978-3-030-15722-7doiSubjects--Topical Terms:

562912
Fuzzy mathematics.

LC Class. No.: QA248.5 / .G467 2019

Dewey Class. No.: 511.313

An introduction to analytical fuzzy plane geometry
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245 1 3 $a An introduction to analytical fuzzy plane geometry $h [electronic resource] / $c by Debdas Ghosh, Debjani Chakraborty.
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505 0 $a Introduction -- Basic ideas on fuzzy plane geometry I -- Fuzzy line -- Fuzzy triangle and fuzzy trigonometry -- Fuzzy Circle -- Fuzzy Parabola -- Fuzzy Pareto-optimality -- Concluding Remarks and Future Directions.
520 $a 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.
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