EAN: 9783030157210

AN INTRODUCTION TO ANALYTICAL FUZZY PLANE GEOME...

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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