Certain Algorithms for Modeling Uncertain Data Using Fuzzy Tensor Product B é zier Surfaces

Musavarah Sarwar and Muhammad Akram
Additional contact information
Musavarah Sarwar: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Muhammad Akram: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan

Mathematics, 2018, vol. 6, issue 3, 1-12

Abstract: Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty in mathematical interpolation models. In the context of surface modeling, fuzzy tensor product B é zier surfaces are suitable for representing and simplifying both crisp and imprecise surface data with fuzzy numbers. The framework of this research paper is concerned with various properties of fuzzy tensor product surface patches by means of fuzzy numbers including fuzzy parametric curves, affine invariance, fuzzy tangents, convex hull and fuzzy iso-parametric curves. The fuzzification and defuzzification processes are applied to obtain the crisp Beziér curves and surfaces from fuzzy data points. The degree elevation and de Casteljau’s algorithms for fuzzy B é zier curves and fuzzy tensor product B é zier surfaces are studied in detail with numerical examples.

Keywords: fuzzy tensor product B é zier surface; fuzzy parametric curves; fuzzy iso-parametric curves; degree elevation algorithm; De Casteljau’s algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/6/3/42/pdf (application/pdf)
https://www.mdpi.com/2227-7390/6/3/42/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:6:y:2018:i:3:p:42-:d:135548

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().