Introduction
We first discuss how we plan to produce random triangular (trapezoidal) fuzzy numbers. Then we define quadratic fuzzy numbers and show how we can produce random sequences of these fuzzy numbers using sequences of random vectors of real numbers. Random quadratic fuzzy numbers are used in Chapters 10 and 27. In the last section we consider producing random sequences of fuzzy vectors \(\overline{V}=(\overline{X}_1,...,\overline{X}_n)\) where the \(\overline{X}_i\) are triangular/trapezoidal fuzzy numbers or quadratic fuzzy numbers. These random sequences of fuzzy vectors have applications throughout these chapters; triangular fuzzy numbers (TFNs) in Chapters 11-12, 15-17; trapezoidal fuzzy numbers (TrFNs) in Chapter 13; and QBGFNs (defined below) in Chapters 6-10, 19 and 27. We also abbreviate “fuzzy numbers” as FNs. Trapezoidal shaped fuzzy numbers have applications in Chapters 13, 20-22 and 26.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Farin, G.: Curves and Surfaces for CADG, 5th edn., pp. 219–224. Academic Press, London (2002)
Jowers, L.J.: Fuzzy Numbers, A Novel Representation Using Bézier Curves. In: UAB Graduate Student Research Day 2005, Birmingham, AL (March 4, 2005)
Jowers, L.J., Buckley, J.J., Reilly, K.D.: Representation of Conic and Parabolic Fuzzy Numbers Using Bézier Curves. In: Proceedings IPMU 2006. 11th International Conference of Information Processing and Management of Uncertainty in Knowledge Based Systems, Paris, France, July 2, 2006, p. 6 (2006)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Buckley, J.J., Jowers, L.J. (2007). Random Fuzzy Numbers and Vectors. In: Monte Carlo Methods in Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76290-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-76290-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76289-8
Online ISBN: 978-3-540-76290-4
eBook Packages: EngineeringEngineering (R0)