Abstract
The topological structure of Fuzzy Numbers was investigated in detail by several authors (e.g., Diamond-Kloeden[44], Puri-Ralescu [123], Ma [104], Goetschel-Voxman [74]). There are some properties that in a classical Mathematical structure (e.g. that of a Banach space) are easily fulfilled, while in the fuzzy setting they do not hold. In this sense, in this chapter we present several negative results through several counterexamples. Some of these results are known but the counterexamples presented in Sections 8.2, 8.3, 8.4 are new, being published for the first time here. Mathematical Analysis on Fuzzy Number’s space is an interesting topic (see Anastassiou [4], Bede-Gal [18], [20], [19], Chalco-Cano-Román-Flores-Jiménez-Gamero [35] Gal [66], Lakshimikantham-Mohapatra [98] Wu-Gong [151]). We study in this chapter mainly integration and differentiability of fuzzy-number-valued functions.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bede, B. (2013). Fuzzy Analysis. In: Mathematics of Fuzzy Sets and Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35221-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-35221-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35220-1
Online ISBN: 978-3-642-35221-8
eBook Packages: EngineeringEngineering (R0)