Open Access Library Journal
2016, Volume 3, e3068
ISSN Online: 2333-9721
ISSN Print: 2333-9705
DOI: 10.4236/oalib.1103068 November 17, 2016
Properties of Fuzzy Length on Fuzzy Set
Jehad R. Kider, Jaafar Imran Mousa
Department of Mathematics and Computer Applications, School of Applies Sciences, University of Technology, Bagdad, Iraq
Abstract
The definition of fuzzy length space on fuzzy set in this research was introduced after
the studies and discussion of many properties of this space were proved, and then an
example to illustrate this notion was given. Also the definition of fuzzy convergence,
fuzzy bounded fuzzy set, and fuzzy dense fuzzy set space was introduced, and then
the definition of fuzzy continuous operator was introduced.
Subject Areas
Fuzzy Mathematics
Keywords
Fuzzy Length Space on Fuzzy Set, Fuzzy Convergence, Fuzzy Cauchy Sequence
of Fuzzy Point, Fuzzy Bounded Fuzzy Set and Fuzzy Continuous Operator
1. Introduction
Zadeh in 1965 [1] introduced the theory of fuzzy sets. Many authors have introduced
the notion of fuzzy norm in different ways [2]-[9]. Cheng and Mordeson in 1994 [10]
defined fuzzy norm on a linear space whose associated fuzzy metric is of Kramosil and
Mickalek type [11] as follows:
The order pair ( ) , XN is said to be a fuzzy normed space if X is a linear space and
N is a fuzzy set on [ ) 0, X × ∞ satisfying the following conditions for every , xy X ∈
and [ ) , 0, st ∈ ∞ .
(i) ( ) ,0 0 N x = , for all x X ∈ .
(ii) For all 0 t > , ( ) , 1 N xt = if and only if 0 x = .
(iii) ( ) , ,
t
N xt N x
α
α
=
, for all 0 α ≠ and for all 0 t > .
(iv) For all , 0 st > , ( ) ( ) ( ) , , , N x yt s N xt N ys ≥ ∧ + + where { } min , b a ab = ∧ .
(v) ( ) lim , 1
t
N xt
→∞
= .
How to cite this paper: Kider, J.R. and
Mousa, J.I. (2016) Properties of Fuzzy Length
on Fuzzy Set. Open Access Library Journal,
3: e3068.
http://dx.doi.org/10.4236/oalib.1103068
Received: September 15, 2016
Accepted: November 13, 2016
Published: November 17, 2016
Copyright © 2016 by authors and Open
Access Library Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).
http://creativecommons.org/licenses/by/4.0/
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