Homeomorphism Between Fuzzy Number Space and the Space of Bounded Functions with Same Monotonicity on $$[-1,1]$$ [ - 1 , 1 ]

2015 ◽  
pp. 70-77 ◽  
Author(s):  
Huadong Wang ◽  
Sicong Guo ◽  
Yong Shi
Keyword(s):  
Fuzzy Number ◽  
Bounded Functions

scholarly journals Homeomorphism Problems of Fuzzy Real Number Space and The Space of Bounded Functions with Same Monotonicity on [-1,1]

2015 ◽  
Vol 10 (6) ◽  
pp. 129 ◽  
Author(s):  
Hua -Dong Wang ◽  
Si -Cong Guo ◽  
Seyed Mojtaba Hosseini Bamakan ◽  
Yong Shi
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hausdorff Metric ◽  
Topological Properties ◽  
New Approach ◽  
Analysis Theory ◽  
Bounded Functions ◽  
Fuzzy Structured Element ◽  
Lp Metric ◽  
Functional Metrics

<p>In this paper, based on the fuzzy structured element, we prove that there is a bijection function between the fuzzy number space ε1 and the space B[−1, 1], which defined as a set of standard monotonic bounded functions with monotonicity on interval [−1, 1]. Furthermore, a new approach based upon the monotonic bounded functions has been proposed to create fuzzy numbers and represent them by suing fuzzy structured element. In order to make two different metrics based space in B[−1, 1], Hausdorff metric and Lp metric, which both are classical functional metrics, are adopted and their topological properties are discussed. In addition, by the means of introducing fuzzy functional to space B[−1, 1], we present two new fuzzy number’s metrics. Finally, according to the proof of homeomorphism between fuzzy number space ε1 and the space B[−1, 1], it’s argued that not only does it give a new way to study the fuzzy analysis theory, but also makes the study of fuzzy number space easier.</p>

Lp-Type of Weighted Fuzzy Number Metrics Induced by Fuzzy Structured Element

2014 ◽  
Vol 981 ◽  
pp. 279-286
Author(s):  
Fei Zhao ◽  
Si Zong Guo
Keyword(s):  
Fuzzy Number ◽  
Traditional Method ◽  
Fuzzy Numbers ◽  
Metric Spaces ◽  
Closed Interval ◽  
The Family ◽  
Bounded Functions ◽  
Objective Fact ◽  
The Difference ◽  
Fuzzy Structured Element

For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents Lp-type of fuzzy number metrics weighted by structured element. Firstly, we define a metric weighted by structured element on the family (B[-1,1]) of all the same monotone and standard bounded functions on closed interval [-1,1] , and discuss the completeness and separability of those metric spaces; Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed bounded fuzzy number space is induced by the metric on function space B[-1,1]. Furthermore, a fuzzy number metric weighted by structured element which is induced by is presented ,and analyze completeness and separability of the induced fuzzy number metric spaces; Lastly, the difference and relationship between and the metric defined by traditional method are shown.

A Displayed Inventory Model Using Pentagonal Fuzzy Number

2016 ◽  
Vol 6 (1) ◽  
pp. 11
Author(s):  
K. Dhanam ◽  
M. Parimaladevi
Keyword(s):  
Fuzzy Number ◽  
Inventory Model

SOME PROPERTIES OF INTUITIONISTIC DODECAGONAL FUZZY NUMBER AND ITS APPLICATION

2020 ◽  
Vol 9 (8) ◽  
pp. 6195-6203
Author(s):  
L. Jeromia Anthvanet ◽  
A Rajkumar ◽  
D. Ajay
Keyword(s):  
Fuzzy Number

Characterizations of the Borel \(\sigma\)-fields of the fuzzy number space

2017 ◽  
Vol 58 ◽  
pp. 265
Author(s):  
Tai-He Fan ◽  
Meng-Ke Bian
Keyword(s):  
Fuzzy Number

On Typical Bounded Functions in the Zahorski Classes

1983 ◽  
Vol 9 (2) ◽  
pp. 483 ◽  
Author(s):  
Rinne
Keyword(s):  
Bounded Functions

An Advanced Optimization Technique for Smart Production Using α-Cut Based Quadrilateral Fuzzy Number

2021 ◽  
Author(s):  
Rakesh Kumar ◽  
Rajesh Kumar Chandrawat ◽  
Biswajit Sarkar ◽  
Varun Joshi ◽  
Arunava Majumder
Keyword(s):  
Fuzzy Number ◽  
Optimization Technique
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