Transcript Yufeng Gui

The Thinking of Grey Information
Coverage
Yufeng
Gui, Xinping Xiao
Wuhan university of technology ,China
Aug.6,2016
Outline for the Presentation

1. Introduce

2. The connotation of the grey theory

3. The research of grey information coverage

4. Future research
1. Introduce
A case - Intelligent transportation system

Path optimization and travel mode selection
Intelligent transportation system (ITS) is the integration of
the advanced information technology, data communication
technology, sensor technology, control technology and
computer technology .
ITS can help travelers to get real-time traffic information, to
choose the best way to travel.
1.Introduce

In the case , The following different types of
data need to be processed.

Traffic flow: an integer value, its scope is a discrete set;

Traffic density: a closed interval.

Visibility: One of the important indicators of of urban road traffic.
When the weather is fine visibility in more than 1000M.
Rainfall (mm) in 0.8-1.2, the visibility is about 500m

Travel time: not more than 2 hours;
----Uncertain number in the value of a certain interval or a discrete set is
grey number. The interval and discrete number set is the information
coverage of grey number.
1. Introduce

Traffic flow -- discrete grey number cover.

Traffic density-- continuous grey number cover, interval grey number.

Visibility --continuous grey number cover, morphological grey number.

travel time- continuous grey number cover, morphological grey number
------All traffic data is dynamic and evolutionary.
1.Introduce
Question 1 : What is the spatial representation and topological relation
of four kinds of forms (embryo, growing, mature, and evidence) for grey
set?
The evolution process of grey set actually describes the process of traffic
travelers to judge the current traffic situation through the supplementary
traffic information.
Question 2 : How to use the model based on grey information coverage
to forecast the travel time（ short-term simulation）?
Question 3 : How to use the based on grey information coverage to
Optimize the path?
2. The connotation of the grey theory
2. The connotation of grey theory


—Evolution uncertainty
Randomness is a kind of uncertainty caused by the destruction of
Law of causality .
Fuzziness is a kind of uncertainty caused by the destruction of the
law of excluded middle.
Grey is a kind of uncertainty caused by the destruction of black and
white (Zhang qishan).
All information must be different.
Difference is information.
Difference leads to uncertainty.
2. The connotation of grey theory

—Evolution uncertainty
The constantly supplement and evolution of information result in
destruction of black and white;

The connotation of “probability” is random uncertainty

The connotation of “fuzzy” is cognitive uncertainty

The connotation of “grey” is evolution uncertainty
2. The connotation of grey theory

—grey set
●Grey set has dynamic evolution. Evolution reflects the dynamics, life
and aging
●Grey sets can be compatible with 0 and 1, with [0, 1], and with the
evolution of dynamic set;
● Grey set is a collection of information from less to more;
● Grey set is the set of elements that are not clearly defined, from the
abstract to the concrete, from the grey to the white;
● Grey set is a set of 4 forms or subsets (embryo, development,
maturity and evidence).
Grey number is dynamic and uncertain information. It may be less
data, and it can be accurate data.
2. The connotation of grey theory

Embryo
—grey set
Supplementary
Supplementary
Supplementary
information
information
information
Growing
Mature
The evolution of the grey set
evidence
2. The connotation of grey theory
—information coverage
●Information is the main difference between the grey theory and other
theories of uncertainty (zhang);
● Grey theory is based on information coverage (Deng);
● Information coverage refers to the use of a set of information to
include, cover a given proposition (Deng);
● The essence of information coverage is: the collection of incomplete
information, the gray of cognition (Deng);
● Only "small sample uncertain objects" can cover with information
(Deng);
● Grey theory and information have a close relationship.
● The basic theory of grey theory is the mathematical theory of grey
information processing (Wang)
3. The research of grey information coverage
3.1 Question
Question 1:
Why to define the mathematical structure of grey information theory
from the topology?
Three kinds of basic structures: Ordering structure, algebraic
structure and topological structure;
Ordering structure (The order relation of grey system theory is
uncertain.)
Algebraic structure(Grey system theory does not accord with
completeness)
Three elements of topological structure: object set, mapping and
axioms;
3.1 Question

Topology: Set family satisfying certain conditions.
Question 2:
How to establish the topological structure of grey
information theory?
3.2 Research progress of grey
information coverage
theoretical basis
Acquiescing rational ,
Principle of difference
information
Grey information coverage ,
four axioms of grey relational
degree
Grey sets operation
Grey number
Acquiescing grey
number ,
Measured grey
number
The interval grey
number,
Morphological,
Continuous,
Discrete grey
Extended grey
number
Grey relational
degree
time
Spectrum grey
relational degree,
entropy grey
relational degree,
Deng Julong，
1982
Zhang qishan ，
1996
Grey whitenization
weight function ,
Axiomatic Grey
relational degree
Deng Julong ，
1985
Liu sifeng,2004
Relative
uncertainty
Yang
yingjie,liu
sifeng，2014
3.3 The topology of the grey information coverage
Definition 1: Let X is a non-empty set of grey information and there is
no information to add . Thus the set T ,which is composed of some
subsets of X, is said to be a topology of X.
(X, T) is called the topological space.
That is, grey information space is general topological space.
Definition 2: Let X is the set of the original information, S is the new set
of new information and T is a topology for X. Thus the relationship
between S and X can be divided into two cases:
3.3 The topology of the grey information coverage
(1) New information set is included in the original information set,
That is
Ts
S  X .
Let
Ts  S  A A  T  . Thus
is a topology on S and is said to be a relative topology derived from S .
Grey information space (S,Ts) is said to be topology subspace of (X,T)
(2) New information set is not included in the original information set , (X,T1) and
(S,T2) are topological space . Thus the topology T generated by topological
base B  U1  U 2 U1  T1 ,U 2  T2  is called product of the topology by T1 and
T2
on product space
X S
3.4 representing method of grey number
Grey number is the product of certain evolution rules. That is :
a  [ D |  ]
Where
D
is Numerical coverage and

is evolution rules . The following
condition hold
（1）Only under the same evolution rules , operation of grey number can be
done.
（2） Operation of grey numbers can be expressed as the operation of the grey
number coverage ；
（3）Under the rules of the same evolution or default,

Can be omitted ；
（4）the same type of numerical coverage can be operate or order.
3.4 representing method of grey number
Under the same evolution rules or the acquiesce rules, classification of grey
number is as follow:
{a1 , a2 , , an }
Discrete grey number


m

[ci , d i ]
Continuous coverage grey number

i 1
a  D  
m
 {a , a , , a }  [c , d ] Mixed coverage of grey numbers
n
i
i
 1 2
i 1

Morphological grey number
[a   , a   ],[a, ), (0, a ]
3.5 Evolution of grey information space

Definition 1 ： Let the topological relation of four kinds of
forms is in different hierarchy for grey sets . Thus the
corresponding space is called grey information hierarchy
space.

Definition 2: the topological network generating by grey
information hierarchy space and subspace in the evolution is
said to be grey information evolution space
3.6 grey nuclear and measure of grey information
Because the information has not changed, the definition of grey nuclear is
used. The measure of grey information refers to the degree of uncertainty, so grey
information entropy is introduced to represent the uncertainty. Aimed at several
types of grey number, grey and grey information formula of measure is as follows:
(1) the discrete grey number
is   1 , 2 ,..., N  ，grey domain
D  d , d ,..., d  , g i is possibility in
If Sample space of grey information
of is discrete information coverage
which the number of Value
di   D 
1
2
is i (
n
i  1, 2,..., n) , H    Grey
information measure . Thus
gi 
1
, i  1,2,..., n
i
An
in
H     gi ln  gi ，i  1,2,..., n
gn  1
Hn  0
3.6 grey nuclear and measure of grey information
(2) Continuous cover grey number
Let a sample space of grey information
 ， grey field of grey number
corresponding continuous information covered is
i
D   a, b， value of di 
, Gi  D
, Gi  G j  , i, j  1,2,..., n, i  j .
di  Gi

Thus Possibility of di  Gi
,hold:
grey
hold
gi   ...
G1
where
a, b
Gi
1
b  a 
is real valued parameters,
Grey information measure definition ：
H     gi ln  gi 
i
dx1...dxi ,
and a
b
.
3.6 grey nuclear and measure of grey information
（3）Mixed covering grey number
H     gi ln  gi   g j ln  g j 
gi   ...
G1
gj 
Gi
1
b  a 
i
dx1...dxi
1
, i  1,2,..., m; j  1,2,..., n
i
An
（4） Morphological grey number


H        ...  f i  x  ln  f i  x   dx
Gi
i
 i

3.6 grey nuclear and measure of grey information
In the evolution of grey information space， Due to the grey information from
the hazy state to evidence state, the amount of information are constantly
replenished and grey nuclear and gray information measure is no longer a
determination of the eigenvalues. we propose the concept about grey original
nuclear, grey transfer nuclear , grey original information measure and
grey transfer information measure .
4. Future research
4. Future research
1.Topological relations of the four forms(Embryo, Growing,
Mature, evidence) of grey set.
2.Operations and properties of grey information covering.
3.
Modeling based on gray information coverage.
hanks