The Thinking of Grey Information Coverage

1. The Thinking of Grey Information Coverage Yufeng Gui, Xinping Xiao Wuhan university of technology ,China Aug.6,2016

2. Outline for the Presentation • 1. Introduce • 2. The connotation of the grey theory • 3. The research of grey information coverage • 4. Future research

3. A case - Intelligent transportation system 1. Introduce • 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.

5. 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.

6. 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.

7. 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?

8. 2. The connotation of the grey theory

9. 2. The connotation of grey theory • 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. • —Evolution uncertainty

10. 2. The connotation of grey theory • The connotation of “probability” is random uncertainty • The connotation of “fuzzy” is cognitive uncertainty • The connotation of “grey” is evolution uncertainty • —Evolution uncertainty The constantly supplement and evolution of information result in destruction of black and white;

11. 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.

12. 2. The connotation of grey theory • —grey set Supplementary information Supplementary information Supplementary information Mature evidence Growing Embryo The evolution of the grey set

13. —information coverage 2. The connotation of grey theory ●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)

14. 3. The research of grey information coverage

15. 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;

16. 3.1 Question • Topology: Set family satisfying certain conditions. Question 2: How to establish the topological structure of grey information theory?

17. 3.2 Research progress of grey information coverage

18. 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:

19. 3.3 The topology of the grey information coverage (1) New information set is included in the original information set, That is . Let . 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 is called product of the topology by T1 and T2 onproduct space

20. 3.4 representing method of grey number Grey number is the product of certain evolution rules. That is : Where 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.

21. 3.4 representing method of grey number Under the same evolution rules or the acquiesce rules, classification of grey number is as follow:

22. 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

23. 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 If Sample space of grey information is ，grey domain of is discrete information coverage , is possibility in which the number of Value is i ( ) , Grey information measure . Thus

24. 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 ， value of grey hold , , . Thus Possibility of ,hold: where is real valued parameters, and . Grey information measure definition ：

25. 3.6 grey nuclear and measure of grey information （3）Mixed covering grey number （4） Morphological grey number

26. 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 .

27. 4. Future research

28. 4. Future research • Topological relations of the four forms(Embryo, Growing, Mature, evidence) of grey set. • Operations and properties of grey information covering. 3. Modeling based on gray information coverage.