Abstract mathematical model of general management information systems

CorapaWs ind. £aSaf, VoL31, No. 3/4, pp. 893 -895,1996

cop~sht 0 1995ct~m ~ P r m Publishedby ~tevier ScienceLtd.Printedin GroatBritain

Pergamon S0360-8352(96)00272.0

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ABSTRACT M A T H E M A T I C A L MODEL OF GENERAL M A N A G E M E N T INFORMATION SYSTEMS + Zhaag O ~ c h e n g Wang Lei and Li Long Appfied Mathematics Department of Sichnan Union University Chen~gdu, Sichuan 610065, P. IL China Alamact: In order to suit general MIS[1] to the change of the management state, this paper pres~s an abstract model which is relatively independent of the managemest state. The basic idea is to determine a new ~ standard, which is not influenced by the current management state but rather make a classification according to the object which is related with the information. Thus, we get the abstract model SS. which contains organization structure subsystem SS l analysis structure mbsystem SS2and relation structure subsystem SS 3. Key words: Outputs

Mathematical Model, General MIS, Dynamic Information Structure, Abstract Object, Classification,

1 THE VERTICAL iilERARCI~CAL INFORMATION STRUCTURE OF GENERAL MIS Based on the classification method that presented in paper [1], we can divide information set of general MIS into three lateral hierarchies according to the abstract object. They are: D=S/G,

= {Di[i ¢ J , }

(1)

1), = D,/G21 = {Dijli e J , , j

EJ2i}

(2)

Dii = Dii/Gsi = {Dii, li e J I,j eJ2i,s eJ~i }

(3)

where, for each lateral hierarchy, Jj, J2i, J3ij represent its index sets, Gi, G2i, G~j repr-~-~nt its equivalent relation sets and D,, b i, Dij represent its partition sets respectively. Thus we get three analysis semi-topoiogies:D°, D~ and D~. Let B~, B 2, B s be their analysis factor set, WI, W2, W3 be their attribute value set of analysis factor set. Then we can give the definitions of the three subsystems. Definition 1. The system SSjis said to be organization structure subsystems of SS, Fits dynamic I/O form is as follows: SS, = (J,G,(D,D°),¢I,) where

J = {Ji,J2i,J3ij}

is

(4) its

input

set,

G = {GI,G2i,Gaij}

is

its

state

set,

(I~),I~)°)= {(D,D°),(I~i,Di°),(]~)ij,Dij°)}is its output set, ~t =(rlll,rlt2,~t3) is its output function and i EJj, j E J2i. Furthermore, rill: G I - , ( D , D °) is the first order output fimction, ~12:G2i --> (Di ,D~)is the second order output function, rl,3: G s - ~ (Dij, D°)is the third order output function.

+ Supported by the National Natural Science Foundation of China 893

894

18th International Conference on Computers and Industrial Engineering

Definition 2. The subsystem SS 2 is said to be analysis structure mbsystem of SS, [fits dynamic I/O form is as follows:

o is input s~. i~o x B = ( D ° X B I , D oi×B2,Dij× where l~o = (D o.Di0.Dij) 0 B.) is state set. W = (W..W2.W.) is output set,"2 = ("2,,r122,r123) isoutput functionand i e J,. j e J 2i.Furthermore, "21:DO x B l ~ Wj isthe firstorder output function. "22: D~ x B 2 --~ W 2 isthe second order output function, .23:D~ x B s ~ W ~ isthe thirdorder output function. Definition3. The system SS3is saidto be relationstructuresubsystem of SS [fitsdynamic I/O form isas follows:

SS, = (D. ]~)× ]~).(RI~). RI~'). ,3) where

l~0 = (D.I),. IT)ii ) i s

input

,6,

set,

I~ × I~ = (D x D.ISi x I),.I~ij × ISij)

is

state

set,

(RI~.RJ~°) = {(RD.RD°).(RI)i.RD°).(RIS0.RD~).} is output set. "3 = ('q,,.",2.',3)is output ~nction and i ~ J,, j EJ2i. Furthermore 1131:D x D --). (RD, RD °) is the first order output function, .32: IT)i x b i --} (RIT)i. RIT)°) is tim second order output function, "33: ISij X Dij ---) ( RDij , RD~) i8 the third order output function. 2

A B S T R A C T M O D E L OF G E N E R A L MIlS

From above three definitions, we get the mathematical model of dynamic information structure of general MIS is as follows; SS = (P. .O.,)

(7,

2.1 The state set:
SS0) = (~'~'i ,'-"-'2 ,~"-'s ]

(8)

the second order state:

S S (2) --- ~(SS ,(2) , SS(2),SS 2 s(2)~/

(9)

the third order state:

SS (3) = (SS (3) i ,SS 2(3),SS 3(3~)

(10)

where SSI '), SSI 2), SSI 3), (i = 1,2,3) represent organization structure subsystem, analysis structure subsystem and relation structure subsystem of each order state. Hence, we get:

SS,=(SS it) l ,SS,(2),SS,(3))

(10

ss,--(ss,0),ss,(2),ss,(3))

02)

0) (2) (3) SS3=(SS3 ,SS3 ,SS~ )

03)

18th International Conference on Computers and Industrial Engineering 2.2

895

Tha input set: P = (P,, P2, P3)

H~"C, el =(JI,D°,D)

0 " , P2 = (Jui,D°,I)i) and Ps = (Ju0,Dij,Dii) are input m of each order state, where i cJ,,

J ~J2i" 2.3 Theoutput set :O = ( O i , O 2 , O 3 ) H~, (14)

o1 =

05)

=

(16)

o, =

are output set of each order state, where i EJ I , j EJ2i. 2.4

The output function set:~I = (T[1,1"~2,~3)

Here, Tll, 1"12, Tl3are mentioned in section 1 of this paper. 3

APPLICATIONS OF THE MODEL

Using the outputs of abstract model of general MIS, we can obtain the tools that are required to the MIS development. With the aids of information partition, we get information classification diaom'ams, which is useful to understand the management system. Each order state outputs its object organization structure diagrams, target function diagrams and the relation matrix respectively. 4 CONCLUDE Based on the theory of system representation[3], we have presemed an ahatmct model of dynamic inftmnation structure of general MIS. Taking the point of system development to study MIS, it clears up some mistakes of traditional methods for system analysis and design, hence, the development of MIS is dependent on the deeply understanding of infotmatiou structure. The abstract model also provides the basis to study further MIS and produce tools applied to the MIS development.

REFERENCES

! Liu Xiaoshi, Zhang Guangcheng A mathematical model ofgnneral MIS information structure. Proc. 3rd conf. CSIAM, Beijing: 1994. Beijing: Univ. ofTsinghua Pr., 1994. 2 He Changzheng, Zhang Guangcheng A dynamic applied model of general MIS information structure. Proc. 3rd conf. CSIAM, Beijing: 1994. Beijing: Univ. ofTsinghua Pr., 1994. 3 George J. Klir. Architecture of systems problem solving. New York: Plenum Pr., 1985. 4 Singh M. G.. Dynamical hierarchical control. North-Holland, 1980.

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