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A Solution for the misery of people in Tanzania

Mr. A.Rajkumar, Dr. A.Victor devadoss, Dr.A.praveen prakash,Mrs.Jose Parveena

Abs tractThe Imperative reasons f or misery of people in Tanzania using combined overlap block f uzzy cognitive maps(COBFCMS) def ined by W.B Vasantha kandasw amy is analyzed in this paper. The combined overlap block FCM’s def ined in this method become eff ective w hen the number of concepts can be grouped and are large in nu mbers. In th is paper w e analyzed the problem and are large in number. In this paper w e analyzed the problem and f ind out the major reasons f or misery of people in Tanzania. This paper has six sections, f irst section gives the inf ormation about development of f uzzy cognitive maps, second section gives preliminaries of f uzzy cognitive maps, and combinied overlap block f uzzy cognitive maps, in section three w e explain about the reasons w hy the peopl e in Tanzania having lif e misery, in section f our w e explain the method of determining the ir hidden pattern, in section f iv e, w e give the concept of the problem, f inal section gives the conclusion based on our studies.

Inde x TermsFCMS, CBFCMS, Mi s ery.

.

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1 INTRODUCTION

olitical scientist R.Axelr od[1] intr oduced cognitive maps for r epr esenting social scientific knowledge and descr ibing the methods that ar e used for decision making
in social and political systems. Then B. Kosko[2,3,4] enhanced the pow er of cognitive maps considering fuzzy values for the concepts of the cognitive map and fuzzy degr ees of interr elationships between concepts. FCMs can successfully r epr esent knowledge and human exper ience, intr oduce concept to r epr esent the essential elements and cause the effect r elationships among the concepts to model the behavior of any system. It is a very convenient, simple and power ful tool, which is used in numer ous fields such as social economic and medical etc. the pur pose of study is to identify r isk gr oups, poverty has var ious manifestations including lack of income and pr oductive r esour ce sufficient to ensur e sustainable livelihoods, hunger and malnutrition ,ill health ,limited or lack of access to education and other basic services, i ncr eased unsafe envir onments and social discr imination. Mor eover the data is an unsupervised one and also ther e is uncertainity in the concepts.
Hence fuzzy tools alone has the capacity to analyze these concepts. Hence it is chosen her e.

2 P RELIM INARIES

———— ——— ——— ——— ———

A.RAJKUMAR is currently working as asst prof. in Hindustan university, Chennai

N.Jose parveena is currently working as asst prof. in K.C.G. College of

Technology, Chennai

Dr. A. Praveen Prakash is currently working as Prof. in Hindustan

university, Chennai

Dr. Victor Devadoss is currently working Prof. inLoyola College, Chennai.

Fuzzy cognitive maps (FCMs) ar e m or e applicable when the
data in the first place is an unsupervised one. The FCMs w or k on the opinion of experts. FCMs model the w orlds as a collection of classes and causal r elation between classes.

Definition 2.1: An FCM is a dir ected graph with concepts like policies, events etc. As nodes and causalities as edges. It r epr esents causal r elationship betw een concepts.

Definition 2.2: W hen the nodes of the FCM ar e fuzzy sets then they ar e called as fuzzy nodes.

Definition 2.3: FCMs w ith edge w eights or causalities fr om the set {-1,0,1} ar e simple

Definition 2.4: The edges eij take values in the fuzzy causal interval [-1,1]. eij =0 indicates no causality eij >0 indicates causal increase Cj increases as Ci increases (Or Cj Decreases as Ci Decreases). E <0 indicates causal decrease or negative causality. C Decreases as C increases (And or C j Increases as Ci Decreases). Simple FCMs have edge values in {-1,0,1}. Then if causality occurs, It occurs to a maximal positive or negative degree. Simple FCMs provide a quick first approximation to an expert stand or printed causal knowledge. If i ncrease (Or decrease) in one concept leads to increase(or decrease) in another, Then we give the value 1.If there exists to relation between the two concepts, The value 0 is given. If increase (or decrease) in one concept decreases(or increases) another, then we give the value -1. Thus FCMs are described in this way. Consider the or concepts C1, ,…, Cn Of the FCM. Suppose the directed graph is drawn using edge weight eij ε {0,1,-1}. The matrix E be defined by E= (eij ), Where the eij is the weight of the directed edge Ci,cj. E is called the adjacency matrix of the FCM, also known as the connection matrix of the FCM. It is important to note that all matrices associated with an FCM are always square matrices with diagonal entries as zero.
Definiton 2.5: Let C1 , C2 ,…. Cn be the nodes of an FCM. Let A=(a1 , a2 ,…., an ). Wher e aiε {0,1}. A is called the instantaneous state vector and it denoted the on off position of th e node at

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an instant
ai =0 if ai is off=1
ai =1 if ai is on, wher e i=1,2,….,n.
Definition 2.6: Let C1 ,C2 , ……, Cn be the nodes of an FCM. LetC1 C2 ,C2 C3 ,…, CiCj, be the edges of the FCM (i j ). Then, the edges form a dir ected cycle. An FCM s said to be cyclic if it possesses a dir ected cycle. An FCM is said to be a cyclic if it does not possess any dir ected cycle.

Definition 2.7: An FCM w ith cycles is said to have a feedback.

Definition 2.8: Wher e ther e is a feedback in an FCM, i.e., When the causal r elations flow thr ough a cycle in a r evolutionary way, The FCM is called a dynamical system.

Definition 2.9: Let C1 C2 , C2 C3 ,…, Ci Cj, be a cycle when Ci is sw itched on and if the causality flows thr ough the edges of a cycle and if it again causes Ci, We say that the dynamical system goes r ound and r ound. This is true for any node Ci , for i=1,2,…,n. The equilibr ium state for this dynamical system is called the hidden pattern.
Definition 2.10: If the equilibrium state of a dynamical system is a unique state vector, Then it is called a fixed point. Consider a FCM with C1 , C2 ,…, CN as nodes. For example let us start the dynamical system by sw itching on C. Let us assume that the FCM settles down w ith C1 and Cn on, i.e. the state vector r emains as (1, 0, 0,…, 0, 1). This state vector (1, 0,
0, …, 0, 1) is called the fixed point.
Definition 2.11 : If the FCM settles down w ith a state vector r epeating in the form A1 A2 … AI A1 . Then this equilibr ium is called limit cycle.
Definition2.12: Finite number of FCMs can be combined together to pr oduce the j oint effect of all the FCMs. Let E1 ,E2
,…, Ep be adj acency matr ices of the FCMs w ith nodes C1 ,C2 ,…,
Cn. Then the combined FCM[5,6,7] is got by adding all the adjacency matr ices E1 ,…, Ep . We denote the combined FCM adjacency matr ix by E= E1 +E2 +…+Ep

Definition: 2.13 : Let P be the pr oblem under investigation. Let

{C1 ,C2 ,…, Cn} be n concepts associated w ith p(n very lar ge).
Now divide the number of concepts {C1 ,C2 ,…,Cn} into classes

S1 ,…, St wher e classes ar e such that
(1) Si Si+ 1   wher e (i=1,2,…, t-1)
(2) si=( c1,…………cn)
(3) (si) sj if i j in gener al
Now we obtain the FCM associated w ith each of the classes S1
,…, St . We deter mine the r elational matrix associated w ith
each S . Using theses matrices w e ob tain a nxn matr ix. This n x
n matr ix is the matrix associated with the combined overlap block FCM(COBFCM) of blacks of same sizes.
Definition 2.14: Suppose A= (a1 ,…, an ) is a vector which is passed into a dynamical system E. Then AE=)a’ 1 ,…,a’ n). After thr esholding and updating the vectors suppose w e get (b 1 ,…,
b n). We denote that by (a’1 ,a’2 ,…, a’n ) (b 1 ,b 2 ,…,b n). Thus
the symbol means that the r esultant vector has been
thr esholded and updated. FCMs have several advantages as
well as some disadvantages. The main advantage of this
method it is simple. It functions on experts opinion’s. when the data happens to be an unsuper vised one the FCM comes handy. This is the only known fuzzy technique that gives the hidden pattern of the situation. As w e have a very w ell known theory, which states that the str ength of the data depends on the number of exper ts opinions w e can use combined FCMs with several exper ts opinions. At the same time the disadvantage of the combined FCM is w hen the w eightages ar e 1 and -1 for the same Ci Cj. We have the sum adding to zer o thus at all times the connection matr ices E 1 ,…, Ek may not be comfortable for addition. This pr oblem w ill be easily over come if the FCM entries ar e only 0 and 1.

3 REASONS FOR MIS ERY O F P EOP LE IN TANZANIA

1) Poverty in Tanzania
Poverty has var ious manifestations including lack of income
and pr oductive r esour ce sufficient to ensur e sustainable livelihoods, hunger and malnutrition, ill health, limited or lack of access to education and other basic services, incr eased unsafe envir onments and s ocial discr imination.
Status of poverty in Tanzania
(a) Lar gely a rur al phenomenon
(b) A factor of subsistence agriculture where the poor are concentrated
(c) Also widespread and increasing in urban communities
(d) Afflicting more intensely the youth , the elderly and persons in large households
(e) Non income poverty is a function of acces s to livelihood enhancing factors including education, survival of infants , nutrition, clean and safe drinking water, social wellbeing and vulnerability to disease
(2) Cr ime in Tanzania
(a) Robbery, armed r obber ies and bur glaries at times
r esulting in loss of life.
(b) Mugging ,neck-lacing of muggers, assaults, violence against w omen and childr en

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(c) Manufactur e, consumption and sell of illicit liquor
“gongo” and cr imes associated w ith alcoholism
(d) Riot and unr est
(e) Embezzlement of public funds ,corruption and bribery
(f) Traffic offences including fatal accidents
Watchtow er Bible society states
“the poor cannot sleep at night b ecause they ar e hungry ,the r ich cannot sleep because the poor ar e awake, w hen ther e is no mor e social inj ustice that br eed cr ime, no mor e haves and have-nots, then ther e will be no mor e assassinations, poison gas attacks ,or terr or ists b ombs.”
(3) Health pr oblems in tanzania
(a) Medical facilities ar e limited and medicines som etimes
unavailable, even in capital city .
(b ) cholera is pr evalent in many ar eas of Tanzania,and
sever al str ains of malar ia ar e endemic .
(c) The HIV infection rate in the population is ar ound seven percent and is even mor e pr evalent among pr ostitutes and their clients.
(d) East Afr ica tr ypanosomiasis (sleeping sickness)is carr ied by the tsetse fly, which is endemic to the northern safari cir cuit of Tanzania
(4) Dr ought
Types:
Meteor ological, Hydr ological, Agr icultural and Socioeconomic

Met eor ological Dr ough t

Meteor ological dr ought is the amount of dryness and the dur at ion of the dry period. Atmospher ic conditions that r esult in deficiencies of pr ecipitation change fr om ar ea to ar ea.

Agr icultur al Dr ought

Agr icultur al dr ought mainly effects food pr oduction and farming. Agr icultur al dr ought and pr ecipitation shortages br ing soil water deficits, r educed gr ound water or r eservoir levels, and so on. Mor e of these effects can be listed by clicking her e. Deficient topsoil moistur e at planting may stop germination, leading to low plant populations.

Hy dr ological Dr ought

Hy dr ological dr ought is associated with the effects of per iods of pr ecipitation shortages on water supply. Water in hydr ologic storage systems such as r eservoir s and r iver s ar e often used for multiple pur poses such as flood contr ol, irrigation, r ecr eation, navigation, hydr opower , and wildlife habitat. Competition for water in these storage systems escalates dur ing dr ought and conflicts between water users incr ease significantly.

Socioeconomic Dr ought

Socioeconomic dr ought occur s when the demand for an economic good exceeds supply as a r esult of a w eather-r elated shortfall in water supply. The supply of many economic goods, such as water , forage, food gr ains, fish, and hydr oelectric power , depends on w eather. Due to var iability of climate, water supply is sufficient in some year s but not satisfactory to meet human and envir onmental needs in other year s. The demand for economic goods is incr easing as a r esult of incr easing population. Supply may also incr ease because of impr oved pr oduction efficiency and technology.
(5)Under developed
Internal causes of under development
A histor ical perspective is essential in or der to under stand why tanzania have failed to take part in the inter national economic development w e have seen in this era of globalisation. w e must bear in mind that w e ar e employing one specific standar d, namely economic gr owth, w hich is differ ent fr om painting a full and balanced pictur e of the continent’s history and cultur e. Most of the issues dealt w ith her e ar e the subj ect of consider able debate, but a fuller account of them is beyond the scope of an article of this kind. The cultur e of corr uption in some Tanzania, saying that those who wanted to start a b usiness or gets a job ther e “still have to pay a brib e”.
But the main r eason for the weak development of tanzania after independence is the failur e of the state. The “development state”, based on a state-contr olled economy with a high level of pr otectionism took on a particular and unfortunate form in Africa. In r eality, these countr ies became what Fr ederick Cooper has called “gatekeeper states” – states that acquir ed most of their r evenue fr om customs duties, concessions to for eign companies, visas, for eign exchange contr ol, and for eign aid. In many ways, this built upon the legacy of the colonial per iod and the slave trade.

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6. Gover nment indiffer ence
(a) Accountable governance at local level
(b) Key policy documents, plans and legislation
(c) Annual Accounts and information on local r evenues. (d) Tr easury and other government notificat ions.
(e) Routine budget and expenditur e statements.
(f) Routine appr oval implementation statements. (g) Financial r egulations and government circulars
(h) National budgets and tr easury disbur sement r eports
(i) Appr oved Distr ict, W ar d and Village plans and budgets
(j ) Financial statements, narrative r eports and audit r eports.
7. Envir onmental problem
(a)Loss of wildlife habitats and biodiversity
(b )Defor estation
(c)Land degradation
(d)Deter ior ation of aquatic systems
(e) lack of accessible, good quality water
(f) envir onmentally pollution.
8.Infr astr uctur e
(a) r oad maintenance is poor
(b) operating the inter nal railway networ k is poor
(c) technology is under developed
(d) The power sector poses Tanzania’s most ser ious

infr astr uctur e challenge.

(e) The port of Dar es Salaam suffers constraints caused by

high tr affic and poor backward linkages w ith transport

networ ks.

(f) Poor access to safe water is another challenge, exacerbated

by poor budget execution in the sector.

9.Illter acy

(a) The quality of education at all levels was far fr om being

satisfactory

(b) The education system is char acterized by poor inter nal

efficiency due to high wastage rates.

(c) The school curr iculum have pr oblems of r elevance and appropr iateness.

(d) The education sector is under funded

10.Lack of globalization

(a) static thinking ,limited to the exper iences and the

know ledge of the owner

(b) Risk to focus too much on existing basis of business

(c) Low willingness to intr oduce mor e sophisticated

structur e

(d) Limited r esour ces(manpow er )

(e) Lack of inter national exper ienced employee

(f) Limited funds to finance investments and initial oper ating

losses for new activates.

11.Poor salary

(a) W or kers w ithout mar ketable skills may face low wages. (b) potential economic exploitation
(c) unpleasant w or king conditions, and few opportunities to
attain skills that w ould allow them to escape their personal and economic situations.
(d) Unexpected costs (such as medical or r epair costs)

4 METHOD OF DETERMINING HIDDEN PATTERN

Let C1 , C2 ,…, Cn be the nodes of an FCM, W ith feedback. Let E be the associated adj acency matr ix. Let us find the hidden patter n when C1 is switched on. When an input is given as the vector A1 = (1, 0, 0, …, 0), the data should pass thr ough the r elation matrix E. this is done by multiplying A1 by the matr ix E. Let A1 E= (a1 ,…., an )w ith the thr eshold oper ation that is by r eplacing ai by 1 if ai >k and ai by 0 if ai <k (k is a suitable positive integer ). We update the r esulting concept, The concept C1 is included in the updated vector by making the
first coor dinate as 1 in the r esulting vector. Suppose A1 E
A2 then consider A2 E and r epeat the same procedur e. This pr ocedur e is r epeated till we get a limit cycle or a fixed point.

5 CONCEPT OF THE PROBLEM

Using the linguistic questionnair e and the expert’s opinion w e

have taken the follow ing eleven concepts C1, C2 ,..., C11

C1 = Poverty
C2 = Cr ime C3 = Health C4 = Dr ought
C5 = Under development
C6 = Gover nment in differ ence
C7 = Envir onmental
C8 = Infr astr uctur e
C9 = illiter acy

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C10 = lack of globalization
C11 = poor salary

Now we pr oceed on to apply the effect of combined overlap block. FCM of equal length. Let us consider the eleven concepts C1, C2 ,..., C11. W e divide these concepts into cyclic

way of classes, each having just four concepts in the follow ing C C
way.
The dir ected graph and the r elation matrix for the class C =
{C1 , C2 , C3 , C7 }. the expert opinion of an expateriot of

Tanzania is given as follows:
C1 C2
C9 C11
C3 C7
C1 C2 C3 C7


C1 0 1 1 0
C2 1 0 0 0
C3 1 1 0 1

C7 1 1 1 0
The directed graph and the relational matrix for the class C =
{ C1 , C6 , C9 , C11 }. Given by the expert is as follows: (Religious NGO)
C1 C6 C9 C11


C1 0 0 1 0
C6 1 0 1 1
C9 1 0 0 1
C11 1 1 1 0
The directed graph and the relational matrix for the class C =
{C5 , C8 , C 9, C10 }. Given by the expert is as follows: Faculty of university
C5 C8

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The combined direct graph and combined overlap block
FCM of equal sizes as follows:

C5 C8 C9 C10

C1

C5 0 1 1 1
C8 0 0 1 1
C9 1 0 0 1 C2
C3
C10 0 1 0 0
C4
The directed graph and the relation matrix for the class C ={C2, C3, C5, C6} Given by the expert is as follows: a politician
C6
C5

C7 C8
C2 C3
C10
C11
C9
C(m) C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11
C5
C2 C3 C5 C6

C1

C2

C3

C4

C6 C5

C6

C7

C8

C9

 0 0 1 1 0 0 0 0 1 0 0 

 0 0 1 0 0 0 0 0 0 0 0 

 1 0 0 0 1 0 0 0 0 0 0 

 

 1 0 1 0 0 0 1 0 0 0 0 

 0 1 1 0 0 1 0 1 1 1 0 

 

 1 1 0 0 1 0 0 0 1 0 1 

 1 0 1 1 0 0 0 0 0 0 0 

 0 0 0 0 0 0 0 0 1 1 0 

 

 1 0 0 0 1 0 0 0 0 1 1 



C2 0 1 0 0
C3 0 0 1 0
C5 1 1 0 1
C6 1 0 1 0

C10  0 0 0 0 0 0 0 1 1 0 0 

C11  1 0 0 0 0 1 0 0 1 0 0 

Now using the matrix A of the combined overlap block FCM, We determine the hidden pattern. Suppose the concept S1 is in

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the on state and another nodes are in the off sate. Let the initial input vector be X={ 1 0 0 0 0 0 0 0 0 0 0 0}
X C(m) = {0 0 1 1 0 0 0 0 1 0 0} =X1
X1 C(m) = {0 0 1 1 0 0 0 0 1 0 0} =X2

X2 C(m) = {3 0 1 0 2 0 1 0 0 1 1} (1 0 1 0 1 0 1 0 0 1 1}=X3
X3 C(m) = {3 1 3 1 1 2 0 2 3 1 0} (1 1 1 1 1 1 0 1 1 1 0}=X4
X4 C(m) = {4 2 4 1 3 1 1 2 4 3 2 } {1 1 1 1 1 1 1 1 1 1 1 1}.
X4 C(m) = {1 1 1 1 1 1 1 1 1 1 1}=X4
Where Denotes the resultant vector after thresholding
and updating.
X4 is the hidden pattern which is the fixed point.

CONCLUSION

While analyzing FCM, When the concept C1 “poverty is in the on state, the other concepts C2, C3, C4, C5, C6, C7, C8, C9, C10 are in the on state, because of poverty there will be crime, health problem, drought, underdevelopment , government indifference, environmental, infrastructure, illiteracy, lack of globalization, poor salary, Therefore poverty is the major reason for people in Tanzania(east Africa).

SUGGESTIONS :

Building strong member controlled cooperatives. Promoting good leadership in the cooperatives
Promoting strong and effective cooperative development
support institutions.
Improving cooperative education and training.
Achieving the target of accelerated growth will require
significant efforts to enhance productivity and increase
investment in both human and physical capital.
Increase investment in human capabilities requiring measures
to increase the incentives and returns for undertaking such
investments, and increased public support in areas where externalities are large i.e.primary educa tion and health care.

ACKNOWLEDGM ENT

The authors wish to thank Dr. W.B. Vasantha Kandasamy.

REFERENCES

[1] Axelrod ,R.(1976).Struc ture o f decision :Th e c ongn itive maps of political elites.Princeton Unive rsity.
[2] Vasantha Kandasamy W .B and Victor Devadoss A.
“Some N ew Fuzzy Techniques” , Jour.of inst.o f Math
& Co mpu ter science.
[3] Kosko ,B., “Fuzzy Co gnitive Maps”, In ternational
Journal of man-machine studies ,jan(1986)
[4] Kosko , B .Neural N etw orks and Fuzzy System
Prentice Hall of India,1997 .
[5] Kosko , B. Hidden patterns in Co mbin ed and adaptive
Knowled ge Networ ks,International Conference of
Neural Ne twor ks(ICNN-86)1988 377-393.
[6] Marbur g Consult, A ttacking the Ro ots of Po ver ty:
Marbur g 1996.
[7] International Cooperative Alliance Regional Office for
east central and southern Africa, report on a survey of
rural saving and credit Cooperative Societies in
Tanzania(2001).
[8] Vasantha Kandasamy W.B and M.Ram Kishore
Symptom-Disease Model in Children using FCM, Ultra sci.11(1999)318-324.

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