A Distributed Agency Methodology applied to Complex Social Systems

Towards a Multi-dimensional Model of the Religious Afﬁliation Preference

Manuel Casta

on–Puga

, Carelia Gaxiola–Pacheco

, Dora–Luz Flores

, Ramiro Jaimes–Mart

ınez

and Juan Ram

on Castro

Facultad de Ciencias Qu

ımicas e Ingenier

ıa, Universidad Aut

onoma de Baja California, Tijuana, Mexico

Facultad de Ingenier

ıa, Arquitectura y Dise

no, Universidad Aut

onoma de Baja California, Ensenada, Mexico

Instituto de Investigaciones Hist

oricas, Universidad Aut

onoma de Baja California, Tijuana, Mexico

Keywords:

Fuzzy Agents, Data Mining, Social Complexity, Distributed Agency, Religion Afﬁliation Preference.

Abstract:

The purpose of the paper is to describe a work-in-progress in the application of a distributed agency and neuro-

fuzzy system methodology to a multi-dimensional model on a complex social system. This work introduces a

study case focuses on decision-making modelling system on religious afﬁliation preferences. We use a type-2

neuro-fuzzy approach to conﬁgure cognitive rules into agent in order to built a multi-agent model for social

simulation.

1 INTRODUCTION

The social systems are complex entities that represent

a whole that cannot be understood by looking at its

parts independently. Another characteristic is the in-

terdependence of the parts conforming the whole: a

change to one of the components in the system may

potentially affect all others (Yolles, 2006).

The main goal of this part of our research is to

develop a computational model of change in reli-

gious afﬁliation preference that incorporates available

mathematical and computational theories that have

not been appropriately considered in models of com-

plex social phenomena.

Even though applications of Multi-Agent Systems

(MAS) have been developed for the social sciences,

MAS have been widely considered in some areas such

as Artiﬁcial Intelligence (AI) (Gilbert, 2007).

1.1 Distributed Agency

The modelling of a realistic social system cannot be

achieved by resorting to only one particular type of

architecture or methodology. The methodology of

Distributed Agency (DA) represents a research av-

enue with promising generalized attributes, with po-

tentially ground-breaking applications in engineering

and in the social sciences—areas in which it mini-

mizes the natural distances between physical and so-

ciological systems.

The methodology of DA represents a general the-

ory of collective behaviour and structure formation,

which intends to redeﬁne agency and reﬂect it in mul-

tiple layers of information and interaction, as opposed

to the traditional approach in which agency is only

reﬂected in individual, atomized and isolated agents

(Suarez and Castanon-Puga, 2010).

1.1.1 Modelling Complex Social System using

Neuro-fuzzy and Distributed Agencies

To build the model of change of religious afﬁlia-

tion will follow the distributed agency methodologi-

cal steps (M

arquez et al., 2011):

1. Determining the levels of agency and their im-

plicit relationships.

2. Data mining.

3. Generating a rule-set.

4. Multi-Agent Modelling (Implementation on a

agent based simulation tool).

5. Validating the model.

6. A simulation and optimization experiment.

7. Analysing the outputs.

Although the methodology covers the entire life-

cycle of a research process, on this paper we are de-

scribing the data mining and generating rule set steps.

We are focused on the neuro-fuzzy approach in order

to set up a rule set into agents.

272

Castañón-Puga M., Gaxiola-Pacheco C., Flores D., Jaimes-Martínez R. and Ramón Castro J..

A Distributed Agency Methodology applied to Complex Social Systems - Towards a Multi-dimensional Model of the Religious Afﬁliation Preference.

DOI: 10.5220/0004000102720277

In Proceedings of the 14th International Conference on Enterprise Information Systems (ICEIS-2012), pages 272-277

ISBN: 978-989-8565-10-5

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

1.1.2 Data Mining and Neuro-fuzzy System

An Interval Type-2 Fuzzy Neural Network (IT2FNN)

are used for automatically generate the necessary

rules. The phase of data mining using Interval Type-2

Fuzzy Logic Systems (IT2FLS) (Castillo et al., 2010;

Castro et al., 2010) becomes complicated, as there

are enough rules to determine which variables one

should take into account. The search method of back-

propagation and hybrid learning (BP+RLS) is more

efﬁcient in other methods, such as genetic algorithms

(Rantala and Koivisto, 2002; Castro et al., 2008).

Since the IT2FNN method seems to produce more

accurate models with fewer rules is widely used as a

numerical method to minimize an objective function

in a multidimensional space, ﬁnd the approximate

global optimal solution to a problem with N variables,

which minimize the function varies smoothly (Ste-

fanescu, 2007).

With the application of this grouping algorithm we

obtain the rules, the agent receives input data from its

environment and choose an action in an autonomous

and ﬂexible way to fulﬁll its function (Peng et al.,

2008).

1.2 Religious Afﬁliation

When literature talks about of religious change, usu-

ally refers to the attachment or religion afﬁliation

(Ortiz, 2006). Although some authors have argued

that the concept can not be limited to this dimension,

membership is one of the most important variables to

study the religious phenomena (Fortuny, 1999).

The religious ﬁeld is conformed by several dy-

namics systems. For example, we can identify

some organizational entities: institutional, socio-

demographic groups and individual.

Within these multiple dimensions interrelated

complex processes are occurring, such changes of al-

legiance, change in commitment and participation,

socialization and subjectivity of standards (through

doctrines, values, practices), reformulation and af-

ﬁrming traditions. These multiple dimensions shape

the religious ﬁeld, and generically is known as reli-

gious change.

1.2.1 Religious Afﬁliation in M

exico

In M

exico, religious afﬁliation has undergone ma-

jor changes since the 1950’s until today. Based on

population censuses, the growth rates of the evangeli-

cal population has been higher than the total Catholic

population

(Jaimes-Mart

ınez, 2007). Baja California

has one of the percentages of highest evangelical pop-

ulation of Northern states

2 CASE OF STUDY

Tijuana is a border city located in north-western of

exico. Belongs to the state of Baja California, and

is one of the fastest growing city in the country due

to high migration rates. The population is mainly

composed by migrants from southern of the country.

They came to the border to further job opportunities,

or looking to migrate to the United States, staying in

the city long time.

2.1 Tijuana’s Multi-cultural and

Religious Complexity

Tijuana is an example of social and religious change.

Its boundary condition has been one factor that has

become a city in full development and expansion, not

only by the strength of the Southern California econ-

omy, but by the early efforts to boost manufacturing

by the federal government.

These factors, combined with growing internal

and international migration, have transformed a town

of Tijuana from a town with 12,181 inhabitants in

1930 to one with 1.2 million in 2000

(Alegr

ıa and

Ord

onez, 2002). It was so from NAFTA, Tijuana was

consolidated as a major call centres maquiladora in-

dustry, with an evident increase in employment and

production, but not productivity or living standards

and welfare (Arias, 2008).

According to some authors, the economic balance,

social and cultural development of these global pro-

cesses, regional and local has had complex effects on

Tijuana’s society, where stands the reconﬁguration of

identities and new forms of social and cultural repro-

duction.

In this sense, the religious sphere in Tijuana has

a great religious diversiﬁcation as a result of differ-

ent waves of migration that have shaped their society.

The evangelical population has experienced rates of

8.90, between 1970 and 1980, while the total population

was 3.16. Although at present growth rate 2.46 points, it is

still higher than that of the population is Catholic and total

population.

Baja California has 7.90% and evangelical population,

surpassed only by one of the ﬁrst entities to which the

Protestant missionaries arrived in the nineteenth century,

Tamaulipas, to 8.65%. Nationally, the percentage of evan-

gelicals is 5.20%.

Tito Alegr

ıa and Gerardo Ord

nez consider the growth

process of Tijuana covers from 1930 to 2000, thanks mainly

to the economic expansion of Southern California.

ADistributedAgencyMethodologyappliedtoComplexSocialSystems-TowardsaMulti-dimensionalModelofthe

ReligiousAffiliationPreference

273

Therefore, religious afﬁliation is also an indicator to

study these processes of reconﬁguration and realign-

ment

(Jaimes-Mart

ınez, 2007).

2.2 Preference for Religious Afﬁliation

in Tijuana

The city has a great diversity of faiths and religious

traditions. Although more numerous the Christian

(Catholic, Protestant, evangelical non-biblical), there

are Buddhists, Muslims, Jews and a variety of groups

and beliefs generically known as New Age

Considering this, we can say that every group or

social stratum in Tijuana has a wide range of choice,

or afﬁnity, in the religious ﬁeld in the city. Each

of them is not only an expression of traditions, cus-

toms and religious practices of different groups have

brought to Tijuana from their places of origin, but the

dynamic formulation of these beliefs in the new envi-

ronment.

3 MODELLING TIJUANA CITY

The principal difference between MAS and our pro-

posed approach is that in our methodology the space

includes transformations performed by a higher level

of agency.

This upper-level agent is composed of lower-level

subcomponents the may enjoy agency in their own

right. It is the responsibility of this intermediate

agent to present its subcomponents with individual

phase-spaces that are tailored to induce the desired

behaviour from the lower-level agents which inhabit

it, when it chooses according to its own objective

function.

Therefore, for our proposed work-in-progress case

study, if we consider a municipality as an agent, this

upper-level agent is composed by subcomponents,

which in our case study of the city of Tijuana, Mex-

ico, will be represented by a location set and Basic

Geo-Statistic Area (AGEB in Spanish) set that com-

pose this city. Locations is the terminology used to

describe wide geographic areas of the city that are

composed of AGEBs. AGEB is the terminology used

to describe small geographic areas of the city that are

composed of blocks.

Between 1990 and 2000 Tijuana just recorded a growth

rate of 8.94 evangelical population, while at the national

level was 2.46.

Syncretic movements oriental religions such as Bud-

dhism, introducing ideas of self-motivation, personal

growth, alternative medicine, psychology, etc.

Figure 1: Levels of agents represented on the social system.

3.1 Levels of Agency

In this example we use three levels of agency: the

upper-level agent is represented by the religion on the

whole city, the intermediate level agents are repre-

sented by the locations and the lower level agents are

the AGEB.

Using a recent census of the reunion sites distri-

bution of the different religious organizations operat-

ing in the city, we know the exact places where they

carry out activities of proselytizing. This information

gives us hints of the inﬂuence of the presence of orga-

nizations in its environment and its impact on socio-

demographic variables.

We are looking for relationships between de-

mographic and economic factors (subtracted from

AGEB) and distribution of meeting places of reli-

gious organizations. We believe that factors such

as poverty, marginalization and other characteristics

related to socio-demographic issues inﬂuencing the

decision-making system of individuals in a complex

and distributed way. Similarly, religious organiza-

tions act as agents who are inﬂuenced by other agen-

cies distributed.

3.2 Data Sets

In the particular case of the city of Tijuana, the data

set used came from the Instituto Nacional de Estadis-

tica y Geograﬁa (INEGI), the Mexican governmental

organization in charge of gathering data at a federal

level including aspects that are geographical, socio-

demographic and economical.

The data set of the city of Tijuana is divided into

363 areas, known as AGEB

(INEGI, 2010).

The data sets for this case study were originally

compiled in an information system that is intrinsi-

cally geographical. These systems helped in the gen-

eration, classiﬁcation and formatting of the required

data—a fact which facilitates the edition of the differ-

ent thematic layers of information, in which one can

The urban AGEB encompass a part or the totality of a

community with a population of 2500 inhabitants or more

in sets that generally are distributed in 25 to 50 blocks.

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274

quantify the spatial structure to visualize and interpret

the areas and different spatial patterns in Tijuana.

For this paper, we going to use de following vari-

ables to exemplify the proposed approach using infor-

mation from 2010 population census in M

exico (IN-

EGI, 2010).

• P15YMAS = Population over 15 years old.

• P15YMSE = Population over 15 years old without

education.

• GRAPROES = Education.

• PEA = Working population.

• PEINAC = Non working population.

• PCATOLICA = Catholic population.

• PNCATOLICA = Non catholic population.

3.3 Neuro-fuzzy Inference System

Using the neuro-fuzzy system for the automatic gen-

eration of rules, this phase of the data extraction from

the data may become complicated, as the process

needs to appropriately establish the number of sufﬁ-

cient norms and variables that the study needs to take

into account.

Using this grouping algorithm, we obtain the ap-

propriate rule-set assigned to each agent representing

an location or a AGEB of it, the agent receives inputs

from its geographical environment and in turn much

choose an action in an autonomous and ﬂexible fash-

ion (Gilbert, 2007).

The purpose of this structure without central con-

trol is to garner agents that are created with the least

amount of exogenous rules and to observe the behav-

ior of the global system through the interactions of its

existing interactions, such that the system, by itself,

generates an intelligent behavior that is not necessar-

ily planned in advance or deﬁned within the agents

themselves; in other words, creating a system with

truly emergent behavior.

From the 2010 census information, we create a

Type-2 Fuzzy Inference System as how we could rep-

resent different agencies as a decision-making system

into agents.

3.3.1 City Level Type-2 Fuzzy Inference Systems

The ﬁgure 2 shows a type-2 fuzzy inference system

for Tijuana city. It depicts a set of input-output vari-

ables and a rule set. Output variables are catholic and

non-catholic as a response of the system. We could

use the difference between both values to make deci-

sions into an agent as a preference decision-making

system.

Figure 2: Fuzzy inference system for Tijuana City.

The ﬁgure 3 shows member function example for

GRAPROES input variable. Type-2 fuzzy inference

system allows us to introduce uncertainty into de sys-

tem, that could be used to represent more dynamic

changes into de Inference System because could be

inﬂuenced by many real time ways.

Figure 3: Fuzzy inference system input and output members

function conﬁguration for Tijuana City.

The Figure 4 depicts the resolution example of the

rules by the fuzzy inference system. Different quan-

titative input values could be introduced and the sys-

tem resolve creating different responses. Depending

of the combination of inputs, we can expect different

responses of the system. An agent will use this in-

ference system as a decision-making system to show

different behaviours depending of the situation.

The Figure 5 represents the response of the sys-

tem to catholic preference, and the Figure 6 for non-

catholic preference. We can see that there are re-

sponse differences, so we can use it to make deci-

sions.

Distributed agents do not necessarily deﬁne agents

in lower-levels of description, but rather consider all

levels of agency that are interconnected in a type of

ADistributedAgencyMethodologyappliedtoComplexSocialSystems-TowardsaMulti-dimensionalModelofthe

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275

Figure 4: Fuzzy inference system rule set evaluation for Ti-

juana City.

Figure 5: PEA vs. GRAPROES type-reduced surface view

for Tijuana City PCATOLICA output.

Figure 6: PEA vs. GRAPROES type-reduced surface view

for Tijuana City PNCATOLICA output.

organism that spreads throughout the system.

3.3.2 Location Level Type-2 Fuzzy Inference

Systems

On location layer, we can build fuzzy inference sys-

tems for agents that represents locations. Figure 7 and

Figure 8 depicts the FIS response for different loca-

tions into the city. As we can see, there are differ-

ences between AGEB agents. At this level, we could

be representing locations agents into a city context.

Figure 7: PEA vs. GRAPROES type-reduced surface view

for location 187 PCATOLICA output.

Figure 8: PEA vs. GRAPROES type-reduced surface view

for location 283 PCATOLICA output.

3.3.3 AGEB Level Type-2 Fuzzy Inference

Systems

On AGEB layer, we can build fuzzy inference sys-

tems for agents that represents locations. Figure 9

and Figure 10 depicts the FIS response for different

AGEB into the same location. As we can see, there

are differences between AGEB agents. At this level,

we could be representing AGEB agents into a location

context.

4 CONCLUSIONS

We use a distributed agency and neural-fuzzy system

approach to develop a computational model of the

decision-making system of agents in order to build a

multi-agent system. We represent different levels of

agency with different cognitive agents. Each agent in

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276

Figure 9: PEA vs. GRAPROES type-reduced surface view

for AGEB 32 PCATOLICA output.

Figure 10: PEA vs. GRAPROES type-reduced surface view

for AGEB 51 PCATOLICA output.

the system are a fuzzy cognitive agent that can choose

religion options based on preferences.

We use the case study of the city of Tijuana, as it

has an updated census of the distribution of meeting

places of religious organizations in the city and their

respective socio-demographic information.

The religious afﬁliation can be modelled with dis-

tributed agency. Establishing different layers of inter-

action between agents and analysing their inﬂuence

on decision-making system of agents in each level,

we can represent the complexity of the phenomenon

of individual preference to a religious afﬁliation.

ACKNOWLEDGEMENTS

We would like to thank to Universidad Aut

onoma de

Baja California for the economic support granted for

this research.

REFERENCES

Alegr

ıa, T. and Ord

onez, G. (2002). Regularizaci

on de la

tenencia de la tierra y consolidaci

on urbana en tijuana,

b.c. Research report, El Colegio de la Frontera Norte,

exico.

Arias, A. L. (2008). Cambio regional del empleo y pro-

ductividad manufacturera en m

exico, el caso de la

frontera y las grandes ciudades,1970-2004. Frontera

Norte, 20(40):79–103.

Castillo, O., Melin, P., and Castro, J. R. (2010). Computa-

tional intelligence software for interval type–2 fuzzy

logic. Journal Computer Applications in Engineering

Education.

Castro, J. R., Castillo, O., Melin, P., Mendoza, O., and

Rodr

ıguez-D

ıaz, A. (2010). An interval type–2 fuzzy

neural network for chaotic time series prediction with

cross–validation and akaike test. Soft Computing for

Intelligent Control and Mobile Robotics, 318:269–

285.

Castro, J. R., Castillo, O., Melin, P., and Rodr

ıguez-D

ıaz,

A. (2008). A hybrid learning algorithm for a class

of interval type–2 fuzzy neural networks. Journal of

Information Sciences, 179(13):2175–2193.

Fortuny, P. (1999). Creyentes y creencias en Guadalajara.

CIESAS, M

exico.

Gilbert, N. (2007). Computational social science: Agent-

based social simulation, pages 115–134. Bardwell,

Oxford.

INEGI (2010). Censo de poblaci

on y vivienda 2010. insti-

tuto nacional de estad

ıstica geograf

ıa e inform

atica.

Jaimes-Mart

ınez, R. (2007). La paradoja neopentecostal.

Una expresi

on del cambio religioso fronterizo en Ti-

juana, Baja California. PhD thesis, El Colegio de la

Frontera Norte, M

exico.

arquez, B. Y., Casta

on Puga, M., Castro, J. R., and

Suarez, E. D. (2011). Methodology for the Model-

ing of Complex Social System Using neuro-Fuzzy and

Distributed Agencies. Journal of Selected Areas in

Software Engineering (JSSE), March:1–8.

Ortiz, O. O. (2006). Cambio religioso en la frontera norte.

aportes al estudio de la migraci

on y las relaciones

transfronterizas como factores de cambio. Frontera

Norte, 18(35):111–134.

Peng, Y., Kou, G., Shi, Y., and Chen, Z. (2008). A descrip-

tive framework for the ﬁeld of data mining and knowl-

edge discovery. International Journal of Information

Technology and Decision Making, 7:639–682.

Rantala, J. and Koivisto, H. (2002). Optimised subtractive

clustering for neuro-fuzzy models.

Stefanescu, S. (2007). Applying nelder mead’s optimiza-

tion algorithm for multiple global minima. Romanian

Journal of Economic Forecasting., pages 97–103.

Suarez, E. D. and Castanon-Puga, M. (2010). Distributed

agency, a simulation language for describing social

phenomena. In IV Edition of Epistemological Per-

spectives on Simulation, Hamburg, Germany. The Eu-

ropean Social Simulation Association.

Yolles, M. (2006). Organizations as complex systems, an

introduction to knowledge cybernetics.

ADistributedAgencyMethodologyappliedtoComplexSocialSystems-TowardsaMulti-dimensionalModelofthe

ReligiousAffiliationPreference

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