Performance evaluating of rural ICT centers (telecenters), applying Fuzzy AHP, SAW-G and TOPSIS Grey, a case study in Iran.
Zolfani, Sarfaraz Hashemkhani ; Sedaghat, Maedeh ; Zavadskas, Edmundas Kazimieras 等
1. Introduction
Telecenters (places where shared access to information and
communication technology (ICT) and IT enabled services are available)
are considered a potential instrument for addressing the asymmetric
information problem and the digital divide, and therefore as development
enablers (Fillip, Foote 2007). The World Summit on Information Society
held in 2003 recognized telecenters as a cost effective way of bringing
the information revolution to developing countries, and thus endowed
with the potential to empower the poor. There are instances of
E-Government projects of this nature in some countries that have yielded
significant positive gains for the poor (Bhatnagar 2009).
The growing concern is that poor people, especially those in rural
areas, have benefited very little from rapid economic growth. While the
migration of the rural poor to urban areas has helped cater to urban
requirements, it has accentuated urban poverty and migration related
social problems. Asymmetric information coupled with poor skill sets are
considered the root cause of the inability of the rural poor to take
advantage of opportunities in the markets created by technology
advancement and policy changes. Addressing the problem of asymmetric
information is expected to empower the rural poor to take advantage of
the market opportunities as well as overcome the skill set deficits in
the long run and therefore enhances inclusiveness. This would also
contribute to faster and more balanced growth of the economy.
Last decade has also seen a marked increase in the number of
projects in developing countries that use information and communication
technologies (ICTs) for social, economic, and political development
(Toyama et al. 2004). A large number of these projects aim at bringing
the benefits of ICTs to communities where individual ownership of
computers is low and use of the Internet is infrequent (Best, Kumar
2008). This trend illustrates the high and ever-increasing expectations
placed on ICT in terms of bringing about improvement in quality of life,
empowerment and economic development for the rural communities (Hosman,
Fife 2008). The prevalent method of reaching out to rural areas in these
projects has been telecenters (Heeks 2008) which provide shared public
access, often intermediated by an operator, to information and
communication technologies and services via computers and the Internet.
Apart from many other areas, rural communities in Iran still depend
on agriculture and small-scale trading for livelihoods. Through a
telecenter, the community is able to access information resources on
farming practices via access business information resources to expand
their businesses. They use a local center as a communication platform
for products and services. Through skills training services, telecenters
help to build a skill base for local business. Traders place online
business orders with urban suppliers.
The idea behind these shared-access facilities is that while the
goal of providing all households access to ICT, that is, universal
service, is not possible for most people of the world, providing shared
access is possible, particularly with the rapid evolution of technology.
Through the use of Internet and mobile technology services, the
communities are able to access social and economic services that could
have been difficult without their presence. Telecenters have developed
and offer services through social enterprising models that balance
between social aspects of the communities therefore offering economic
empowerment opportunities to the rural population.
The importance of development and utilizing information and
communication technology and their applications in villages will get
greater importance by knowing that more than 40% of world population
live in villages, rural population in the region of Asia and Oceania is
60% and in Iran they consist 30% of total population. More than 1
billion around the world don't know much about primary tools of
information and communication technology. Although, regarding the issue
of rural urban migration, development of information and communication
technologies in villages has found a special place. There are 68200
villages in Iran, of which nearly 50,000 are equipped with
telecommunication instruments and facilities, but in our country,
development of information and communication technologies has not been
achieved practically and in reality (Jalali et al. 2005; Hashemkhani
Zolfani et al. 2011).
20 year landscape of cultural, economic and social development of
Iran has been set up based on wisdom, therefore it is prescribed that
people must have the opportunity of accessing information; as a result,
relatively good and considerable actions in development of rural
information and communication technologies have been started in the
country. Having strategic document of rural information and
communication technologies helps to integrate and coordinate all actions
that must be done in country by governmental and private sectors and
this will help prevent additional costs (Ministry of IT and
Communication 2004; Hashemkhani Zolfani et al. 2011).
Some general roles of the rural telecenter can be defined as
follows: creating a knowledge center in rural community, educating
people and enriching living standards, realizing grass roots access to
global information through the Internet, promoting the sale of local
products through the Internet and e-Commerce, providing government
information such as natural disaster warning to local communities, and
attracting visitors from all over the world by demonstrating local
culture and beautiful scenery.
The project of equipping 10,000 villages of country with rural
information and communicative technology offices (Rural Telecenters) had
been started from 2005 and finally was finished in 2010. The process of
developing project of rural ICT centers in Iran is shown in Table 1.
After accomplishing the wide project of equipping rural areas, it
seems that this project needs evaluating the facilities and equipment of
rural ICT centers (Rural Telecenters). These centers aren't the
same as others. The aim of this research is performance evaluation of
rural ICT centers in Iran which was established more than 3 years ago
and we are going to compare the achievements (if any) with the main
purposes of establishing them. In this regard, 3 rural ICT centers have
been selected as case studies. In this research, after identifying
important criteria from literature review, Fuzzy AHP is applied for
calculating weight of each criterion and then 3 rural ICT center are
evaluated by SAW-G and TOPSIS GREY. The process of evaluating rural ICT
centers is shown in Figure 1.
[FIGURE 1 OMITTED]
2. Literature review
The recent researches about rural ICT centers are listed below:
Naik et al. (2012) argue that sustainability of these centers can
be enhanced considerably if government services are embedded. Also,
designing these telecenters with embedded G2C services would
significantly improve effectiveness of their delivery and strengthen
government information network, to foster inclusive growth.
Hashemkhani Zolfani et al. (2011) investigated economical and
social Effects of rural telecenters in Iran. Their findings emphasized
the strong positive effects of telecenters on education, training,
culture and social aspects of rural communities.
Naik (2011) suggests an alternative model for rural telecenters,
the e-governance embedded rural telecenters (EGERT), in which
e-governance is an important service to be provided, and details the
contentious issues clustered round the role of the government; the
viability of partnership models with the private and NGO sectors; the
institutional design for rural telecenters; the services to be rendered
by the centers and the likely markets for them; the location of the
centers and support in the form of infrastructure and manpower; and the
technology to support the institutional design.
Mohamed et al. (2010) found that ICT is critical for sustainable
development. In effect, many respondents agreed that due to the
geographical separation and multifaceted nature of international
sustainable development, it cannot be carried out without ICT's
support. However, for ICT infrastructure to be translated into
worthwhile returns, the organization must adopt knowledge-oriented ICT
infrastructure. This is substantiated by ICT's role in decision
quality, knowledge sharing, inter-organizational links, and the
contribution to the resolution of the implicit conflict between
sustainability and economic growth.
Dolo and Mackenzie (2010) employed a multi-method, user-centered
approach to assess how participants make the most of Malian telecenter
resources to meet needs, connect with others, and achieve goals. Their
findings indicate while Malians as empowered change agents are impacted
by deployments such as telecenters, they also affect and impact
telecenters and create unanticipated new knowledge. Their study reveals
the importance of recognizing the needed skills and identifying actors
to promote successful community growth and adaptation. Although results
indicate no direct correlation between technology use and wellbeing
unless directly demonstrated, the use of the telecenter to connect with
others was important to respondents. This research suggests a U-centric
model, an alternative model for cooperative change that is cyclical,
encourages ongoing evaluation, and effectively uses local resources.
Naivinit (2009) suggests that livelihood changes in specific areas,
with a rise in self-esteem being one of the most noticeable changes.
Moreover, financial opportunities, including career enhancement and
product development, have expanded as a result of accessing CTs. In
regard to gender, although it is found that there is only a small
difference in financial opportunity between women and men, the indings
point to more positive changes for women than men in terms of health
enhancement and social connectedness, while men benefit slightly more in
self-esteem and education.
Rao (2008) highlights the status of ICTs in India and their role in
social development, and discusses the case of telecenters, their benefit
and overview of current initiatives deals with the sustainability of
telecenters and analyses the emerging scenario using Gartner's Hype
Cycle. This study concludes that many ICT initiatives in India lack a
comprehensive plan in addressing the target population, struggle to
sustain due to insufficient infrastructure and are too ambitious as they
are not equipped with appropriate technologies in serving the rural
communities. To be successful, a telecenter model needs to be built upon
the principles of multi-stakeholder partnership involving the
government, private organizations for combining innovation,
responsiveness with stability and public participation, and needs to
include massive numbers of excluded people into the information world.
Kawooya (2004) reports on a case study of the school-based
telecenter (SBT) model to assess appropriateness of the school-centered
approach to universal access. The SBTs, established on a pilot basis,
utilize VSAT-based technology to connect schools and neighboring
communities to the internet. This paper documents the appropriateness of
school-based access points for neighboring communities at two selected
School Net-Uganda site schools. School-based access has policy
implications for developing countries' approach to universal access
and lifelong learning in the emerging knowledge society.
3. Delivered and deliverable services in Iran's rural ICT
centers (Hashemkhani Zolfani et al. 2011)
In 2005, the first telecenter of Iran was established in Gharnabad
village located in Golestan province and we have perceived their
significant progress since then. Some of deliverable services in these
telecenters are as follows:
The most significant contribution to 'development' from
telecenter networks emerge from computer based training. Supporting
school curricula with appropriate ICT applications, computers for
children, graphic design, hardware, web design and Internet are some of
the more popular programs offered by telecenters. However, lack of
standardization of computer based training has been an impediment to
e-literacy programs.
Using information technology and accessing educational services
have increasingly become easier and the presence of such telecenters can
prepare a way for creating a knowledge center in rural community. Some
deliverable educational services of those telecenters are as follows:
3.1. Public training
Sharing experiences, skills and expertise, identifying new or
re-usable solutions for common problems, and sharing knowledge on
diverse daily topics are some positive effects of telecenters on public
training; some other aspects of public training derived from telecenters
are noted as bellows:
--Training health related issues.
--Training agriculture.
--Training ranching.
--Training the computer, the internet.
--Other public training.
3.2. Classic training
It is found that people in far-away communities are able to reach
academic sources via the internet connection. To some extent,
information sources on the internet replaced traveling to a library.
This saved travel costs and time. Additionally, rural people did extend
their knowledge and skills in computer and internet usage through
training courses at telecenters. Telecentres provide communities
accessing to the internet and are good places for knowledge sharing and
academic education.
--Training illiterate and low literate ones (Literacy movement
organization).
--Single course education such as apiculture, piscine culture, and
things like that based on needs.
--Remote education of elementary, guidance and high school levels.
--Higher education universities and using virtual universities.
--Other classic educations.
3.3. Special training
Information communication technologies (ICTs) are fast becoming
essential tools in the delivery of information, knowledge and education
all over the world. The role of ICT-based telecenters in supporting
educational and community development in both rich and poor countries is
critical.
Some of the notable impacts of telecenters on social training can
be summarized as below:
--Training dealing with natural events.
--Defense training.
--Women specific training.
--Special technical and professional training.
--Other special training.
3.4. Cultural services
As the structure of the world is evolving, the importance of being
knowledgeable is getting more significance. Knowledge centered economy
would replace traditional economy of the world. Will the villages have
an independent economy for themselves, or they have to follow these
evolutions? It seems that economy is similar in villages and cities and
if the criterion is knowledge, we must provide suitable facilities for
villagers to be able to access new economy through these telecenters.
Today, with new phenomena such as electronic business, virtual
production, credit card, electronic banking; it seems that the
opportunities of advancement for villagers have increased. With this in
mind, these telecenters can be helpful for the mentioned purposes. In
the following, some instances of economic services of these centers are
presented:
--Introducing agricultural, animal and other products in national
and international markets.
--Performing banking and financial affairs through installing ATM
in centers.
--Remote job finding and remote working.
--Electronic business.
--Other economic services.
3.5. Social services
Although village councils have been developed, but there are no
integrated offices or institutions to transfer their experiences to the
next groups. These centers not only can facilitate the relationship
between villagers and authorities, but also they can be applied as
centers for holding council meetings in villagers' presence.
Moreover, they can connect the villagers, council and state
organizations to each other and present following services in social
context:
--Holding the meetings of village council.
--Holding virtual conferences.
--Holding computer based elections.
--The base of associations and groups of NGO.
--Other social services.
3.6. Governmental services
These centers can be utilized as a connection point of electronic
government with the villages so that the villagers can conduct their
communication with governmental sectors through these centers. These
centers can be exploited as a settlement place for the following
governmental organizations that generally operate in villages:
--Virtual office of agricultural ministry.
--Virtual office of health ministry.
--Virtual office of education ministry.
--Virtual office of environment organization.
--Virtual office of agricultural bank.
--Virtual office of post bank.
--Virtual office of rural cooperative organization.
--Virtual office of other organizations related to villages.
Since any organization can not have an independent office in
villages, placing all governmental organizations together in one place
not only is cost effective but also encourages them to perform better by
consultation and avoids duplication of work. Besides, at the moment many
villages have university graduated persons, hence this center can
attract them to work and they can work as employees or representatives
of one or more of these state organizations. If these centers become
successful, the demographic problem in villages can easily be solved and
updated so that the authorities and decision makers can make plans based
on real statistics for villagers.
3.7. Other services
Services provided by rural telecenters are diverse. These
telecenters can develop like IT parks of country with the aim of a
center for growth of rural IT. Also, they can act as educational centers
or commercial service centers and like that. In the following, some of
the services of these telecenters are described:
--General services of internet such as: electronic post, video
communication and conferences and internet telephone services, VOIP and
fax.
--Coffee net services, ATM machines, rural IT parks, service
kiosks.
--Firms and office information and commercial services.
--Medical information services.
--Other similar services.
Many other services can be delivered to villagers by this rural
base and revolutionize their lives in economic, cultural, scientific,
educational and social aspects. These telecenters can simultaneously
have educational and commercial applications. They can be utilized as
information and village news centers, rural research centers, village
library, internet access centers, rural ISP internet servicing centers,
the center for tourists' access to information and electronic
services and finally the centers for coordinating the services and state
organizations, if supported correctly, it can be a turning point in
development of villages of Iran at the beginning of third millennium.
Seven important services presented in rural ICT centers are
considered as a framework for evaluating as illustrated in Figure 2.
[FIGURE 2 OMITTED]
4. Methodology
Over the past decades the complexity of economic decisions has
increased rapidly, thus highlighting the importance of developing and
implementing sophisticated and efficient quantitative analysis
techniques for supporting and aiding economic decision-making
(Zavadskas, Turskis 2011). Multiple criteria analysis (MCA) provides a
framework for breaking a problem into its constituent parts. MCA
provides a means to investigate a number of alternatives in light of
conflicting priorities. Over the last decade, a set of new MCDM methods
have been developed. These new methods have been modified and applied to
solve sophisticated practical and scientific problems. Solving modern
decision making problems in most cases is based on integrated model of
different approaches. There is a wide range of methods based on
multicriteria utility theory: SAW (MacCrimon 1968); TOPSIS (Hwang, Yoon
1981); COPRAS (Zavadskas et al. 2010b); and other methods (Turskis,
Zavadskas 2010; Zavadskas, Turskis 2010). Uncertain and vague future
causes lots of difficulties for decision-makers. The multi criteria
decision-making could be applied to assess different alternatives of
future activities.
The best strategy can be selected from available scenarios and
information. In strategic decisions, dealing with uncertainty, the
values of criteria could be determined at intervals--from pessimistic
value to optimistic value. There is a wide range of methods based on
multicriteria utility theory with grey numbers operations to the
problems solution: TOPSIS-grey (Lin et al. 2008; Zavadskas et al.
2010a), SAW-G (Zavadskas et al. 2010a), COPRAS-G (Zavadskas et al.
2010b), ARAS-G (Turskis, Zavadskas 2010).
4.1. Analytic hierarchy process
Analytic hierarchy process (AHP), proposed by Thomas L. Saaty in
1971 (Saaty 1980), is able to solve the multiple criteria decision
making problems. AHP utilizes three principles to solve problems
(Aydogan 2011):
1. Structure of the hierarchy.
2. The matrix of pair wise comparison ratios, and
3. The method for calculating weights.
Analytic hierarchy process (AHP) is a powerful method to solve
complex decision problems. Any complex problem can be decomposed into
several sub-problems using AHP in terms of hierarchical levels where
each level represents a set of criteria or attributes relative to each
sub-problem. The AHP method is a multicriteria method of analysis based
on an additive weighting process, in which several relevant attributes
are represented through their relative importance. AHP has been
extensively applied by academics and professionals, mainly in
engineering applications involving financial decisions associated to
non-financial attributes. During the past, there were 13 major
conditions that have been discovered to well fit the utilization of AHP
such as setting priorities, generating a set of alternatives, choosing a
best policy alternatives, determining requirements, allocating
resources, predicting outcomes, measuring performance, designing system,
ensuring system stability, optimization, planning, resolving conflict,
and risk assessment (Saaty 1980).
With this method, a complicated system is converted to a
hierarchical system of elements. In each hierarchical level, pair-wise
comparisons of n elements are made by using a nominal scale and the
value [m.sub.ij] is assigned to represent the judgment concerning the
relative importance of decision element [e.sub.i] over [e.sub.j].
These comparisons compose a pair-wise comparison matrix M =
{[m.sub.ij]}. In order to find the weight of each element, or the score
of each alternative, the priority vector (or eigenvector) W =
[([w.sub.1], [w.sub.2,], ..., [w.sub.n]).sup.T] of this comparison
matrix is calculated based on solving the equation (1):
Mw = [[lambda].sub.max] w, [[lambda].sub.max] [greater than or
equal to] n. (1)
It indicates that the eigenvector corresponding to the largest
eigenvalue ([[lambda].sub.max]) of the pair-wise comparisons matrix
reflects the relative importance of the decision elements. This
conventional AHP approach gives reasonably good approximation only when
the decision-maker's preferences are consistent. However, the
descriptions of linguistic variable (such as 'judgment' or
'preference') are usually vague and the verbal attitudes of
decision-maker's requirements on evaluation process always contain
ambiguity and multiplicity of meaning. AHP is ineffective when applied
to ambiguous problem. Thus, fuzzy sets could be incorporated with the
pair-wise comparison, as an extension of AHP, to solve this kind of
uncertainty (Lee 2010).
4.2. Fuzzy AHP method
In the proposed methodology, AHP with its fuzzy extension, namely
fuzzy AHP, is applied to obtain more decisive judgments by prioritizing
the market segment selection criteria and weighting them in the presence
of vagueness. There are numerous fuzzy AHP applications in the
literature that propose systematic approaches for selection of
alternatives and justification of problem by using fuzzy set theory and
hierarchical structure analysis (Efendigil et al. 2008; Onut et al.
2010). DMs usually find it more convenient to express interval judgments
than fixed value judgments due to the fuzzy nature of the comparison
process (Bozdag et al. 2006). This study concentrates on a fuzzy AHP
approach introduced by Chang (1996), in which triangular fuzzy numbers
are preferred for pairwise comparison scale. Extent analysis method is
selected for the synthetic extent values of the pairwise comparisons.
Some papers published used the fuzzy AHP procedure based on extent
analysis method and showed how it can be applied to selection problems
(Cebeci, Ruan 2007; Kahraman et al. 2003, 2004). The outlines of the
fuzzy sets and extent analysis method for fuzzy AHP are given below.
A fuzzy number is a special fuzzy set F = {(x, [[mu].sub.F] (x), x
[member of] R}, where x takes its values on the real line, R:
-[infinity] [less than or equal to] x [less than or equal to] [infinity]
and [[mu].sub.F] (x) is a continuous mapping from R to the closed
interval [0, 1]. A triangular fuzzy number (TFN) expresses the relative
strength of each pair of elements in the same hierarchy and can be
denoted as M = (l, m, u), where l [less than or equal to] m [less than
or equal to] u. The parameters l; m; u; indicate the smallest possible
value, the most promising value, and the largest possible value
respectively in a fuzzy event.
Triangular type membership function of M fuzzy number can be
described as in Equation 1.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
A linguistic variable is a variable whose values are expressed in
linguistic terms (Onut et al. 2008). The concept of a linguistic
variable is very useful in dealing with situations, which are too
complex or not well defined to be reasonably described in conventional
quantitative expressions (Zadeh 1965).
In this study, the linguistic variables that are utilized in the
model can be expressed in positive TFNs for each criterion as in Figure
3.
[FIGURE 3 OMITTED]
The linguistic variables matching TFNs and the corresponding
membership functions are provided in Table 2. Proposed methodology
employs a Likert Scale of fuzzy numbers starting from [??] to [??]
symbolize with tilde (~) for the fuzzy AHP approach. Table 2 depicts AHP
and fuzzy AHP comparison scale considering the linguistic variables that
describes the importance of criteria and alternatives to improve the
scaling scheme for the judgment matrices.
By using TFNs via pairwise comparison, the fuzzy judgment matrix
[??]([a.sub.ij]) can be expressed mathematically as in Equation 2:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The judgment matrix [??] is an n x n fuzzy matrix containing fuzzy
numbers [[??].sub.ij].
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Let X = {[x.sub.1], [x.sub.2], ...[x.sub.n]} be an object set,
whereas U = {[u.sub.1], [u.sub.2,]...[u.sub.n]} is a goal set. According
to fuzzy extent analysis, the method can be performed with respect to
each object for each corresponding goal, [g.sub.i], resulting in m
extent analysis values for each object, given as [M.sup.1.sub.gi],
[M.sup.2.sub.gi], ..., [M.sup.n.sub.gi], i = 1,2, ...,n where all the
[M.sup.j.sub.gi](j = 1,2, ...,m) are TFNs representing the performance
of the object [x.sub.i] with regard to each goal [u.sub.j]. The steps of
Chang's extent analysis (1996) can be detailed as follows (Kahraman
et al. 2003, 2004):
Step 1: The fuzzy synthetic extent value with respect to the ith
object is defined as:
[S.sub.i] = [m.summation over (j=1)] [M.sup.j.sub.gi] [cross
product] [[[n.summation over (i=1)] [m.summation over (j=1)]
[M.sup.j.sub.gi]].sup.-1] (5)
To obtain [m.summation over (j=1)] [M.sup.j.sub.gi], perform the
fuzzy addition operation m extent analysis values for a particular
matrix such that operation m extent analysis values for a particular
matrix such that
[m.summation over (j=1)] [M.sup.j.sub.gi] = ([m.summation over
(j=1)] [l.sub.j], [m.summation over (j=1)] [m.sub.j], [m.summation over
(j=1)] [u.sub.j]) (6)
and obtain [[[n.summation over (i=1)] [m.summation over (j=1)]
[M.sup.j.sub.gi]].sup.-1], perform the fuzzy addition operation of
[M.sup.j.sub.gi] (j = 1,2, ...,m) values and such that
[[[n.summation over (i=1)] [m.summation over (j=1)]
[M.sup.j.sub.gi]].sup.-1] = ([n.summation over (i=1)] [l.sub.i],
[n.summation over (i=1)] [m.sub.i], [n.summation over (i=1)] [u.sub.i])
(7)
and then compute the inverse of the vector in Equation 6 such that
[[[n.summation over (i=1)] [m.summation over (j=1)]
[M.sup.j.sub.gi]].sup.-1] = (1/[n.summation over (i=1)] [u.sub.i],
1/[n.summation over (i=1)] [m.sub.i], 1/[n.summation over (i=1)]
[l.sub.i]). (8)
Step 2: The degree of possibility of [M.sub.2] [greater than or
equal to] [M.sub.1] is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
and can be equivalently expressed as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
where d is the ordinate of the highest intersection point D between
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] (see Figure 4). To compare
[M.sub.1] and [M.sub.2], both the values of V ([M.sub.1] [greater than
or equal to] [M.sub.2]) and V ([M.sub.2] [greater than or equal to]
[M.sub.1]) are required.
[FIGURE 4 OMITTED]
Step 3: The degree possibility of a convex fuzzy number to be
greater than k convex fuzzy numbers [M.sub.i] (i = 1, 2, ..., k) can be
defined by Equation 10.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
Assume that:
d'([A.sub.i]) = min ([S.sub.i] [greater than or equal to]
[S.sub.k]). (12)
For k = 1, 2, ..., n; k [not equal to] i. Then, the weight vector
is given by as in Equation 12:
W' = [(d'([A.sub.1]), d'([A.sub.2]),...
d'([A.sub.n])).sup.T], (13)
where [A.sub.i] (i = 1, 2,... n) has n elements.
Step 4: The normalized weight vectors are defined as:
W = [(d([A.sub.1]), d([A.sub.2]),... d([A.sub.n])).sup.T], (14)
where W is a non fuzzy number.
4.3. SAW-G method
The Simple Additive Weighting method with grey number can be
described as the following steps (Zavadskas et al. 2010a).
Step 1: Selecting the set of the most important criteria,
describing the alternatives.
Step 2: Constructing the decision-making matrix [cross product] X.
Step 3: Normalization process for getting comparable scales. The
normalized values are calculated as follows:
[[bar.w].sub.ij] = [w.sub.ij]/max [w.sub.ij], [[bar.b].sub.ij] =
[b.sub.ij]/max [w.sub.ij]; (15)
[[bar.w].sub.ij] = min [b.sub.ij]/[w.sub.ij], [[bar.b].sub.ij] =
min [b.sub.ij]/[b.sub.ij]. (16)
If min [x.sub.ij] is preferable
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
Step 4: Determining weights of the criteria [q.sub.i].
Step 5: Weighted-normalized decision-making matrix is obtained
according to equation (18):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)
where [q.sub.i] is the weight of the j-th attribute.
Step 6: The next step is to calculate optimality criterion L which
is determined as maximal value of [L.sub.i]:
[L.sub.i] = [1/n] [m.summation over (j=1)] [[[[bar.w].sub.j] +
[[bar.b].sub.j]]/2]. [[bar.w].sub.ij] = [w.sub.ij]/max [w.sub.ij],
[[bar.b].sub.ij] = [b.sub.ij]/max [w.sub.ij]. (19)
Step 7: Optimal alternative is determined as maximal value of
[L.sub.i].
4.4. TOPSIS Grey
The TOPSIS method was developed by Hwang and Yoon (1981). TOPSIS
method belongs to MCDM (Multi-criteria decision-making method) group and
identifies solutions from a finite set of alternatives based upon
simultaneous minimization of distance from an ideal point and
maximization of distance from a negative ideal point. TOPSIS can
incorporate relative weights of criteria. The only subjective input
needed is weights. Lin et al. (2008) developed TOPSIS method with grey
number operations to the problem solution with uncertain information.
Zavadskas et al. (2010a, 2010b) used TOPSIS method with grey numbers
operations to risk assessment of construction project for contractor
selection for constructions works.
The TOPSIS method is one of the best described mathematically and
not simple for practical using. Lin et al. (2008) proposed the model of
TOPSIS method with attributes values determined at intervals that
includes the following steps:
Step 1: Selecting the set of the most important attributes,
describing the alternatives.
Step 2: Constructing the decision-making matrix [cross product] X.
Grey number matrix [cross product] X can be defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)
where [cross product][x.sub.ij] denotes the grey evaluations of the
i-th alternative with respect to the j-th attribute; [[cross
product][x.sub.i1], [cross product][x.sub.i2], ..., [cross
product][x.sub.im]] is the grey number evaluation series of the i-th
alternative.
Step 3: Construct the normalized grey decision matrices. The
normalized values of maximizing attributes are calculated as:
[cross product][[bar.x].sub.ij,b] = [cross
product][x.sub.ij]/[max.sub.i] ([b.sub.ij]) = ([w.sub.ij]/[max.sub.i]
([b.sub.ij]), [b.sub.ij]/[max.sub.i] ([b.sub.ij])). (21)
The normalized values of minimizing attributes are calculated by
Lin et al. (2008):
[cross product][[bar.x].sub.ij,w] = 1 - [cross
product][x.sub.ij]/[max.sub.i] ([b.sub.ij]) = (1 -
[b.sub.ij]/[max.sub.i] ([b.sub.ij]); 1 - [w.sub.ij]/[max.sub.i]
([b.sub.ij])). (22)
Step 4: Determining weights of the criteria [q.sub.j].
Step 5: Construct the grey weighted normalized decision-making
matrix.
Step 6: Determine the positive and negative ideal alternatives for
each decision-maker. The positive ideal alternative [A.sup.+], and the
negative ideal alternative [A.sup.-] can be defined as:
[A.sup.+] = {([max.sub.i][b.sub.ij] | j [member of] J),
([min.sub.i][w.sub.ij] | j [member of] J') | i [member of] n} =
[[x.sub.1.sup.+], [x.sub.2.sup.+],...[x.sub.m.sup.+]] (23)
and
[A.sup.-] = {([min.sub.i][w.sub.ij] | j [member of] J),
([max.sub.i][b.sub.ij] | j [member of] J') | i [member of] n} =
[[x.sub.1.sup.-], [x.sub.2.sup.-],...[x.sub.m.sup.-]] (24)
Step 7: Calculate the separation measure from the positive and
negative ideal alternatives, [d.sup.+.sub.i] and [d.sup.-.sub.i], for
the group. There are two sub-steps to be considered: the first one
concerns the separation measure for individuals; the second one
aggregates their measures for the group.
Calculate the measures from the positive and negative ideal
alternatives individually. For decision-maker k, the separation measures
from the positive ideal alternative [d.sub.i.sup.+] and negative ideal
alternative [d.sub.i.sup.-] are computed through weighted grey number
as:
[d.sub.i.sup.+] = [{[1/2][m.summation over
(j=1)][q.sub.j][[[absolute value of [x.sup.+.sub.j] -
[[bar.w].sub.ij]].sup.p] + [[absolute value of [x.sup.+.sub.j] -
[[bar.b].sub.ij]].sup.p]]}.sup.1/p], (25)
[d.sub.i.sup.-] = [{[1/2][m.summation over (j=1) [q.sub.j]
[[[absolute value of [x.sup.-.sub.j] - [[bar.w].sub.ij]].sup.p] +
[[absolute value of [x.sup.-.sub.j] -
[[bar.b].sub.ij]].sup.p]]}.sup.1/p], (26)
In equations (19) and (20), for p [greater than or equal to] 1 and
integer, [q.sub.j] is the weight for the attribute j, which can be
determined by attribute weight determination methods. If p = 2, then the
metric is a weighted grey number Euclidean distance function. Equations
(25) and (26) will be as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)
Step 8: Calculate the relative closeness [C.sub.i.sup.+], to the
positive ideal alternative for the group. The aggregation of relative
closeness for the i-th alternative with respect to the positive ideal
alternative for the group can be expressed as:
[C.sub.i.sup.+] = [d.sub.i.sup.-]/[d.sub.i.sup.+] +
[d.sub.i.sup.-], (29)
where 0 [less than or equal to] [C.sub.i.sup.+] [less than or equal
to] 1. The larger the index value is, the better the evaluation of
alternative will be.
Step 9: Rank the preference order. A set of alternatives now can be
ranked by the descending order of the value of [C.sub.i.sup.+].
5. Results
5.1. Using FAHP method for criteria prioritization
Fuzzy AHP is used for determining the weights of main and
sub-criteria. For pair wise comparison decision making in FAHP, a
questionnaire was utilized to get experts' point of view. The
experts are the senior managers in the three mentioned telecenters with
the following background; all information about the experts of present
study is shown in Table 3.
Paired comparison matrix is a matrix which is formed using
experts' viewpoints as it is illustrated in Table 4. FAHP method is
then applied for prioritizing.
After processing the fuzzy data, the final weights of criteria are
obtained. According to each indicator's weight which is shown in
Table 5, public training and cultural services are the most important
criteria of all.
The description of the abbreviations used in Tables 3 and 4 are
presented as below; C1: Public Training, C2: Classic Training, C3:
Special Training, C4: Cultural Services, C5: Social Services, C6:
Governmental Services and C7: Other Services.
5.2. Evaluation of rural ICT centers by SAW-G and TOPSIS Grey
Ranking of alternatives by SAW-G and TOPSIS Grey technique and the
weights that are calculated in last stage (Fuzzy AHP), is performed.
The initial decision-making matrix with values determined at
intervals is presented in Table 6. In Table 6 given notations [q.sub.j]
are the criteria weights and [A.sub.1],...[A.sub.5] are alternatives. In
this table the group of experts evaluated each candidate according to
each criterion. The evaluation has done on a scale from 1 to 9, where 9
meant "very important" and 1 "not important at all"
Based on formula 15 normalize values of each criterion is obtained
in Table 7 based on information of Table 6. The results of the
calculation for each alternative are presented in Table 8.
According to the SAW-G and TOPSIS Grey and the weight that
calculated with FAHP methods the order of alternatives ranks is:
[A.sub.2] [??] [A.sub.3] [??] [A.sub.1].
6. Conclusion
In this study Fuzzy AHP, SAW-G and TOPSIS Grey are applied for
performance evaluation of rural ICT centers (Telecenters) in Iran and
for this aim three telecenters were selected as a case study in Golestan
Province in north of Iran where the first telecenter in Iran was
established. The second telecenter in Iran was also established in
Golestan Province. Each work needs time to bring about positive changes
and based on our study, we have concluded that telecenters need at least
three years to develop their predetermined purposes in rural areas.
Gharnabad, Livan and Bala Jadeh villages selected for this study were
established more than three years ago and all of them have their own
websites. Important criteria for this study have been identified via
previous researches which are public training, classic training, special
training, cultural services, social services, governmental services and
other services. Results of Fuzzy AHP show that public training and
cultural services are more important criteria for the evaluating of
rural ICT centers since knowledge domain in villages is lower than
cities these years and these centers will help to increase people's
knowledge level in villages. After that cultural services has gained the
third priority and social services, governmental services and finally
other services don't seem to have very great importance for
villages these days but it can be predicted that as people's
knowledge level in villages improves, these two criteria are likely to
gain higher significance in near future. The results of SAW-G and TOPSIS
Grey method are the same and Gharnabad telecenter has been evaluated as
the best center, Livan telecenter was placed at the second and Bala
Jadeh telecenter was the last. Developing knowledge in all areas of each
country is very important and rural ICT centers have a key role in this
sector. This study can be used as an evaluation framework for rural ICT
centers in Iran and other countries.
Appendix
Gharnabad Village
Gharnabad village is located in 20th Km. of Gorgan in Golestan.
Most of the people of Gharnabad are farmers and ranchers; some of them
also have freelance jobs and industrial jobs. Agricultural products of
this village are: cotton, wheat, barley, rice, potato, and soya bean. In
the area of ranching, they generally breed cows and they are at primary
stage of self-efficiency in production.
The first rural telecenter of Iran was established in Gharnabad in
2004 based on the scope of economic, cultural and social development
applying IT findings and communication and through villagers'
assistance.
In this center, all state organizations as connectors of electronic
government can deliver most of their services in an integrated way to
villagers in the village. Moreover, this center is a place for accessing
the villagers to virtual education, virtual library, electronic
business, electronic banking and other computer and internet related
issues. The approach of establishing rural telecenter is mostly
economical. These telecenters are assumed to be influential in social
and cultural affairs through financing and bring an operational form out
of future information community.
This telecenter was built in a two floor building each one has 280
square meters area.
The first floor has an amphitheater, internet services provider
(ISP), Quran education classes, English language and agriculture
promotion for different ages of girls, boys, men, women and children.
The second floor is designed for IT research center and rural
communication. In this center all state organizations have suitable
virtual space in order to perform their required researches together or
obtain information and statistics required by related organizations in
village, and deliver their services to the villagers directly in situ.
This center gives the student the opportunity to perform their
researches in shorter time and higher quality through ADSL of center and
make the villagers engaged in research.
This center, besides its internal network, provides services needed
by villagers through ISP so that they can use functional services of
center and remote users can have job and find job all over the world.
Electronic books that are stored and read out in multimedia form in
data sector can connect illiterate and uneducated to the world of
knowledge by sound and film and be effective in productivity. The most
important factor of growth of a rural community is optimizing its
cultural, social and economic condition that through establishing this
telecenter we witnessed the growth of those factors in Gharnabad
village. It is worth mentioning that a branch of post bank is located in
this center.
Livan Village
Eastern Livan village is located in Golestan province and southwest
of Bandar Gaz and it is 10 Km. far from Bandar Gaz. From the north, this
village ends to Caspian Sea, from the south, it ends to the forests of
Albors mountains (Jahan Moora), from the east, and it ends to Nokandeh
city and from the west it reachs to Hashtikeh village. The second rural
telecenter of Iran inaugurated in autumn of 2005 in eastern Livan
village. This center was run with the effort of villagers and private
and governmental sectors' support. This telecenter is alike the
first one regarding its extent and facilities. In this center, like
Gharnabad's rural telecenter, several services are presented such
as: electronic banking, promotional and computer education, research
works, remote working services, and post and internet services. Holding
different meetings of local non-governmental associations and
organizations and diverse training for different governmental sections
are done here, hence this center is considered effective by the youth
and authorities.
Regarding high number of educated people in this village and
surrounding villages, it is predicted that this center would become a
place for holding educational courses up to university levels and used
as a connecting point of the region with virtual universities for
developing remote education.
Bala Jade Village
Bala Jade is a beautiful village in Alborz northern slope having
dense forest in its south which has impressive landscape. This village
is located in Golestan province and in the central part of Kordkoy. Bala
Jade has mild climate due to its vicinity of the forest, the sea and the
mountain. It is cold in winter and mild in summer. There are two rivers
on the east and west of the village. It has also scenic heels named Anar
heel, Noordele and Sezdar natural heel. The castles of Bala Jade are
Tagh Castle, Shah neshin castle and Ghasran Castle.
This telecenter is alike the first and second one regarding its
extent and facilities. In this center, several services are presented
such as: electronic banking, doing researches, distant education
especially for illiterate or low-literate people, technical and
professional training, training health related issues, training dealing
with natural events and post and internet services.
doi: 10.3846/20294913.2012.685110
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Sarfaraz Hashemkhani Zolfani (1), Maedeh Sedaghat (2), Edmundas
Kazimieras Zavadskas (3)
(1) Shomal University, Department of Industrial Engineering, P. O.
Box 731, Amol, Mazandaran, Iran
(2) Young Research Club, Sari Branch Azad University, P. O. Box
194-48164, Sari, Iran
(3) Vilnius Gediminas Technical University, Institute of Internet
and Intelligent Technologies, Sauletekio al. 11, LT-10223 Vilnius,
Lithuania
E-mails: (1)
[email protected]; (2)
[email protected]; (3)
[email protected] (corresponding
author)
Received 30 December 2011; accepted 07 April 2012
Sarfaraz HASHEMKHANI ZOLFANI got a B.S in Industrial Management and
M.S. in Industrial Engineering-Productivity and System Management from
Shomal University of Amol, Iran. He was accepted in M.S. without
national exam because he was ranked as the top student and regarding his
good GPA in B.S. He is the author of more than 40 scientific papers in
International Conferences and International Journals which were
published, accepted or under reviewing. His research interests include
Performance Evaluation, Strategic Management, Decision-making Theory,
Supply Chain Management, (Fuzzy) Multi Criteria Decision Making and
Marketing.
Maedeh SEDAGHAT got a B.S. in English Language Translation and an
M.S. in Executive Master of Business Administration (EMBA). She is a
graduate of Payame Noor University, Babol, Iran. She was graduated with
high GPA in both B.S and M.S courses. She is the author of more than 10
scientific papers in International Journals which were published,
accepted or under reviewing. Her research interests include Productivity
Improvement, Entrepreneurship, Outsourcing, Performance Evaluation,
Decision-making Theory, Supply Chain Management and (Fuzzy) Multi
Criteria Decision Making.
Edmundas Kazimieras ZAVADSKAS.Prof., Head of the Department of
Construction Technology and Management at Vilnius Gediminas Technical
University, Vilnius, Lithuania. He has a PhD in Building Structures
(1973) and Dr Sc. (1987) in Building Technology and Management. He is a
member of the Lithuanian and several foreign Academies of Sciences. He
is Doctore Honoris Causa at Poznan, Saint-Petersburg, and Kiev
universities as well as a member of international organisations; he has
been a member of steering and programme committees at many international
conferences. E. K. Zavadskas is a member of editorial boards of several
research journals. He is the author and co-author of more than 400
papers and a number of monographs in Lithuanian, English, German and
Russian. Research interests are: building technology and management,
decision-making theory, automation in design and decision support
systems.
Table 1. Comparative comparison of Iran's telecom
network performance between 2005 and 2010
Index 2005 2006
1 Fixed telephone 20340060 22626944
diary
2 Penetration index 29/71 32/57
of fixed telephone
3 Mobile phone diary 8510513 15385289
4 Penetration index 12/43 22/20
of mobile phone
5 Villages that have 47955 51058
communication
6 Rural ICT Centers 963 2287
7 Urban public 141912 167366
telephone
8 Remote public 64774 89460
telephones
9 Data access ports 14897 16392
10 Number of Internet 8800000 12000000
users
11 Development 716 956
of information
transfer network
(city)
Index 2007 2008
1 Fixed telephone 2352089 24709447
diary
2 Penetration index 33/45 33/95
of fixed telephone
3 Mobile phone diary 24509714 31423104
4 Penetration index 34/20 43/20
of mobile phone
5 Villages that have 52784 53845
communication
6 Rural ICT Centers 5590 8200
7 Urban public 186198 217819
telephone
8 Remote public 124314 162055
telephones
9 Data access ports 36806 50818
10 Number of Internet 12800000 21000000
users
11 Development 1182 1220
of information
transfer network
(city)
Index 2009 2010
1 Fixed telephone 25410361 25466778
diary
2 Penetration index 34/04 34.40
of fixed telephone
3 Mobile phone diary 35427101 42000000
4 Penetration index 47/90 53.10
of mobile phone
5 Villages that have 52596 53000
communication
6 Rural ICT Centers 9812 10000
7 Urban public 228000 241000
telephone
8 Remote public 176600 186000
telephones
9 Data access ports 91016 303000
10 Number of Internet 26500000 27500000
users
11 Development 1223 1223
of information
transfer network
(city)
(http://www.tci.ir/s40/page5.aspx?lang=Fa)
* Statistics of Iran's telecom network performance
(comparative comparison for years 2005 to 2010, Iran
ICT Corporation 2011 report)
Table 2. Linguistic variables describing criteria's weights
and rating values
Linguistic scale Fuzzy Membership function
for importance numbers for
fuzzy AHP
Just equal
Equal importance [??] [[mu].sub.M] (x) =
(3 - x)/(3 - 1)
Weak importance of [??] [[mu].sub.M] (x) =
one over another (x - 1)/(3 - 1)
[[mu].sub.M] (x) =
(5 - x)/(5 - 3)
Essential or strong [??] [[mu].sub.M] (x) =
importance (x - 3)/(5 - 3)
[[mu].sub.M] (x) =
(7 - x)/(7 - 5)
Very strong importance [??] [[mu].sub.M] (x) =
(x - 5)/(7 - 5)
[[mu].sub.M] (x) =
(9 - x)/(9 - 7)
Extremely preferred [??] [[mu].sub.M] (x) =
(x - 7)/(9 - 7)
If factor i has one of the above
numbers assigned to it when compared
to factor j, then j has the
reciprocal value when compared with i
Linguistic scale Domain Triangular
for importance fuzzy scale
(l, m, u)
Just equal (1.0, 1.0, 1.0)
Equal importance 1 [less than or (1.0, 1.0, 3.0)
equal to] x [less
than or equal to] 3
Weak importance of 1 [less than or (1.0, 3.0, 5.0)
one over another equal to] x [less
than or equal to] 3
3 [less than or
equal to] x [less
than or equal to] 5
Essential or strong 3 [less than or (3.0, 5.0, 7.0)
importance equal to] x [less
than or equal to] 5
5 [less than or
equal to] x [less
than or equal to] 7
Very strong importance 5 [less than or (5.0, 7.0, 9.0)
equal to] x [less
than or equal to] 7
7 [less than or
equal to] x [less
than or equal to] 9
Extremely preferred 7 [less than or (7.0, 9.0, 9.0)
equal to] x [less
than or equal to] 9
If factor i has one of Reciprocals of above
the above numbers [??] [approximately equal to]
assigned to it when (1/[u.sub.1], 1/[m.sub.1],
compared to factor j, 1/[l.sub.1])
then j has the
reciprocal value when
compared with i
Table 3. Background information of experts
Variable Items NO Variable Items NO
1. Education Bachelor 2 3. Gender Male 8
background Master 5 Female 2
PhD 3
2. Groups Government 4 4. Age 31-40 6
Researcher 6 41-50 4
Table 4. Fuzzy pair-wise comparison matrix
C1 C2 C3 C4
C1 1, 1, 1 1, 1, 3 1, 3, 5 1/3, 1, 1
C2 1/3, 1, 1 1, 1, 1 1, 3, 5 1/5, 1/3, 1
C3 1/5, 1/3, 1 1/5, 1/3, 1 1, 1, 1 1/9, 1/7, 1/5
C4 1, 1, 3 1, 3, 5 5, 7, 9 1, 1, 1
C5 1/5, 1/3, 1 1, 3, 5 3, 5, 7 1/3, 1, 1
C6 1/7, 1/5, 1/3 1/5, 1/3, 1 1, 1, 3 1/3, 1, 1
C7 1/9, 1/7, 1/5 1/7, 1/5, 1/3 1, 1, 1 1/9, 1/7, 1/5
C5 C6 C7
C1 1, 3, 5 3, 5, 7 5, 7 ,9
C2 1/5, 1/3, 1 1, 3, 5 3, 5, 7
C3 1/7, 1/5, 1/3 1/3, 1, 1 1, 1, 1
C4 1, 1, 3 1, 1, 3 5, 7, 9
C5 1, 1, 1 1, 1, 3 3, 5, 7
C6 1/3, 1, 1 1, 1, 1 1, 1, 3
C7 1/7, 1/5, 1/3 1/3, 1, 1 1, 1, 1
Table 5. The final weights of criteria
Criteria C1 C2 C3 C4 C5 C6 C7
Final weights 0.25 0.19 0.008 0.25 0.22 0.08 0.002
Table 6. Initial decision-making matrix with values
Alternatives
[cross product] [cross product] [cross product]
[x.sub.1] [x.sub.2] [x.sub.3]
Optimum max max max
[A.sub.1] 5 6 7 7.5 7 8
[A.sub.2] 8 9 8 9 7.5 8
[A.sub.3] 7 8 7 8 7.5 8
Optimal value 9 9 8
Alternatives Criteria
[cross product] [cross product] [cross product]
[x.sub.4] [x.sub.5] [x.sub.6]
Optimum max max max
[A.sub.1] 7 7.5 7 8 8 9
[A.sub.2] 8 9 7.5 8 8 9
[A.sub.3] 7.5 8 8 9 8 9
Optimal value 9 9 9
Criteria
[cross product]
[x.sub.7]
Optimum max
[A.sub.1] 7 8
[A.sub.2] 7.5 8
[A.sub.3] 8 9
Optimal value 9
Table 7. Normalized decision-making matrix
Alternatives
[cross [cross [cross
product] product] product]
[X.sub.1] [X.sub.2] [X.sub.3]
[w.bar.sub.1] [w.bar.sub.2] [w.bar.sub.3]
[b.bar.sub.1] [b.bar.sub.2] [b.bar.sub.3]
max max max
Weights 0.25 0.25 0.19 0.19 0.008 0.008
[q.sub.j]
[A.sub.1] 0.555 0.667 0.777 0.833 0.875 1
[A.sub.2] 0.888 1 0.888 1 0.937 1
[A.sub.3] 0.777 0.888 0.777 0.888 0.937 1
Normalized values of criteria
[cross [cross
product] product]
[X.sub.4] [X.sub.5]
[w.bar.sub.4] [w.bar.sub.5]
[b.bar.sub.4] [b.bar.sub.5]
max max
Weights 0.25 0.25 0.22 0.22
[q.sub.j]
[A.sub.1] 0.777 0.833 0.777 0.888
[A.sub.2] 0.888 1 0.833 0.888
[A.sub.3] 0.833 0.888 0.888 1
[cross [cross
product] product]
[X.sub.6] [X.sub.7]
[w.bar.sub.6] [w.bar.sub.7]
[b.bar.sub.6] [b.bar.sub.7]
max max
Weights 0.08 0.08 0.002 0.002
[q.sub.j]
[A.sub.1] 0.888 1 0.777 0.888
[A.sub.2] 0.888 1 0.833 0.888
[A.sub.3] 0.888 1 0.888 1
Table 8. Weighted-normalized decision-making matrix
Alternatives
[cross product] [cross product] [cross product]
[x.sub.1] [x.sub.2] [x.sub.3]
[cross product] [cross product] [cross product]
[x.sub.1-1] [x.sub.1-2] [x.sub.1-3]
[[bar.w]. [[bar.w]. [[bar.w].
sub.1-1] sub.1-2] sub.1-3]
[[bar.b]. [[bar.b]. [[bar.b].
sub.1-1] sub.1-2] sub.1-3]
[A.sub.1] 0.138 0.166 0.147 0.158 0.007 0.008
[A.sub.2] 0.222 0.25 0.168 0.19 0.007 0.008
[A.sub.3] 0.194 0.222 0.147 0.168 0.007 0.008
[A.sup.+] 0.25 0.138 0.19 0.147 0.008 0.007
[A.sup.-] 0.138 0.25 0.147 0.19 0.007 0.008
Weighted-normalized values of criteria
[cross product] [cross product]
[x.sub.4] [x.sub.5]
[cross product] [cross product] [cross product]
[x.sub.2] [x.sub.3] [x.sub.4]
[[bar.w]. [[bar.w]. [[bar.w].
sub.2] sub.3] sub.4]
[[bar.b]. [[bar.b]. [[bar.b].
sub.2] sub.3] sub.4]
[A.sub.1] 0.17 0.195 0.194 0.208 0.071 0.08
[A.sub.2] 0.183 0.195 0.222 0.25 0.071 0.08
[A.sub.3] 0.195 0.22 0.208 0.222 0.071 0.08
[A.sup.+] 0.22 0.17 0.25 0.194 0.08 0.071
[A.sup.-] 0.17 0.22 0.194 0.25 0.071 0.08
Weighted-normalized values of criteria
TOPSIS grey SAW-G
[cross product]
[x.sub.5]
[[bar.w]. [a.sup [a.sup [c.sup Rank
sub.5] .+] .-] .+]
[[bar.b].
sub.5]
[A.sub.1] 0.001 0.001 0.1046 0.0724 0.330 3
[A.sub.2] 0.001 0.001 0.1042 0.0673 0.7645 1
[A.sub.3] 0.001 0.002 0.0956 0.0471 0.7131 2
[A.sup.+] 0.002 0.001
[A.sup.-] 0.0012 0.002
Weighted-normalized
values of criteria
SAW-G
L Rank
[A.sub.1] 0.110 3
[A.sub.2] 0.132 1
[A.sub.3] 0.124 2
[A.sup.+]
[A.sup.-]
