Revista de Matema´tica: Teor´ıa y Aplicaciones 2011 18(2) : 249–263
cimpa – ucr issn: 1409-2433
preference of effective factors in
suitable selection of microtunnel
boring machines (mtbm) by using the
fuzzy analytic hierarchy process
(fahp) approach
preferencia de factores de efectividad
en la seleccio´n apropiada de ma´quinas
taladradoras de microtu´nel (mtbm)
usando el enfoque del proceso
jera´rquico anal´ıtico difuso (fach)
Alireza Jafari∗ Mohammad Ataie†
Sayed Mohammad Esmaiel Jalali‡
Ahmad Ramazanzadeh§
Received: 6 Apr 2010; Revised: 20 May 2011;
Accepted: 1 Jun 2011
249
250 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
Abstract
The development of underground infrastructure, environmental
concerns, and economic trend is influencing society. Due to the in-
creasingly critical nature of installations of utility systems especially
in congested areas, the need for monitoring and control system has
increased. The microtunneling system will therefore have to provide
for possibility of minimized surface disruption. Suitable selection of
Microtunneling Boring Machine (MTBM) is the most curial decision
that manager must be done. Because once the trenchless excavation
has started, it might be too late to make any changes in equipment
without extra costs and delays. Therefore, the various factors and
parameters are affecting the choice of machine. In this paper dis-
cusses a developed methodology based on Fuzzy Analytic Hierarchy
Process (FAHP) in order to determine weights of the criteria and
sub criteria and then ranking them. Within the proposed model,
four criteria site, machinery, structural, labor force impact and 18
sub-criteria are specified. The linguistic level of comparisons pro-
duced by experts are tapped and constructed in a form of triangular
fuzzy numbers in order to construct fuzzy pair wise comparison ma-
trices. Therefore, FAHP uses the pair wise comparison matrices for
determining the weights of the criteria and sub-criteria.
Keywords: Microtunnel Boring Machines (MTBMs); Fuzzy Analytic
Hierarchy Process (FAHP); trenchless technology.
Resumen
El desarrollo de infraestructura subterra´nea, con preocupaciones
ambientales y tendencias econo´micas, esta´ influyendo a la sociedad.
Debido a la naturaleza crecientemente cr´ıtica de las instalaciones de
sistemas utilitarios, especialmente en a´reas congestionadas, ha au-
mentado la necesidad de sistemas de monitoreo y control. Por lo
tanto el sistema de microtunelacio´n ayudara´ a minimizar la super-
ficie perturbada. La seleccio´n adecuada de Ma´quinas Taladradoras
de Microtu´nel (MTBM, por sus siglas en ingle´s) es la decisio´n ma´s
juiciosa que puede hacerse, puesto que una vez que la excavacio´n
sin zanjas ha iniciado, podr´ıa ser muy tarde para hacer cambios en
el equipo sin un costo ni atrasos adicionales. Luego, los diversos
factores y para´metros afectan la escogencia de la ma´quina. En este
art´ıculo se discute una metodolog´ıa desarrollada, que se basa en el
∗Faculty of Mining Engineering, Petroleum & Geophysics, Shahrood University of
Technology, Hafte-Tir Square, Shahrood, Iran. E-Mail: ataei@shahroodut.ac.ir
†Same address as A. Jafari. E-Mail: ataei@shahroodut.ac.ir
‡Same address as A. Jafari. E-Mail: jalalisme@shahroodut.ac.ir
§Same address as A. Jafari. E-Mail: aramezanzadeh@gmail.com
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
selection of microtunnel boring machines (mtbm)... 251
Proceso Jera´rquico Anal´ıtico Difuso (FACH) para determinar pe-
sos de los criterios y subcriterios, y luego ordenarlos. En el modelo
propuesto se especifican cuatro criterios de sitio, maquinaria, es-
tructura, impacto de la fuerza laboral y 18 subcriterios. Los niveles
lingu¨´ısticos de comparaciones producidos por expertos se construyen
en forma de nu´meros difusos triangulares para construir matrices de
comparacio´n difusa por parejas. Por lo tanto el FAHP usa las ma-
trices de comparacio´n por parejas para determinar los pesos de los
criterios y subcriterios.
Palabras clave: Ma´quinas Taladradoras de Microtu´nel (MTBMs), Pro-
ceso Jera´rquico Ana´ıtico Difuso (FAHP), tecnolog´ıa sin zanjas.
Mathematics Subject Classification: 90C99.
1 Introduction
The conventional method (open-cut), which traditionally has been used
for construction, replacement, and repair of conduit construction. This
method includes direct installation of utility system into open-cut trenches
(Najafi, 2005). The problems connected to this method which has resulted
the open-cut method is more time consuming and does not always yield
the most cost-effective method of pipe installation (FSTT, 2006). Due to
the increasingly critical nature of installation of utility systems especially
in congested area, which has resulted in a growing demand for trenchless
technology as an alternative to traditional construction methods (Read.G,
2004). Microtunneling, one of the trenchless construction methods. Ac-
cording to ASCE’s Standard Construction Guidelines for microtunneling,
microtunneling can be defined as “a remotely controlled and guided pipe
jacking technique that provides continuous support to the excavation face
and does not require personnel entry into the tunnel” (ASCE, 2001). Nev-
ertheless, microtunnel machines are very expensive and few contractors
have extensive experience with this technology. Therefore, in order to
make a right decision on suitable selection of microtunnel machine and
eventually successful completion of a trenchless construction project re-
quires a clear understanding of effective and major criteria that will be
play important role in the selection of the suitable microtunneling ma-
chine. Because once the trenchless excavation has started, it might be
too late to make any changes in equipment without extra costs and de-
lays (Moser and Folkman, 2008). A number of related criteria make the
decision making process more complicated and more difficult to reach a
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
252 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
solution. Therefore, evaluating all known criteria related to the microtun-
nel machines selection by using the decision making process is extremely
significant.
Therefore, the main objective of this paper is to present a systemic
procedure the fuzzy analytic hierarchy process (FAHP) for determining
weights of the criteria and sub criteria and then ranking them. The study
was supported by results that were obtained from a questionnaire carried
out to know the opinions of the experts in this subject, where expert’s com-
parison judgments are represented as fuzzy triangular numbers in order to
construct fuzzy pair wise comparison matrices. Therefore, the fuzzy ana-
lytic hierarchy process (FAHP) uses the pair wise comparison matrices for
determining the weights of the criteria and sub-criteria. Therefore, first,
noteworthy factors in suitable selection of Microtunnel Boring Machines
are described and then the basic principles of fuzzy set theory together
with FAHP in next section are illustrated.
2 Summary of parameters affecting the selection
microtunnel boring machines
Four groups of factors that have relation with MTBM selection such as,
geological and geotechnical properties, machinery and environmental in-
corporating with human are affecting the choice of MTBMs. These are
considered as a major criteria. Distribution of main criteria and sub crite-
ria are illustrated in Table 1. In order to suitable selection of MTBM with
the help of site information and appropriate factors, firstly, a comprehen-
sive questionnaire including main criteria and their sub criteria of MTBM
selection is designed to quantify the degree of importance and affecting
factors in the process. Then, nineteen decision makers from different ar-
eas evaluate the importance of these factors with the help of mentioned
questionnaire. Each person filling the questionnaire has to mark one of
the following categories for each parameter: 1: Very Weak Importance;
2: Weak Importance; 3: Moderate Importance; 4: Strong Importance; 5:
Very Strong Importance.
3 Membership function
An element of the variable can be a member of the fuzzy set through a
membership function that can take values in the range from 0 to 1. Mem-
bership functions (MF) can be chosen by the user arbitrarily based on the
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
selection of microtunnel boring machines (mtbm)... 253
Factors Subcriteria
Soil characteristics Type of soil
Permeability
Abrasive
Granulometric
Shear strength
Time depended behavior
Plasticity
Water content
Effective stress
Machine characteristics Flexibility
Thrust
Torque
Capability of control deviance
from their path
Construction characteristics Shape
Length
Diameter
Depth
Environmental and labor force impact Downfall of atmospheric
Allowable of subsidence
Experience and proficiency
of labor force
Involved Surface
Table 1: Distribution of parameters affecting the choice of MTBM.
user’s experience or can also be designed using machine learning methods
(e.g., artificial neural networks, genetic algorithms, etc.). There are dif-
ferent shapes of membership functions; triangular, trapezoidal, piecewise-
linear, Gaussian, bell shaped, etc. In this study, triangular membership
functions are used. In this study expert’s comparison, judgments are rep-
resented as fuzzy triangular numbers in order to construct fuzzy pair wise
comparison matrices. In this study, triangular membership functions are
used. Triangular MF is shown in Fig. 1.
In Fig. 1, points l, m, and u in the triangular MF represent the
x coordinates of the three vertices of µM(x) in a fuzzy set M (l: lower
boundary and u: upper boundary where the membership degree is zero,
m: the center where membership degree is 1). Each triangular has linear
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
254 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
Figure 1: A triangular fuzzy number.
representations on its left and right side such that its membership function
can be defined as:
µA =

0 if x < l
x−l
m−l if l ≤ x ≤ m
u−x
u−m if m ≤ x ≤ u
0 if x ≥ u.
These methods may give different ranking results and most methods are
tedious in graphic manipulation requiring complex mathematical calcu-
lation. The detailed description of FAHP method is illustrated in the
following section.
4 Fuzzy Analytic Hierarchy Process (FAHP)
The analytic hierarchy process (AHP) method first proposed by Saaty
(1980) shows the process of making a choice among a set of alternatives
and which provides a comparison of the considered options (Saaty, 1980;
Wei, Chien, & Wang, 2005). AHP divides a complicated system under
study into a hierarchical system of elements. Pair-wise comparisons are
made of the elements of each hierarchy by means of a nominal scale. Since
the evaluation, criteria are subjective and qualitative in nature; it is diffi-
cult for the experts and decision makers to express the preferences using
exact numerical values and to provide exact pair-wise comparison judg-
ments (Felix Chan, et al, 2007). Therefore, the traditional AHP still can-
not really reflect the human thinking style (Kahraman, Cebeci, & Ulukan,
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
selection of microtunnel boring machines (mtbm)... 255
2003). In order to overcome all these deficiency, FAHP methodology,
which is based on the concept of fuzzy set theory, was developed for solv-
ing the hierarchical problems. FAHP can adequately handle the inherent
uncertainty and imprecision of the human decision making process.
5 Methodology of FAHP
The proposed FAHP model to choice of suitable microtunnel boring ma-
chines (MTBMs) was originally introduced by Chang (1996). Put X =
{x1, x2, x3, . . . , xn} be an object set, and G = {g1, g2, g3, . . . , gn} be a goal
set. According to the method of Chang’s extent analysis, each object is
taken and extent analysis for each goal is performed respectively. There-
fore, m extent analysis values for each object can be obtained, with the
following signs:
M1gi ,M
2
gi , . . . ,M
m
gi , i = 1, 2, . . . , n (1)
where all the M jgi (j = 1, 2, . . . ,m) are triangular membership functions.
The steps of Chang’s extent analysis (Chang, 1996) are composed of the
following steps:
Step 1. Quantification of fuzzy number’s value with respect to the i–th
object is defined as
si =
m∑
j=1
M jgi ⊗
 n∑
i=1
m∑
j=1
M jgi
−1 . (2)
To obtain
∑m
j=1M
j
gi, the fuzzy addition operation of m extent anal-
ysis values for a particular matrix is performed such as
m∑
j=1
M jgi =
 m∑
j=1
lj ,
m∑
j=1
mj,
m∑
j=1
Uj
 . (3)
And to obtain [
∑n
i=1
∑m
j=1M
j
gi]
−1, the fuzzy addition operation of
M jgi (j = 1, 2, . . . ,m) values is performed such as
n∑
i=1
m∑
j=1
M jgi =
(
n∑
i=1
li,
n∑
i=1
mi,
n∑
i=1
Ui
)
. (4)
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256 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
Detailed specification of Hamadan city sewers are illustrated in the
following section. Then the inverse of the vector above is computed,
such as  n∑
i=1
m∑
j=1
M jgi
−1 = ( 1∑n
i=1 Ui
,
1∑n
i=1mi
,
1∑n
i=1 li
)
. (5)
Step 2. As M1 = (l1,m1, u1) and M2 = (l2,m2, u2) are two triangular
fuzzy numbers, the degree of possibility ofM2 = (l2,m2, u2) ≥M1 =
(l1,m1, u1) is defined as
V (M2 ≥M1) = sup
y≥x
[min(µM1(x), µM2(y))] (6)
Moreover, can be expressed as follows:
V (M2 ≥M1) = hgt(M1 ∩M2) = µM2(d) (7)
µM2(d) =

1 if m2 ≥ m1
0 if l1 ≥ u2
l1−u2
(m2−u2)−(m1−u1) otherwise.
(8)
Where, d is the ordinate of the highest intersection point D be-
tween µm1 and µm2 to compare M1 and M2, we need both values of
V (M1 ≥M2) and V (M2 ≥M1) (see Fig. 2).
Figure 2: The intersection between M1 and M2.
Step 3. The degree possibility for a convex fuzzy number to be greater
than k convex fuzzy number Mi (i = 1, 2, . . . , k) can be defined by
V (M ≥M1,M2, . . . ,Mk) = V [(M ≥M1)]and . . . and(M ≥Mk)]
= minV (M ≥Mi), i = 1, 2, . . . , k.(9)
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selection of microtunnel boring machines (mtbm)... 257
Assume that d(Ai) = minV (Si ≥ Sk) for k = 1, 2, . . . , n; k 6= i.
Then the weight vector is given by
W ′ = (d′(A1), d′(A2), . . . , d′(An))T (10)
where Ai(i = 1, 2, . . . , n) are n elements.
Step 4. Via normalization, the normalized weight vectors are
W = (d(A1), d(A2), . . . , d(An))T (11)
where W is a non-fuzzy number.
These methods may give different ranking results and most methods
are tedious in graphic manipulation requiring complex mathematical cal-
culation. Decision makers from different backgrounds may define different
weight vectors. They usually cause not only the imprecise evaluation but
also serious persecution during decision process. For this reason, FAHP is
proposed to consider subjective judgments and to reduce the uncertainty
and vagueness in the decision process. Therefore, we proposed a group
decision based on FAHP to improve pair-wise comparison. Firstly each
decision maker (D), individually carry out pair-wise comparison by using
Saaty’s (Saaty, 1980) 1-9 scale (Table 2).
Comparison index score
Extremely preferred 9
Very strongly preferred 7
Strongly preferred 5
Moderately preferred 3
Equal 1
Intermediate values between the two adjacent judgments 2,4,6,7,8
Table 2: Pair-wise comparison scale (Saaty, 1980).
Then, a comprehensive pair-wise comparison matrix for site sub crite-
ria is built as in Table 3 by integrating nineteen decision makers’ grades
through Eq. (12) (Chen, Lin, & Huang, 2006). By this way, decision
makers’ pair-wise comparison values are transformed into triangular fuzzy
numbers as in Table 3. Moreover, for other cases pair-wise comparisons
are constituted:
Xij = (aij , bij , cij)
lij = min
k
{aijk},mij = 1
k
∑
k=1
bijk, uij = max
k
{cijk}. (12)
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
258 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
After forming fuzzy pair-wise comparison matrix for all criteria, weights
of all criteria and sub-criteria are determined by the help of FAHP. For
instance, firstly synthesis values must be calculated. From (Table 3), syn-
thesis values respect to main goal are calculated like in Eq. (2):
S11 = (6.7, 13.2, 39.9) ⊗ (0.004, 0.011, 0.025) = (0.028, 0.143, 0.98)
S12 = (2.95, 9.2, 17.9) ⊗ (0.004, 0.011, 0.025) = (0.012, 0.099, 0.44)
S13 = (2.8, 9.02, 19) ⊗ (0.004, 0.011, 0.025) = (0.011, 0.097, 0.47)
S14 = (3.95, 11.1, 33.4) ⊗ (0.004, 0.011, 0.025) = (0.016, 0.12, 0.82)
S15 = (6.8, 12.2, 34.2) ⊗ (0.004, 0.011, 0.025) = (0.028, 0.132, 0.84)
S16 = (2.9, 7.4, 13.4) ⊗ (0.004, 0.011, 0.025) = (0.012, 0.08, 0.33)
S17 = (5.8, 10.9, 34.2) ⊗ (0.004, 0.011, 0.025) = (0.024, 0.12, 0.84)
S18 = (4.8, 9.7, 19.9) ⊗ (0.004, 0.011, 0.025) = (0.02, 0.105, 0.49)
S19 = (4.2, 9.8, 19.9) ⊗ (0.004, 0.011, 0.025) = (0.017, 0.106, 0.75)
Then the degree of possibility ofMi overMj (i 6= j) can be determined
by Eq. (8) for structure sub-criteria as below:
V (s11 ≥ s12) = 1, V (s11 ≥ s13) = 1, V (s11 ≥ s14) = 1, V (s11 ≥ s15) = 1,
V (s11 ≥ s16) = 1, V (s11 ≥ s17) = 1, V (s11 ≥ s18) = 1, V (s11 ≥ s19) = 1,
V (s12 ≥ s11) = 0.9, V (s12 ≥ s13) = 1, V (s12 ≥ s14) = 0.95,
V (s12 ≥ s15) = 0.93, V (s12 ≥ s16) = 1, V (s12 ≥ s17) = 0.96,
V (s12 ≥ s18) = 0.99, V (s12 ≥ s19) = 0.99, V (s13 ≥ s11) = 0.91,
V (s13 ≥ s12) = 1, V (s13 ≥ s14) = 0.95, V (s13 ≥ s15) = 0.93,
V (s13 ≥ s16) = 1, V (s13 ≥ s17) = 0.96, V (s13 ≥ s18) = 0.98,
V (s13 ≥ s19) = 0.98.
V (s14 ≥ s11) = 0.97, V (s14 ≥ s12) = 1, V (s14 ≥ s13) = 1,
V (s14 ≥ s15) = 0.98, V (s14 ≥ s16) = 1, V (s14 ≥ s17) = 1,
V (s14 ≥ s18) = 1, V (s14 ≥ s19) = 1, V (s15 ≥ s11) = 0.99,
V (s15 ≥ s12) = 1, V (s15 ≥ s13) = 1, V (s15 ≥ s14) = 1,
V (s15 ≥ s16) = 1, V (s15 ≥ s17) = 1, V (s15 ≥ s18) = 1,
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
selection of microtunnel boring machines (mtbm)... 259
V (s15 ≥ s19) = 1, V (s16 ≥ s11) = 0.83, V (s16 ≥ s12) = 0.94,
V (s16 ≥ s13) = 0.95, V (s16 ≥ s14) = 0.89, V (s16 ≥ s15) = 0.85,
V (s16 ≥ s17) = 0.89, V (s16 ≥ s18) = 0.92, V (s16 ≥ s19) = 0.92,
V (s17 ≥ s11) = 0.97, V (s17 ≥ s12) = 1, V (s17 ≥ s13) = 1,
V (s17 ≥ s14) = 1, V (s17 ≥ s15) = 0.98, V (s17 ≥ s16) = 1,
V (s17 ≥ s18) = 1, V (s17 ≥ s19) = 1, V (s18 ≥ s11) = 0.92,
V (s18 ≥ s12) = 1, V (s18 ≥ s13) = 1, V (s18 ≥ s14) = 0.97,
V (s18 ≥ s15) = 0.94, V (s18 ≥ s16) = 1, V (s18 ≥ s17) = 0.97,
V (s18 ≥ s19) = 1, V (s19 ≥ s11) = 0.95, V (s19 ≥ s12) = 1,
V (s19 ≥ s13) = 1, V (s19 ≥ s14) = 0.98, V (s19 ≥ s15) = 0.96,
V (s19 ≥ s16) = 1, V (s19 ≥ s17) = 0.98, V (s19 ≥ s18) = 1.
With the help of eq. (10), the minimum degree of possibility can be
stated as below:
d′(c11) = min(1, 1, 1, 1, 1, 1, 1, 1) = 1
d′(c12) = min(0.9, 1, 0.95, 0.93, 1, 0.96, 0.99, 0.99) = 0.9
d′(c13) = min(0.91, 1, 0.95, 0.93, 1, 0.96, 0.98, 0.98) = 0.91
d′(c14) = min(0.97, 1, 1, 0.98, 1, 1, 1, 1) = 0.97
d′(c15) = min(0.99, 1, 1, 1, 1, 1, 1, 1) = 0.99
d′(c16) = min(0.83, 0.94, 0.95, 0.89, 0.85, 0.89, 0.92, 0.92) = 0.83
d′(c17) = min(0.97, 1, 1, 1, 0.98, 1, 1, 1) = 0.97
d′(c18) = min(0.92, 1, 1, 0.97, 0.94, 1, 0.97, 1) = 0.92
d′(c19) = min(0.95, 1, 1, 0.98, 0.96, 1, 0.98, 1) = 0.95.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
260 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
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,1
.2
,3
)
(0
.4
,1
.3
,3
)
(0
.3
,1
.1
,3
)
(0
.3
,0
.9
,1
.4
)
E
ff
ec
ti
v
e
st
re
ss
(0
.3
,0
.8
,1
.4
)
(0
.4
,1
.3
,7
)
(0
.4
,1
.4
,7
)
(0
.3
,1
,2
.3
)
(0
.3
,0
.8
,1
.4
)
T
im
e
d
ep
en
d
ed
P
la
st
ic
it
y
W
a
te
r
E
ff
ec
ti
v
e
b
eh
av
io
r
ta
b
le
st
re
ss
T
y
p
e
o
f
so
il
(1
,2
.1
,9
)
(0
.6
,1
.3
,1
.8
)
(0
.7
1
,1
.4
,3
)
0
.7
,1
.5
,3
)
A
b
ra
si
v
e
(0
.4
,1
.3
,2
)
(0
.1
4
,0
.9
,1
.8
)
(0
.3
,1
,2
.3
)
(0
.1
4
,1
.1
4
,2
)
G
ra
n
u
lo
m
et
ry
(0
.4
,1
.8
,7
)
(0
.3
,1
.1
,1
.8
)
(0
.3
,1
.2
,3
)
(0
.4
,1
.3
,3
)
S
tr
en
g
th
(1
,1
.9
,7
)
(0
.7
,1
.2
,1
.8
)
(0
.7
,1
.3
,3
)
(1
,1
.4
,3
)
T
im
e
d
ep
en
d
ed
b
eh
av
io
r
(1
,1
,1
)
(0
.1
4
,0
.8
,1
.4
)
(0
.3
,0
.8
,1
)
(0
.1
4
,0
.9
,1
.7
)
P
la
st
ic
it
y
(0
.7
,1
.7
,7
)
(1
,1
,1
)
(0
.6
,1
.2
,3
)
(0
.7
,1
.3
,3
)
W
a
te
r
ta
b
le
(1
,1
.4
,3
)
(0
.3
,1
,1
.8
)
(1
,1
,1
)
(1
.1
,1
.3
,3
)
E
ff
ec
ti
v
e
st
re
ss
(0
.6
,1
.5
,7
)
(0
.3
,0
.9
,1
.4
)
(0
.4
,1
,2
.3
)
(1
,1
,1
)
Table 3: Fuzzy comprehensive pair-wise comparison matrix for sub criteria
of site.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
selection of microtunnel boring machines (mtbm)... 261
Priority weights form vector W ′ = (1, 0.9, 0.91, 0.97, 0.99, 0.83, 0.97,
0.92, 0.95). After the normalization of these values priority weights respect
to main goal are calculated as W = (0.12, 0.11, 0.11, 0.12, 0.12, 0.01,
0.11, 0.11, 0.11). The importance of sub criteria must be computed, after
computation of each criterion. Likewise the pervious stages in order to
the importance of pair wise matrix for each criterion are computed, which
their final weights are shown Fig. 3 to Fig. 6.
Figure 3: Global priority weights
of site sub criteria.
Figure 4: Global priority weights
of machinery’s sub criteria.
Figure 5: Global priority weights
of structural’s sub criteria.
Figure 6: Global priority weights
of environmental and labor force
impact sub criteria.
According to Fig. 3 to Fig. 6, type of soil, thrust, diameter and
involved surface with get highest local weight 0.12, 0.36, 0.34, 0.4 respec-
tively among their sub criteria are known as effective agent among them.
Rev.Mate.Teor.Aplic. (ISSN 1409-2433) Vol. 18(2): 249–263, July 2011
262 a. jafari – m. ataie – s.m.e. jalali – a. ramazanzadeh
6 Conclusion
Suitable MTBM selection is a key factor to success in trenchless projects
from the safety, time saving and associated costs point of views. On
the other hand, the decision making process for selecting the appropriate
MTBM poses a complex task which needs to consider many technical,
economical, social and environmental factors. In this paper, the FAHP
method has been presented to reduce the difficulties in taking into consid-
eration the many decision criteria and to handle the inherent uncertainty
and imprecision of the human decision making process. Based on the
developed FAHP approach, soil type, strength, flexibility, diameter and
interference with traffic can be considered as the critical factors.
Acknowledgement
The authors would like to thank the experts who helped us in this research.
Grateful thanks are recorded to Dr. M.Najafi (USA) for kind help and
guidance.
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