InterCriteria Decision Making Approach for Iron Powder
Briquetting
Lyubka Doukovska
1
, Dimitar Karastoyanov
1
, Nikolay Stoymenov
1
and Ivan Kalaykov
2
1
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences
Acad. G. Bonchev str., bl. 2, 1113 Sofia, Bulgaria
2
Örebro University, School of Science and Technology
SE-701 82 Örebro, Sweden
Keywords: InterCriteria decision making, Index matrix, Impact briquetting.
Abstract: In this paper, we present approach, called ‘InterCriteria Decision Making’ that utilizes the apparatus of
index matrices and intuitionistic fuzzy sets which from an existing multiobject multicriteria evaluation table
generates a new table that contains estimations of the pairwise relations among the set of evaluating criteria.
In the presented paper for the analysis purposes we have used experimental results of impact briquetting of
iron powder. In this study we illustrate the application of the one original methodology to the data achieved
for the following parameters - distance, speed and acceleration of the impacting bodies. The research and
the obtained results will show relations between the briquetting process parameters which will lead to
increase in its efficiency.
1 INTRODUCTION
Producing briquettes using metal chips and powder
is an actual scientific problem which is reflected in a
lot off publications. This technology recently is
being applied more widely as per (Penchev, 2014;
Radeva et al., 2014; Gustavson at al., 2014;
Doremus at al., 2010; Scoglund, 2001). The positive
results related to the density increasing with the
impact power increases are a reason for investigating
the effect using iron powder. In paper (Gustavson at
al., 2014) it is shown that when compacting iron
powder with impact speed 15 [m/s] a cylindrical
sample of size height Н = 20 [mm], diameter D = 25
[mm] and density ρ = 7.4 [gr/cm
3
] has been
produced. At the same time the monolith material
has a density ρ = 7.5 [gr/cm
3
]. This is mainly
influenced by the high impact energy determined by
the higher speed.
In this study we illustrate the application of the
one original methodology to the data achieved for
the following parameters - distance, speed and
acceleration of the impacting bodies. These are
analyzed by means of high speed camera and the
applicable software. The impact energy (Е
у
) and
power (F
у
) are calculated. To get more experimental
data an Xray tomograph Nikon XTH 225 Compact
Industrial CT Scanner has been used. They are part
of the equipment of the Smart Lab at IICT.
In process of the metal chips briquetting,
mechanical and hydraulic presses with nominal
force of several hundred to several thousand kN are
used. The goal is to obtain briquettes with good
density - the ratio H/D for different materials vary
within wide limits (H/D = 0.8 – 0.25), where H is
the height, and D is the diameter of the briquette.
The greater is the density of the briquettes, the
smaller are the losses in the transport and melting.
Basic data used to evaluate the effect of briquetting
operation is the specific density of the briquette (ρ,
[g/cm
3
]), and specific contact pressure for
briquetting (P, [MPa]).
In the presented paper we have analyzed
experimental results of iron powder briquetting. The
experiments are conducted using a complicated
(combined) impacting device, shown on Figure 1.
292
Doukovska L., Karastoyanov D., Stoymenov N. and Kalaykov I.
InterCriteria Decision Making Approach for Iron Powder Briquetting.
DOI: 10.5220/0005888402920296
In Proceedings of the Fifth International Symposium on Business Modeling and Software Design (BMSD 2015), pages 292-296
ISBN: 978-989-758-111-3
Copyright
c
 2015 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Main element of this device is a cold rocket
engine 12, working on pressurized air with pressure
up to 33 [MPa]. The usage of such an engine allows
for a combined impact with power F
y
and additional
power R.
Figure 1: Laboratory stend for a complicated impact
investigation:
1 – main plate weight of 220 [kg]; 2 – plastic element for
elastic impact investigation; 3 – plastic impact sensor; 4 –
inductive speed sensors; 5 – lower position inductive air
on/off sensor; 6 – falling part rails; 7 – trigger; 8 –
solenoid valve; 9 – air pressure controller; 10 – upper
position inductive air on/off sensor; 11, 15 – light sensor
and source for the falling part speed measurement; 12 –
cold rocket engine; 13 – falling part with weight of 6.17
[kg]; 14 – plate for sensors 4, 5, 11; 16 – control panel.
To conduct the iron powder briquetting
experiments we use the same stand and equipment
as we did for the iron chips. The size of the particles
of the iron powder we used (brand AS29-100) is
determined using Fritch Analysette 22 Nano Tec+.
After high speed filming of the impact the
material is processed using Vicasso 2009 product
and as a result we have diagrams of the distance,
speed and acceleration. Based on that we determine
the impact speed V
y
and acceleration A
y
. Then the
impact energy and power are being calculated using
this data.
2 INTERCRITERIA DECISION
MAKING APPROACH
The presented multicriteria decision making method
is based on two fundamental concepts: intuitionistic
fuzzy sets and index matrices. It is called
‘InterCriteria decision making’.
Intuitionistic fuzzy sets defined by Atanassov
(Atanassov, 1983; Atanassov, 1986; Atanassov,
1999; Atanassov, 2012) represent an extension of
the concept of fuzzy sets, as defined by Zadeh
(Zadeh, 1965), exhibiting function µ
A
(x) defining the
membership of an element x to the set A, evaluated
in the [0; 1] - interval. The difference between fuzzy
sets and intuitionistic fuzzy sets (IFSs) is in the
presence of a second function ν
A
(x) defining the non-
membership of the element x to the set A, where:
0 ≤ µ
A
(x) ≤ 1,
0 ≤ ν
A
(x) ≤ 1,
0 ≤ µ
A
(x) + ν
A
(x) ≤ 1.
The IFS itself is formally denoted by:
A = {〈x, µ
A
(x), ν
A
(x)〉 | x ∈ E}.
Comparison between elements of any two IFSs,
say A and B, involves pairwise comparisons between
their respective elements’ degrees of membership
and non-membership to both sets.
The second concept on which the proposed
method relies is the concept of index matrix, a mat-
rix which features two index sets. The theory behind
the index matrices is described in (Atanassov, 1991).
Here we will start with the index matrix M with
index sets with m rows {C
1
,…,C
m
} and n columns
{O
1
,…,O
n
}:
11 1 1 1
1
1
1
1
1, , , ,
,, ,,
,, ,,
,, ,,
,
kln
iikilin
jjkjljn
m mjmlmn
kln
CO CO CO CO
iCO CO CO CO
jCO CO CO CO
mCO CO CO CO
OOOO
M
Ca a a a
Ca a a a
Ca a a a
Ca a a a
=
KKK
KKK
MMOMOMOM
KKK
MMOMOMOM
KKK
MMOMOMOM
KKK
where for every p, q (1 ≤ p ≤ m, 1 ≤ q ≤ n), C
p
is a
criterion (in our case, one of the twelve pillars), O
q
in an evaluated object, a
C
p
O
q
is the evaluation of the
q-th object against the p-th criterion, and it is
defined as a real number or another object that is
comparable according to relation R with all the rest
elements of the index matrix M, so that for each i, j,
k it holds the relation R(a
C
k
O
i
, a
C
k
O
j
). The relation R
has dual relation , which is true in the cases when
relation R is false, and vice versa.
For the needs of our decision making method,
pairwise comparisons between every two different
R
InterCriteria Decision Making Approach for Iron Powder Briquetting
293

criteria are made along all evaluated objects. During
the comparison, it is maintained one counter of the
number of times when the relation R holds, and
another counter for the dual relation.
Let be the number of cases in which the rel-
ations R(a
C
k
O
i
, a
C
k
O
j
) and R(a
C
l
O
i
, a
C
l
O
j
) are simul-
taneously satisfied. Let also be the number of
cases in which the relations R(a
C
k
O
i
, a
C
k
O
j
) and its
dual (a
C
l
O
i
, a
C
l
O
j
) are simultaneously satisfied. As
the total number of pairwise comparisons between
the object is n(n – 1)/2, it is seen that there hold the
inequalities:
.
For every k, l, such that 1 ≤ k ≤ l ≤ m, and for
n ≥ 2 two numbers are defined:
.
The pair constructed from these two numbers
plays the role of the intuitionistic fuzzy evaluation of
the relations that can be established between any two
criteria C
k
and C
l
. In this way the index matrix M
that relates evaluated objects with evaluating criteria
can be transformed to another index matrix M* that
gives the relations among the criteria:
The final step of the algorithm is to determine
the degrees of correlation between the criteria,
depending on the user’s choice of µ and ν. We call
these correlations between the criteria: ‘positive
consonance’, ‘negative consonance’ or ‘dissonance’.
Let α, β ∈[0; 1] be given, so that α + β ≤ 1. We
call that criteria C
k
and C
l
are in:
• (α, β) - positive consonance, if µ
C
k
,C
l
> α
and ν
C
k
,C
l
< β
;
• (α, β) - negative consonance, if µ
C
k
,C
l
< β
and ν
C
k
,C
l
> α
;
• (α, β) - dissonance, otherwise.
Obviously, the larger α and/or the smaller β, the
less number of criteria may be simultaneously
connected with the relation of (α, β) - positive con-
sonance. For practical purposes, it carries the most
information when either the positive or the negative
consonance is as large as possible, while the cases of
dissonance are less informative and can be skipped.
3 EXPERIMENTAL RESULTS
In the presented paper for the analysis purposes we
have used experimental results of impact briquetting
of iron powder. Figure 2 shows the distance, speed
and acceleration diagrams when briquetting iron
powder.
a)
b)
c)
Figure 2: Distance (a), speed (b) and acceleration (c)
diagrams when briquetting iron powder.
,kl
S
μ
,kl
S
ν
R
,,
(1)
0
2
kl kl
nn
SS
μν
−
≤+≤
,,
,,
2, 2
(1) (1)
kl kl
kl kl
CC CC
SS
nn nn
μν
μν ==
−−
11 11 1 1
11
1
1,C,C ,C,C
,C ,C ,C ,C
*
.
,,
,,
mm
mm mmmm
m
CC C C
mCC C C
CC
M
C
C
μν μ ν
μν μ ν
=
K
K
MMOM
K
Fifth International Symposium on Business Modeling and Software Design
294

Figure 2 shows also that the acceleration and
hence the force when briquetting iron powder is
38.4% higher compared to the corresponding values
when briquetting iron chips.
Our experiments show that in order to improve
the capabilities of this deformation process,
additional investigations are required. We also prove
that to have a better density in detail’s walls, where
we have big tension powers, a lubricant has to be
added.
The analysis shows that for specific energy
Е
c
=488 [J/cm
3
] and impact speed V
y
=7.37 [m/s] a
cylindrical compacted iron powder sample has been
produced, having density of ρ=6.7582 [gr/cm
3
].
These impact process parameters can be assumed the
best ones achieved for rocket engine thrust of R=226
[kN].
Based on the experimental research the values of
eleven parameters of the iron powder briquetting
process have been obtained:
1 - V
y
– Impact speed, [m/s];
2 - A
у
– Impact acceleration, [m/s
2
];
3 - H
Δ
– Trimming height, [mm];
4 - Н – Briquette height, [cm];
5 - D – Briquette diameter, [cm];
6 - V – Briquette volume, [cm
3
];
7 - G – Briquette weight, [gr];
8 - ρ – Briquette density, [gr/cm
3
];
9 - E
у
– Impact energy, [J];
10 - E
c
– Impact specific energy, [J/cm
3
];
11 - F
y
– Power of impact, [N].
Table 1: Membership pairs of the intuitionistic fuzzy InterCriteria correlations for the iron powder briquette.
μ
1 2 3 4 5 6 7 8 9 10 11
1
1.000 0.528 0.389 0.417 0.333 0.417 0.611 0.611 1.000 0.611 0.528
2 0.528 1.000 0.694 0.167 0.250 0.167 0.306 0.639 0.528 0.861 1.000
3 0.389 0.694 1.000 0.361 0.278 0.361 0.167 0.333 0.389 0.611 0.694
4 0.417 0.167 0.361 1.000 0.722 1.000 0.694 0.306 0.417 0.028 0.167
5 0.333 0.250 0.278 0.722 1.000 0.722 0.722 0.500 0.333 0.278 0.250
6 0.417 0.167 0.361 1.000 0.722 1.000 0.694 0.306 0.417 0.028 0.167
7 0.611 0.306 0.167 0.694 0.722 0.694 1.000 0.611 0.611 0.333 0.306
8 0.611 0.639 0.333 0.306 0.500 0.306 0.611 1.000 0.611 0.722 0.639
9 1.000 0.528 0.389 0.417 0.333 0.417 0.611 0.611 1.000 0.611 0.528
10 0.611 0.861 0.611 0.028 0.278 0.028 0.333 0.722 0.611 1.000 0.861
11 0.528 1.000 0.694 0.167 0.250 0.167 0.306 0.639 0.528 0.861 1.000
These have been analysed applying InterCriteria
decision making approach. The results are presented
in Тable 1.
The results show a strong relation between the
parameter pairs: 1 (‘Impact speed‘) – 9 (‘Impact
energy‘); 2 (‘Impact acceleration‘) – 11 (‘Power of
impact‘); 4 (‘Briquette height‘) – 6 (‘Briquette
volume‘); 2 (‘Impact acceleration‘) – 10 (‘Impact
specific energy‘); 10 (‘Impact specific energy‘) – 11
(‘Power of impact‘); 5 (‘Briquette diameter‘) – 6
(‘Briquette volume‘); 5 (‘Briquette diameter‘) – 7
(‘Briquette weight‘).
Part of these relations is due to the specific
physical properties of the briquettes, which confirms
the reliability of the proposed InterCriteria decision
making approach. The benefit here is that this allows
for finding strong dependencies as well as such
where the relations are not so visible.
The graphical interpretation results with the
intuitionistic fuzzy pairs of InterCriteria
consonances is shown on Figure 3.
Figure 3: Geometrical visualisation of the InterCriteria
correlations for the case of iron powder briquette onto
the intuitionistic fuzzy interpretational triangle.
InterCriteria Decision Making Approach for Iron Powder Briquetting
295

4 CONCLUSION
The research conducted shows that when producing
rectangular form briquettes presence of air is
observed in the final product. This is due to not
absolutely complete filling of the peripheral part of
the briquette. As a result the briquettes are of low
density and decreased quality. To increase the
product quality it is proposed elements with smaller
size to be used. A possible solution is using iron
powder.
The present paper proves the application of this
original InterCriteria decision making approach,
which eases the analysis if the relations between the
criteria, giving better production quality.
ACKNOWLEDGEMENTS
The research work reported in the paper is partly
supported by the project AComIn “Advanced
Computing for Innovation”, Grant №316087, funded
by the FP7 Capacity Programme (Research Potential
of Convergence Regions) and partly supported under
the Project № DFNI-I-02-5/2014.
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