Selection of a suitable additive manufacturing process for soft robotics application using three-way decision-making

Abstract

Additive manufacturing technology has fostered its significant application in soft robotics fabrication due to the design freedom and ease of realizing complex geometries. The selection of an appropriate additive manufacturing process (out-of-material extrusion, vat photopolymerization, and powder bed fusion) is vital for the fabrication of soft robotics as the process greatly influences the quality of the part further affecting the functionality and service life. These pneumatically actuated robots in their service life are subjected to fatigue loading and handling of very delicate tasks; thus, the porosity (including pores characterization) and surface roughness are two critical quality parameters which should be considered while choosing the fabrication process. In this study, a three-way decision-making (a multi-criteria decision-making tool) approach is implemented for selecting an appropriate additive manufacturing process for the fabrication of high-quality parts for soft robotics applications. The results (ranking of AM processes) obtained using the proposed approach are compared with the conventional decision-making techniques, namely TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), MOORA (Multi-Objective Optimization by Ratio Analysis), and VIKOR (VIseKriterijumska Optimizacija). The sensitivity analysis carried out in this work also suggests that three-way decision-making is as effective as other MCDM tools and the vat photopolymerization process is the most suitable out of all for fabricating TPU actuators.

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The International Journal of Advanced Manufacturing Technology
https://doi.org/10.1007/s00170-024-13398-x
ORIGINAL ARTICLE
Selection ofasuitable additive manufacturing process forsoft
robotics application using three‑way decision‑making
SudhanshuGangwar1· PrateekSaxena1 · NaveenVirmani2· TobiasBiermann3,4· CarlSteinnagel4·
RolandLachmayer4
Received: 2 August 2023 / Accepted: 4 March 2024
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024
Abstract
Additive manufacturing technology has fostered its significant application in soft robotics fabrication due to the design
freedom and ease of realizing complex geometries. The selection of an appropriate additive manufacturing process (out-
of-material extrusion, vat photopolymerization, and powder bed fusion) is vital for the fabrication of soft robotics as the
process greatly influences the quality of the part further affecting the functionality and service life. These pneumatically
actuated robots in their service life are subjected to fatigue loading and handling of very delicate tasks; thus, the porosity
(including pores characterization) and surface roughness are two critical quality parameters which should be considered
while choosing the fabrication process. In this study, a three-way decision-making (a multi-criteria decision-making tool)
approach is implemented for selecting an appropriate additive manufacturing process for the fabrication of high-quality parts
for soft robotics applications. The results (ranking of AM processes) obtained using the proposed approach are compared
with the conventional decision-making techniques, namely TOPSIS (Technique for Order of Preference by Similarity to
Ideal Solution), MOORA (Multi-Objective Optimization by Ratio Analysis), and VIKOR (VIseKriterijumska Optimizacija).
The sensitivity analysis carried out in this work also suggests that three-way decision-making is as effective as other MCDM
tools and the vat photopolymerization process is the most suitable out of all for fabricating TPU actuators.
Keywords Additive manufacturing· Soft robotics· Multi-criteria decision-making· Three-way decision-making· Soft
matter
Nomenclature
3WDM Three-way decision-making
AM Additive manufacturing
MCDM Multi-criteria decision-making
μXCT Micro X-ray computed tomography
SLS Selective laser sintering
SLM Selective laser melting
SLA Stereolithography
FDM Fused deposition modeling
TPU Thermoplastic polyurethanes
Greek symbols
ʎ Risk avoidance factor
Ɖ Decision
Ł Expected loss
ζ Degrees of grey relational
Pc Conditional probability
f(c) Summary loss function
w Weightage
1 Introduction
Additive manufacturing (AM) (ISO/ASTM 529001) is a
product realization technique in a layer-by-layer manner,
also referred to as layered manufacturing, 3D printing, and
rapid prototyping. Part fabrication in AM starts with a CAD
(computer aided design) file followed by slicing and printing
* Prateek Saxena
prateek@iitmandi.ac.in
1 School ofMechanical andMaterials Engineering, Indian
Institute ofTechnology Mandi, Mandi175005, India
2 Institute ofManagement Studies (IMS) Ghaziabad,
UttarPradesh, India
3 Cluster ofExcellence PhoenixD (Photonics, Optics,
andEngineering – Innovation Across Disciplines),
Welfengarten 1A, 30167Hannover, LowerSaxony, Germany
4 Institute ofProduct Development (IPeG), Gottfried Wilhelm
Leibniz Universität Hannover, Ander Universität 1, Lower
Saxony, 30823Garbsen, Germany

The International Journal of Advanced Manufacturing Technology
using a 3D printing machine [1]. In the last few decades, rev-
olutionary growth has been seen in the field of AM because
of several advantages offered by this technology such as ease
in realizing complex shapes, more design freedom and flex-
ibility, product customization, less lead time and print time
[2]. AM is a broad science consisting of various processes
under its cluster for different material applications. The most
common and commercialized AM processes are material
extrusion: FDM (Fused Deposition Modeling); powder bed
fusion: SLS (Selective Laser Sintering) [3], SLM (Selective
Laser Melting), MJ (Material Jetting) [4]; and vatphotopoly-
merization: SLA (Stereolithography) and BJ (Binder Jetting)
[5]. These AM processes find their widespread industrial
application in the fields of aerospace, medical devices, and
robotics [6–8].
The field of robotics was earlier used to be regarded as
hard robotics meaning that the robots were made of rigid
materials such as metal and alloys [9]. These are big and
bulky in size and are normally used to perform heavy-duty
tasks. To mirror the functional behavior of human and ani-
mal muscles and allow for cooperative robotic systems, the
field of soft robotics has emerged. The individual part of
the soft robot is termed an actuator. The movement of a
soft robot is controlled partly by the deformation of the soft
materials (such as silicone, TPU: thermoplastic polyure-
thanes, and other flexible materials) and the desired behav-
ior of the robot can be obtained using the material property
known as compliance. Compliance refers to the ability of a
soft material to undergo elastic deformation upon applica-
tion of load or force. Compliance is a reciprocal of stiffness
which is more related to rigid materials. These soft robots
are relatively very small as compared to conventional robots
or hard robots and differ greatly in terms of application [10].
Soft robots are mostly compliant and possess a large number
of strains. Compliance is the most interesting and integral
property which makes soft robots find their application in
biomedical [11] and biomimetics. The movement of a soft
robot is controlled partly by the deformation of the soft
materials are also used for the actuation of the robots using
external stimuli such as light, heat, and pressure.
Additive manufacturing finds its vast application in the
fabrication of soft robotic parts because most of the soft
robots are small in size and very complex in geometry due to
the presence of microfluidic channels for actuation purposes.
The traditional method for the manufacturing of soft robots
is moulding but it is very difficult to manufacture advanced
soft robots with complex inner geometry using traditional
methods [12]. AM makes this task very convenient due to its
advantageous abilities. Various AM processes are available
in literature for the fabrication of soft robots such as devel-
oping a bladder like the geometry of elastomeric PDMS
(polydimethylsiloxane) material using stereolithography
process [13], development of the soft pneumatic actuator
using DLP (digital light processing), direct laser writing
for printing of high-resolution micro-robots [14], FL3DP
(freeform liquid 3D printing) [15], and DIW (direct ink writ-
ing) [16] for printing the actuators, FDM (fused deposition
modeling) technology for soft pneumatic grippers, printing
the human-like fingers using SLS process [17], and manu-
facturing of the high accuracy actuators using MJ (material
jetting) [18].
The quality of 3D printed parts is of utmost importance
when it comes to soft robots as the quality of soft robots
and actuators directly influences the life of the actuators.
The context of soft robots’ quality refers to the volumetric
morphology like microstructure, porosity, density, pore vol-
ume, sphericity of pores, pore size distribution, and surface
morphology like surface roughness. Porosity [19] and sur-
face roughness are of main concern as porosity can reduce
the overall life as most of the actuators are subject to fatigue
loading and these pores present can act as potential sites for
crack generation and propagation which can lead to cata-
strophic or premature failure of the part. Similarly, surface
roughness is also an important quality parameter because up
to an extent it can assist in gripping action [20] but if it is on
the higher side it can hamper the delicate tasks or parts soft
robots handle or deal with.
As quality includes various parameters which should be
close to the ideal values for a certain application for a part
with acceptable quality standards and in a similar fashion
each AM process also involves a lot of parameters such as
layer height, infill, print bed temperature, velocity of print,
print time, and nozzle temperature which can be varied for
a printing process. Combining all these variations in AM
process parameters and quality parameters, it becomes a
very complicated problem for a user to select the best AM
process for the printing of a good-quality soft robotic part.
For solving such complex problems, MCDM (multi-criteria
decision-making) is an advanced mathematical tool which
deals with problems involving several alternatives (AM pro-
cess parameters in this study) and multiple selection criteria
(quality attributes in this study), to provide users with an
optimal solution.
As per the related work, MCDM helps in solving these
complex problems and provides users with the best alternative
among all keeping the solution optimized. Different MCDM
techniques are available, such as TOPSIS (Technique for Order
Preference by Similarity to Ideal Solution), VIKOR (VIekriter-
ijumsko KOmpromisno Rangiranje), MOORA (Multi-Objec-
tive Optimization based on Ratio Analysis), BWM (best worst
method), AHP (analytic hierarchy process), and 3WDM (three-
way decision-making). 3WDM is a relatively new and more
flexible approach as compared to other existing approaches.
These different MCDM techniques find their application in
different domains such as economics [21], and product design
[22]. Geographical surveying, sustainable energy, automobile,

The International Journal of Advanced Manufacturing Technology
and additive manufacturing [23], [24–27] for selection of AM
processes and materials. There exist some studies on the selec-
tion of AM processes using fuzzy models [28]. Also, research-
ers have developed some good MCDM models and working
to enhance their effectiveness [29].
From the literature, it is very evident that appropriate selec-
tion is vital for optimized and enhanced performance be it in
terms of materials for different applications or selection of
additive manufacturing processes itself. Currently, there is no
study available for the selection of AM processes using com-
parative MCDM tools for polymer AM processes that find
their application in soft robotics; this work aims to fill that
gap. Silicone elastomers are the most prominent material for
soft robotics applications due to their good compliance and
functional behavior and printing compatibility with different
AM processes such as material extrusion (MEX) [30]. Even
with this advanced compatibility and advantages from a mate-
rial and process standpoint, silicone-printed soft actuators lack
sufficient strength required. Recent experimental studies from
Gangwar etal. [31] and Pricci etal. [32] reported that addi-
tively manufactured silicone actuators can withstand only a
very small actuation force (range ~10–15N). This raises the
need for a material which is soft and strong as well and TPU
is one such potential material. In this study, TPU with shore
hardness grade A is chosen as it is much softer than grade D.
The selection of AM process based on only quality and AM
process compatibility issue is addressed in this research work.
In this paper, a 3WDM approach is implemented for the selec-
tion of the best AM process (research objective) for a good-
quality soft robotic actuator. Three AM processes (SLS, SLA,
and FDM) consisting of nine alternative settings of layer height
are used against five selection criteria (quality parameters) for
selecting the best AM process out of nine alternatives based on
optimized quality characteristics. These nine alternatives are
used to print the cubic samples (two each for one alternative)
for obtaining the experimental data for the decision matrix. In
addition, three other existing MCDM techniques (TOPSIS,
MOORA, and VIKOR) are also used for the same decision
matrix and the results of 3WDM are compared to assess the
feasibility of the 3WDM approach. Lastly, sensitivity analysis
is also done to verify the effect of pre-existing obtained results
(ranking of alternatives) on changing the weights of the selec-
tion criteria as the weights are user-specific. This study will
act as a reference base in the area of AM of soft robots and
also for the further work mentioned in the conclusion section.
2 Manufacturing process
In this work, three AM processes, namely FDM, SLS, and
SLA, are identified and implemented for developing a soft
material sample. FDM is a solid filament-based AM process
that uses filaments of materials that are wound on a spool.
The filament is fed into a liquefier chamber where it melts
and then passes through a nozzle to further deposit on the
heated printbed to print a layer of the materials. The feed-
ing of filaments is continuous and the nozzle continuously
prints layer over layer to fabricate the final part. SLS is a
powder bed fusion process that uses polymer powder mate-
rials. The powder material is spread on the print bed from
the feedstock bed with the help of a roller. Furthermore, the
spread powder layer is selectively sintered, with the help of
a laser. On solidification of one layer, the print bed lowers
down allowing the spread of the next powder layer on top of
the already sintered layer and this follows the sintering of the
newly recoated layer. This process continues similarly until
the final 3D part is obtained. Stereolithography is a photo
polymerization-based 3D printing process [33]. It uses a vat
of liquid monomer resin which is cured with the help of an
UV (ultraviolet) laser. After curing one layer, the build plat-
form is immersed in the liquid resin vat and again the laser
cures the layer on top of the previous layer and this process
is repeated until full part realization.
In this study, soft material named TPU is used for fab-
ricating the samples. Three different AM processes (SLS,
SLA, and FDM) are used for printing the samples. Table1
shows the materials, their properties, and the corresponding
AM process used for the printing samples.
3 Mathematical approach for3WDM
Obtaining values of alternatives and quality attributes are
integral and necessary step before applying any MCDM
techniques. The selection of alternatives is achieved on the
basis desired properties required; as in this case, the low
porosity and surface roughness are of utmost importance.
The values of the quality attributes are achieved by the cor-
responding experimental or computational methodology
(experimental for this study) (refer Section4).
3.1 Three‑way decision making MCDM technique
This section explains the mathematical formulation and
systematic solving approach of the 3WDM MCDM tech-
nique. The 3WDM is implemented in three parts for
Table 1 AM processes, materials, and their properties
AM process Material Physical form Shore hardness Tensile
strength
(MPa)
SLS TPU Powder 82A 3.7
SLA TPU Resin 80A 3.5
FDM TPU Filament 82A 4.5

The International Journal of Advanced Manufacturing Technology
solving a complex multi-alternative involved problem for
an optimal solution. In part one, the initial stage a decision
matrix (quality matrix in this paper) is established among
different alternatives and selection criteria (attributes in
this paper) based on the quantitative results. The matrix
is further normalized in the same stage. In part two, the
calculation stage of 3WDM implementation deals with the
mathematical calculation of different functions specific to
3WDM, i.e., the summary loss function, relative loss coef-
ficient and conditional probability of different alternatives,
and the AM process parameters in this study. In the final
stage, the decision-making stage involves generating the
3WDM results for the problem and providing the best AM
process parameter setting for the best quality soft part. All
three stages with mathematical formulae below are dis-
cussed in great detail with the process flow schematic of
the 3WDM algorithm shown in Fig.1.
3.1.1 Initial stage
The first part of the initial stage deals with the establish-
ment of the decision matrix including both the alternative
and the selection criteria/attributes. This decision matrix
is used to select the best AM process for sound-quality soft
parts. The decision matrix consists of m alternative AM
process print settings A1, A2, A3……..Am and n selection
criteria or attributes C1, C2, C3….Cn with its values (Cj),
and weightage chosen for each attribute wj (0 ≤ wj ≤ 1)
and
∑n
J=1
w
j
=
1
.
The alternative AM processes are SLS, SLA, and FDM
processes and the selection criteria or attributes are taken
as porosity, Feret diameter, pore volume, sphericity, and
roughness. Generally, attributes are chosen as per the need
and specific requirement for the application of the part;
this study is focused on soft robotics and materials so the
concerning attributes are selected as selection criteria as
these can hamper the quality of the fabricated actuator
from the alternative AM processes. The numerical values
of the attributes can be taken from experiments, simula-
tions, expert guesses, hit and trial, data handbook, bench-
mark data, material datasheet, etc. In this paper, all the
values of attributes are obtained by performing experi-
ments in the laboratory.
A decision matrix based on a dataset of alternatives and
attributes is established as:
In the second part of the initial stage, the matrix
obtained in Eq.1 is to be normalized; this is done using a
ratio model which converts the all-attribute values into a
number ranging [0, 1].
(1)
X
=
[
a
i
,
j]m×n
Furthermore, the attributes or the selection criteria are
categorized into two classes: positive criteria and negative
criteria. The positive criteria and negative criteria are cor-
related positively and negatively respectively with the deci-
sion-making results. In this study, the sphericity is positively
correlated with the final decision-making, i.e., the higher the
better, while all other attributes (porosity, maximum Feret
diameter, pores volume, and roughness) are negatively cor-
related meaning the lowest of these values are beneficial for
the final decision-making.
A unified rule is applied to unify the effect of these two
criterion values:
With the help of conversion and unification rule, the final
normalized decision-making matrix is obtained as:
3.1.2 Calculation stage
The calculation stage involves three sub-steps, namely sum-
mary loss function, conditional probability, and expected
losses between the alternative AM processes. Let Sj and -Sj
be two states (representing positive and negative solutions) of
alternative AM processes. Ai meets the attribute Cj and Ai does
not meet the attribute Cj, respectively. Corresponding to each
state, there exist three decisions. These are acceptance (ƉAC),
abstaining (ƉAB), and rejection (ƉRJ) in 3WDM. In literature,
the relative loss [34] function is calculated; in a similar fash-
ion, the relative loss function is derived by Yuchu Qin [35]
from the normalized criterion value ci, j and shown in Table2,
where “ʎj” is a risk avoidance coefficient corresponding to Cj
ranges as 0 ≤ ʎj ≤ 1.
The relative loss is explained as [35]: the cost associated
with the correct decision is 0; the cost associated with rejection
is ci, j when Ai meets Cj; the cost associated with acceptance
is 1- ci, j when Ai does not meet Cj; the cost associated with
abstaining for both the states lies within the range of rejection
and acceptance. Taking reference from Table3, each normal-
ized criterion value is converted in the form of a relative loss
function:
(2)
b
i,j=
a
i,j
�∑
m
i=1a2i,
j
(3)
c
i,j=
{
bi.jif Cjis a positive criterion
1−b
i
,
j
if C
jis a negative criterion
(4)
Y
=
[
c
i
,
j]m×n
(5)

The International Journal of Advanced Manufacturing Technology
Fig. 1 Solution flow chart for
three-way decision-making
(3WDM) MCDM technique

The International Journal of Advanced Manufacturing Technology
Now using the weighted averaging operator, the relative
loss functions of each alternative AM process (i.e., all n
relative loss functions f(ci,1), f(ci,2) …...f(ci,n)) are combined
as a summary loss function:
(6)
The next step is the calculation stage, the calculation of
conditional probability for each alternative AM process. Con-
ditional probability is one of the key elements in 3WDM. In
a few cases (for 3WDM only), the conditional probability
values are fixed for different alternatives of the decision
matrix, but in most of the cases of MCDM techniques, differ-
ent values are calculated for different alternatives. This calcu-
lation of probability can be done using TOPSIS [36], but it
does not give the relative importance of the alternatives; TOP-
SIS is a distance-based approach to finding the degree of rela-
tive closeness from the ideal solution; i.e., the basis for the
conclusion is how near or far the alternative is from the ideal
solution. Another effective and better method for determining
the conditional probability and the relationship between data-
sets is grey relational analysis, inspiring from [35]. In this
study, the grey relational analysis is used to find the condi-
tional probability for different alternatives. To calculate the
conditional probability first, grey relational coefficients
between the alternative AM processes Ai and
maxn
j
=
1{
ci,j
}
and
between Ai and
minn
j
=1
{
ci,j
}
are calculated as:
(7)
𝜁
+
i,j=
minm
i=1minn
j=1



ci,j−maxn
j=1

ci,j



+0.5 maxm
i=1maxn
j=1



ci,j−maxn
j=1

ci,j






ci,j−maxn
j=1

ci,j



+0.5 maxm
i=1maxn
j=1



ci,j−maxn
j=1

ci,j



(8)
𝜁
−
i,j=
minm
i=1minn
j=1


ci,j−minn
j=1

ci,j




+0.5 maxm
i=1maxn
j=1


ci,j−minn
j=1

ci,j







ci,j−minn
j=1

ci,j



+0.5 maxm
i=1maxn
j=1



ci,j−minn
j=1

ci,j



Furthermore, the degrees of grey relational of Ai corre-
spond to
max
n
j
=
1{
ci,j
}
and of Ai corresponding to
minn
j
=1
{
ci,j
}
are calculated as:
(9)
𝜁
+
i=
∑n
j=1wj𝜁
+
i,
j
Lastly, the conditional probabilities of Ai are calculated as
the relative closeness of the grey relation of Ai, as:
(10)
𝜁
−
i
=
∑n
j
=1wj𝜁
−
i,
j
Table 2 Relative loss functions
for two states Sj and -Sj derived
from ci,j
Decision Sj-Sj
ƉAC 0 1-ci, j
ƉAB ʎj ci, j ʎj (1-ci, j)
ƉRJ ci, j 0
Table 3 Quality matrix with
attributes value corresponding
to each alternative
Alternatives Porosity (%
vol.)
Surface rough-
ness in μm)
Maximum Feret
diameter (mm)
Sphericity of
pores
Maximum pore
volume (mm3)
A12.6 13 5.37 0.14 0.76
A22.3 17 1.66 0.35 0.07
A30.4 13.50 1.25 0.32 0.04
A43.1 19 4.22 0.19 0.82
A51.1 9.25 9.03 0.30 0.43
A63.1 16.35 8.50 0.21 2.03
A70.5 20.50 6.97 0.27 0.07
A80.11 2.95 0.11 0.82 0.0001
A90.12 4.20 0.12 0.85 0.001

The International Journal of Advanced Manufacturing Technology
where S stands for the alternative AM processes, and Ai
meets a combination of all n criteria.
As a last step of the calculation stage, the expected losses
are computed for each alternative AM process Ai. As per
[37], in 3WDM, the total probability for S and S- states is
(11)
P
c
(
S
|[
Ai
])
=
𝜁
+
i
𝜁+
i
+𝜁−
i
given as Pc(S| [Ai]) + Pc(S−| [Ai]) = 1. Combining the sum-
mary loss function (Ł) (Eq.12-14) and the conditional prob-
abilities (Pc) (Eq.11), the expected losses of Ai when mak-
ing a decision Ɖ# (# = AC, AB, RJ) are calculated as:
(12)
(13)
3.1.3 Decision‑making stage
The decision-making stage involves two steps to reach the
final solution, in the first step; the decision results are gen-
erated based on the decision rules developed [35] based
on Bayesian decision theory. In our case, the minimum
porosity attribute is the basis for the decision-making. The
decisions rules are as:
1) If Ł (ƉAC |[Ai]) ≤ Ł (ƉAB |[Ai]) and Ł (ƉAC |[Ai]) ≤ Ł (ƉRJ
|[Ai]), then ƉAC decision is made for the alternative Ai;
2) If Ł (ƉAB |[Ai]) ≤ Ł (ƉAC |[Ai]) and Ł (ƉAB |[Ai]) ≤ Ł (ƉRJ
|[Ai]), then ƉAB decision is made for the alternative Ai;
3) If Ł (ƉRJ |[Ai]) ≤ Ł (ƉAC |[Ai]) and Ł (ƉRJ |[Ai]) ≤ Ł (ƉAB
|[Ai]), then ƉRJ decision is made for the alternative Ai.
Based on the above three decision rules, the decision-
making results can be generated. With 3WDM unlike
other MCMD techniques, there is no ranking of alterna-
tives but all the alternatives are classified in different sets
of accepted set, abstaining set, and rejection set, and from
these sets, the best alternative is chosen. In general, we do
not choose the rejection set as those are the worst alterna-
tives as per the solution or decision-making results. So, if
the decision ƉAC is made for alternative Ai, that alternative
will be put in the accepted set and similarly for the abstain-
ing set and rejection set, respectively.
In the last step, the best alternative out of all in the deci-
sion matrix is chosen from the accepted set. If the accepted
and the rejected set is empty, then a user should choose from
the abstaining set.
(14) 4 Case study
4.1 AM process selection forsoft robotics using
3WDM
In this section, the proposed three-way decision-making
(3WDM) approach is implemented with a numerical example
in the context of quality assessment of soft robotics material
printed using AM, i.e., to choose the appropriate 3D print-
ing process (with parameters) for best quality. Later on, the
proposed approach is compared with existing MCDM tech-
niques (TOPSIS, MOORA, and VIKOR) for feasibility and
variation in results.
Before discussing the 3WDM application and its vali-
dation, the materials, machines, and methodology are dis-
cussed in the below sections:
4.2 Printing andquality assessment methodology
3D printing gives the user a lot of freedom in terms of design
as well as parameter setting. Several parameters like infill,
support structure, nozzle diameter, print speed, and print bed
temperature can be varied at the user end, but in this study,
the parameter varied is layer height among different AM pro-
cesses. Figure2 shows a detailed outline and classification of
the processes and parameters with several samples printed.
More flexible (MF) and more rigid (MR) are inbuilt SLS
printer variation settings with differences in energy content
supplied to the powder material, more rigid, more energy,
and more flexible, less energy supplied. Process parameter
setting is the variation in layer height. For example, SLAt100
means the SLA process with a layer height of 100 μm. MR
and MF settings are for SLS that can also be decoded simi-
larly to SLAt100.

The International Journal of Advanced Manufacturing Technology
4.3 Quality attributes
Five quality attributes are chosen for this study (AM process
selection for soft robotics using 3WDM and comparison with
other MCDM) with 9 alternatives (AM process parameter set-
tings). These attributes are namely porosity, sphericity, maxi-
mum Feret diameter of pores, maximum pore volume, and sur-
face roughness. All the attributes are briefly explained below:
• Porosity: presence of micron-sized voids inside the3D
volume of part.
• Sphericity: ability of a pore to be spherical. Keyhole
refers to the opposite of sphericity.
• Maximum Feret diameter: measure of the largest pore
size along a specified direction.
• Maximum pore volume: the amount of volume possessed
by the largest pore present.
• Surface roughness: presence of irregularities on the sur-
face of a part.
The procedure followed to get the experimental data for
the decision matrix is shown in Fig.3. First, the samples
were printed with different AM processes shown in the left
block, and furthermore, these samples were scanned using
μXCT (micro X-ray computed tomography) for porosity
analysis [38], with pore characterization using Dragonfly
software and image processing software (CTAn, CT analy-
sis). In addition, roughness measurement is done using a
diamond probe. The porosity (in 2D and 3D), pores charac-
terization, and roughness visualization are clustered in the
right block of Fig.3.
4.4 Implementation of3WDM technique
4.4.1 Quality matrix
Quality matrix refers to the tabulated quantitative data
of the quality attributes corresponding to each alternative
used for the assessment shown in Table3. Two samples
Fig. 2 AM processes and
parameter settings classification
with corresponding materials

The International Journal of Advanced Manufacturing Technology
are printed for each print setting and the numerical values
quoted in the table are the average of the values of the
two samples. The quality matrix is the first step in the
application of the 3WDM and other MCDM techniques.
In this paper, the quality matrix (values of alternatives and
attributes) is obtained by performing the experiments in
the laboratory.
The decision process involves the selection of AM pro-
cess and configuration from 9 alternatives: MRt75 (A1),
MRt200 (A2), MFt75 (A3), MFt200 (A4), FDMt100 (A5),
FDMt200 (A6), FDMt300 (A7), SLAt50 (A8), and SLAt100
(A9)refer Table3. The weights for attributes are assumed
as 0.40, 0.15, 0.15, 0.10, and 0.20 for porosity, maximum
Feret diameter, maximum pore volume, surface roughness,
and sphericity, respectively; these weights are user-specific
and chosen considering the severity of the parameter.
4.5 3WDM stepwise calculation
The various steps involved in the calculation of the 3WDM
approach are as follows:
a) Formulate a decision matrix (quality matrix in this
study) inclusive of all the alternatives and the attributes/
selection criteria. In this study, the decision matrix is the
quality matrix consisting of 9 alternative AM processes
and 5 attributes/selection criteria tabulated in Table3.
b) Normalization of the decision matrix is established in
step (i) with the help of Eq. (2). In the decision-making
matrix, only sphericity is the positive criterion, the rest
are the negative criteria, and the normalization is done
considering this fact and using Eq. (3) The weighted
normalized matrix Y is shown in Eq. (15).
(15)
Y
=ci,j9×5=












0.1812
0.1604
0.0279
0.2161
0.0767
0.2161
0.0348
0.0076
0.0083
0.0306
0.0400
0.0318
0.0447
0.0217
0.0385
0.0483
0.0069
0.0099
0.0506
0.0156
0.0117
0.0397
0.0850
0.0801
0.0656
0.0010
0.0011
0.0204
0.0510
0.0466
0.0276
0.0437
0.0306
0.0393
0.1195
0.1239
0.0483
0.0044
0.0025
0.0521
0.0273
0.1290
0.0044
0.0000
0.0000












Fig. 3 Experimental process illustration for the printing of soft material samples and visual representation of characterization (μXCT) process
and results (porosity, pore characterization, and roughness) obtained

The International Journal of Advanced Manufacturing Technology
c) Calculation of the summary loss function correspond-
ing to each alternative AM process using Eq. (5). The
normalized values of each attribute in matrix Y are con-
verted into a relative loss function (f(ci, j)) , in which the
value for risk avoidance coefficient (ʎ) is taken as 0.4.
then according to Eq. (6), and considering the weight
values, the summary loss function is calculated for each
alternative and shown in Table4.
d) Calculation of conditional probabilities using the Eqs.
(7)-(11). The calculated conditional probabilities corre-
sponding to each alternative AM Pc(S| [Ai]) process
are shown in Table5.
e) Calculation of expected losses (Ł) using Eqs. (12)-
(14). The expected losses of each AM process cor-
responding to three decisions (accept, abstain, and
reject) are shown in Table6.
f) Generate the decision-making results as per the clas-
sification rules. The 3WDM results obtained for AM
process selection for soft robotics are obtained in
three sets:
AAC = {A9, A8, A3, A7, A5, A2,}, AAB = {A1}, and
ARJ = {A4, A6}
g) Selection of the best AM process will be done using
the sets obtained in step (6). A9 is the best AM
process followed by A8, A3, A7, A5, and A2 in the
acceptance set, and there are A4 and A6 alternatives
in rejection set. Our preference would be to choose
from the acceptance set, and if the acceptance set is
empty, the user chooses from the abstaining set as
per 3WDM.
5 Results anddiscussion
5.1 Comparative analysis
The 3WDM results were compared with the other
existing MCDM techniques (TOPSIS, VIKOR, and
MOORA); the comparison is shown in Table7. This
comparison helps demonstrate the effectiveness of
Table 4 Summary loss functions for each alternative
AM process Function Decision (S) (-S)
A1f(c1)ƉAC 0 0.3312
ƉAB 0.2675 0.1325
ƉRJ 0.6687 0
A2f(c2)ƉAC 0 0.2715
ƉAB 0.2914 0.1086
ƉRJ 0.7284 0
A3f(c3)ƉAC 0 0.1206
ƉAB 0.3517 0.0482
ƉRJ 0.8793 0
A4f(c4)ƉAC 0 0.3804
ƉAB 0.2478 0.1521
ƉRJ 0.6195 0
A5f(c5)ƉAC 0 0.2546
ƉAB 0.2981 0.1018
ƉRJ 0.7453 0
A6f(c6)ƉAC 0 0.4944
ƉAB 0.2022 0.1977
ƉRJ 0.5055 0
A7f(c7)ƉAC 0 0.1926
ƉAB 0.3229 0.0770
ƉRJ 0.8073 0
A8f(c8)ƉAC 0 0.1351
ƉAB 0.3459 0.0540
ƉRJ 0.8648 0
A9f(c9)ƉAC 0 0.1433
ƉAB 0.3426s 0.0573
ƉRJ 0.8566 0
Table 5 Conditional
probabilities values A1A2A3A4A5A6A7A8A9
Pc (S|[Ai]) 0.3089 0.4747 0.7402 0.2706 0.5595 0.0515 0.6536 0.9846 0.9893
Table 6 Expected losses
calculated values corresponding
to each alternative
A1A2A3A4A5A6A7A8A9
Ł (ƉAC |[Ai]) 0.2289 0.1426 0.0313 0.2775 0.1121 0.4689 0.0667 0.0020 0.0015
Ł (ƉAB |[Ai]) 0.1742 0.1953 0.2728 0.1780 0.2116 0.1980 0.2377 0.3414 0.3396
Ł (ƉRJ |[Ai]) 0.2065 0.4174 0.6508 0.1676 0.4170 0.0260 0.5276 0.8513 0.8475
Table 7 3WDM result comparison with other MCDM techniques
MCDM technique Ranking of alternatives
TOPSIS A9 > A8 > A3 > A7 > A5 > A2 > A1 > A4 > A6
VIKOR A9 > A8 > A3 > A2 > A5 > A7 > A1 > A4 > A6
MOORA A8 > A9 > A3 > A2 > A5 > A1 > A7 > A4 > A6
3WDM AAC = {A9, A8, A3, A7, A5, A2, }, AAB = { A1},
and ARJ = { A4, A6}.

The International Journal of Advanced Manufacturing Technology
3WDM. As per 3WDM, the best AM process is A9 followed
by A8 and A3.
The ranking results from the other MCDM techniques
also show that the top potential AM processes are A8,
A9, and A3 among all 9 alternatives. Also, all the MCDM
techniques including 3WDM regarded A4 and A6 as the
worst AM process for best-quality soft robotic parts. This
comparison shows that the 3WDM technique is as effective
as other existing MCDM techniques.
Further sensitivity analysis is also done to check the effect
of the best AM process on changing the weightage of selec-
tion criteria by a user. The analysis is discussed in the sub-
sequent section.
5.2 Sensitivity analysis
Sensitivity analysis is a statistical tool used to examine
the variation in the ranking of different alternatives due to
changes in the weights of the selection criteria or attrib-
utes. Five trials are considered for sensitivity with differ-
ent weights of attributes as shown in Table8. For trial 1,
the maximum weightage is given to porosity as 0.60 and a
Table 8 Different trial
specification data corresponding
to each attribute for sensitivity
analysis
Attributes Weights
Original values Trial 1 Trial 2 Trial 3 Trial 4 Trial 5
Porosity 0.40 0.60 0.10 0.10 0.10 0.10
Surface roughness 0.10 0.10 0.60 0.10 0.10 0.10
Maximum Feret diam-
eter of pores
0.15 0.10 0.10 0.60 0.10 0.10
Sphericity 0.20 0.10 0.10 0.10 0.60 0.10
Pores volume 0.15 0.10 0.10 0.10 0.10 0.60
Fig. 4 Results of the sensitivity
analysis of 9 alternatives using
5 trials
Table 9 Top AM process
alternatives as per sensitivity
analysis for each trial
Trial number Top AM
process alter-
natives
Original values A9 > A8 > A7
Trial 1 A9 > A8
Trial 2 A9 > A8 > A7
Trial 3 A9 > A8 > A7
Trial 4 A9 > A8
Trial 5 A9

The International Journal of Advanced Manufacturing Technology
weightage of 0.10 for the rest of the attributes. Similarly,
the other 4 trials with corresponding weights are shown in
Table8. It was observed that the ranking of alternatives was
almost the same, which shows the reliability of the results.
Sensitivity analysis results shown in radar chart Fig.4
depict that for trial 1, the top alternative AM processes are
A9, A8, and A7 [39]. A detailed Table9 shows the top best
alternatives corresponding to each trial. The same can be wit-
nessed in the radar chart. Sensitivity results suggest that A9
(SLAt100) is the best AM process for the fabrication of soft
robotic parts considering the quality of the printed part. Since
there is a little varation in the sensitivity analysis results upon
changing the weights of different attributes, this signifies that
the initial weights given fit well and the maximum weight
(0.4) should be given to the porosity attribute. This is also
institutive that the Feret diameter and pores volume will vary
with porosity so they should be given the lower weightage
(0.15) than the porosity. Spherecity is independent of poros-
ity so a higher weight (0.20) should be given to it. Since
there is no variation in results, a weight of 0.1 holds good for
surface roughness as well.
6 Conclusions
In this paper, a three-way decision-making (3WDM)
approach is explained and implemented for a case study
on the selection of a suitable AM process for quality parts
in a soft robotic application. Along with 3WDM three
other (TOPSIS, VIKOR, and MOORA), existing MCDM
approaches with the same decision matrix and identical
weights are implemented to obtain the result and ranking
of AM processes. All the results of different MCDM are
compared and found to be approximately the same mak-
ing 3WDM as effective as existing MCDM approaches.
The top best alternative process for soft robotics applica-
tion comes out to be A9 (SLAt100), A8 (SLAt50), and A7
(FDMt300); i.e., these AM process are best to fabricate parts
for soft robotics application with sound quality. This paper
also demonstrates the sensitivity analysis which is essential
if the weights are user-specific to examine the robustness of
the alternatives and deviations in the rankings if any, i.e.,
change in the ranking of the alternatives with a significant
change in the weights and the same top alternatives (A8, A9,
and A7) holds good. This study will also serve as a reference
base for selection of AM processes for printing TPU of high
quality for applications in soft robotics and help in optimiz-
ing resources with minimal efforts of printing. In the future
another studyupon incorporating other attributes relating to
strength, deflection and actuation forces of soft robotics can
be done to further cross-verify if the same ranking; the AM
processes stay true or not.
Author contribution Sudhanshu Gangwar: investigation, formal analy-
sis, data curation, funding acquisition, writing—original draft; Prateek
Saxena: conceptualization, funding acquisition, supervision, writing—
review and editing; Naveen Virmani: conceptualization, software,
writing—review; Tobias Biermann: supervision, writing—review and
editing; Carl Steinnagel: supervision, writing—review; Roland Lach-
mayer: resources, funding acquisition, supervision, writing—review
and editing.
Funding The authors would like to thank the DAAD (Deutscher Aka-
demischer Austauschdienst), Germany, for funding under the DAAD-
KOSPIE exchange program. The authors would also like to thank the
Science and Engineering Research Board (SERB), Department of
Science and Technology (DST), India, under start-up research grant
(SERB-SRG) project titled “3D printing of continuous carbon fiber
reinforced polymer composites using Fused Filament Fabrication” -
project number SRG/2022/002225. The project “Computer tomograph
for optomechatronic systems” was funded by the Deutsche Forschun-
gsgemeinschaft (DFG, German Research Foundation) - project num-
ber 432176896, and Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany’s Excellence Strategy within the
Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453)
are also acknowledged for providing the financial assistance for car-
rying out this study.
Declarations
Conflict of interest The authors declare no competing interests.
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