A multi-criteria decision-making tool with information redundancy treatment for design evaluation

Abstract

This article introduces a multi-criteria decision making (MCDM) method that takes into account interdependency of criteria. Recognizing information redundancy in related criteria the proposed approach offers their weight formation based on their interaction. Further, normalized estimated criteria and their weights are aggregated by means of Fuzzy Heavy Weighted Averaging (FHWA) operator. The approach is illustrated with a numerical case study of engineering design selection problem. Keywords— Multi-criteria decision making, design assessment, fuzzy logic, information redunduncy

Full text

A multi-criteria decision-making tool with
information redundancy treatment for design
evaluation
Nikolai Efimov-Soini*, Mariia Kozlova, Pasi Luuka, Mikael Collan
School of business and management
Lappeenranta University of Technology
Lappeenranta, Finland
*spb2010@mail.ru
Abstract — This article introduces a multi-criteria decision
making (MCDM) method that takes into account
interdependency of criteria. Recognizing information
redundancy in related criteria the proposed approach offers their
weight formation based on their interaction. Further, normalized
estimated criteria and their weights are aggregated by means of
Fuzzy Heavy Weighted Averaging (FHWA) operator. The
approach is illustrated with a numerical case study of
engineering design selection problem.
Keywords— Multi-criteria decision making, design assessment,
fuzzy logic, information redunduncy
I. INTRODUCTION
The design evaluation is a crucial task on the conceptual
design stage, as far as the concept chosen in this stage
influences the whole further product life-cycle [1]. On the one
hand, the information about concepts is often incomplete,
uncertain and evolving. On the other hand, key decision criteria
are often interdependent that hinders unbiased decision-
making.
This paper proposes a method suitable for the design
evaluation. In contrast to existing techniques [2], the distinct
feature of the new method is that it takes into account
information redundancy of evaluating criteria. The latter allows
more accurate decision-making. In this paper, the flow meter
case is used to illustrate the proposed method.
II. THE PROPOSED APPROACH
The proposed method is based on the procedure presented
in [3] and incorporates in addition information redundancy
treatment. It contains six main steps:
1. Transformation of data vector into fuzzy numbers to
capture imprecision and uncertainty of estimates;
2. Normalization of fuzzy numbers in order to transform
them into comparable units and enable aggregation;
3. Distinguishing between cost and benefit criteria and
taking a complement from cost ones;
4. Creating weights by using interaction matrix of
criteria;
5. Aggregation of the fuzzy vector with given weights by
means of FHWA operator;
6. Forming rankings from resulting aggregated fuzzy
numbers [4].
The interaction matrix in the step 4 is a special matrix that
reflects dependence (or independence) of criteria to each other.
The interaction matrix can be defined as:
(1)
Where denoting presence/absence of interaction.
We assume , meaning that variable does not interact
with itself. The interaction vector is created by cardinality of
interactions presented:
(2)
Further, it is scaled to a unit interval by
(3)
where denoting maximum possible interactions with
variable. The weights are formed by taking the complement of
the the interaction vector: (4)
Thus, the weight vector reflects information redundancy in
the criteria. The more the interdependence between one
criterion with others, the lower its weight in the final estimate.
A Fuzzy Heavy Weighted Averaging (FHWA) operator [3]
is used for aggregation. FHWA of dimension n is a mapping
operator that maps Un → U that has an associated weighting
vector W of dimension n such that the sum of the weights is
between [1,n] and
 
1,0
i
w
, then:



n
iiin awaaaFHWA 1
21 ˆ
)
ˆ
,,
ˆ
,
ˆ
(
(5)
where (
n
aaa ˆ
,,
ˆ
,
ˆ21 
), are now fuzzy triangular numbers
For details on other steps, see [5].
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Proceedings of NSAIS16 - 2016 Lappeenranta Finland - ISBN 978-952-265-986-6

III. CASE ILLUSTRATION
The application of the above algorithm is illustrated with a
selection problem among designs of three different flow
meters: electromagnetic (EM), turbine and ultrasonic. The flow
meters are used for measuring of the flow of liquids or gases in
the different areas, such as construction, oil and gas, nuclear
power etc. For these devices eight important criteria are
identified: the cost of device, the work time, the electricity
consumption, the accuracy, the amount of liquids on which
they can operate, the easiness of installation, the processing of
the electronic signal, and the shelf-time. The specifications on
each flow meter type is presented in Table I [6].
TABLE I. SPECIFICATIONS OF THE FLOW METER DESIGNS
EM
(Piterflow
RS50)
Turbine
(Okhta
T50)
Ultrasonic
(Vzloyt
MR)
1. Cost, rubles
16150
4240
34800
2. Work time, hours
80000
100000
75000
3. Consumption, V*A
6
0
12
4. Accuracy, m3/hour
36±2%
30,00±2%
35±2%
5. Operatied liquids
Water, and
sold water,
dirty water
Only clear
water
All liquids
6. Easiness of
installation
Easy
Elementary
Average
7. Processing of the
electronic signal
Yes
No
Yes
8. Shelf-time, years
4
5
2
Detailed computations in accordance with the defined
algorithm are left outside this extended abstract, however, we
dwell upon the weight formation here. Table II presents the
interaction matrix of eight defined criteria numbered
consequently.
TABLE II. INTERACTION MATRIX
1
2
3
4
5
6
7
8
1
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
4
1
0
0
0
0
0
0
0
5
1
0
1
0
0
1
1
0
6
0
0
0
0
1
0
1
0
7
1
0
1
0
1
1
0
0
8
0
0
0
0
0
0
0
0
Sum
4
1
2
1
4
2
4
0
The interaction matrix shows that e.g. cost of the design is
influenced by its durability, accuracy, amount of operated
liquids and ability to process the electronic signal. Thus, the
overall interaction of the first criterion with others is equal to 4
(defined as cardinality). Scaling it to unit interval with the total
possible interactions equal to 8 returns 0.5. Hence, the weight
of this criterion, computed as the complement is equal to 0.5.
The overall weight vector defined in this manner is [0.5 0.875
0.75 0.875 0.5 0.75 0.5 1].
Aggregation of normalized fuzzified criteria with their
weights provides the final fuzzy estimates for each design
represented on Fig. 1.
Fig. 1. Final fuzzy numbers for each flowmeter.
According to the Kaufmann and Gupta method [4] a unique
linear order of fuzzy numbers can be found by using some
properties of the numbers as criteria for ordering. In this
method, the following three properties are used: removal
number, mode and divergence. If the first criterion does not
give a unique linear order, then the second criterion is used,
and ultimately the third criterion is applied as well. In our case
the first criterion is enough to obtain the final ranking. In
particular, the removal for a triangular fuzzy number is
calculated as:
(6)
The final ranking (Table III) of these fuzzy estimates
proposes electromagnetic flow meter as the best one, followed
by turbine and ultrasonic designs.
TABLE III. RANKINGS FOR EM, TURBINE AND ULTRASONIC DESIGNS
Flow meter
Final ranking
EM
1
Turbine
2
Ultrasonic
3
IV. CONCLUSIONS
This paper introduces a new multi-criteria decision-making
method that treats information redundancy in evaluating
criteria. The approach is illustrated on engineering design
selection problem. The results show its effectiveness in
removing the effect of interdependent criteria from the final
estimate. The proposed approach is suitable for the majority of
MCDM problems and can potentially find its application in a
variety of industries and academic fields.
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Proceedings of NSAIS16 - 2016 Lappeenranta Finland - ISBN 978-952-265-986-6

REFERENCES
[1] Ullman, David G. 2010 – The mechanical design process/David G.
Ullman, 4th edition ISBN 978-0-07-297574-1-ISBN 0-007-297574 (alk.
paper). McGraw-Hill series in mechanical engineering.
[2] Concept selection methods – a literature review from 1980 to 2008. G.
Okudan, S. Tauhid. International Journal of Design Engineering, Vol. 1,
No. 3, 2008, pages 243-277.
[3] Collan, M. and Luukka, P. (2015). Strategic R&D project Analysis:
Keeping it simple and smart,Using fuzzy scorecards to collect data for
strategic R&D projects & analyzing and seleting projects with a system
that uses new fuzzy weighted averaging operators, Submitted
[4] Kaufmann, M. and M. Gupta (1985). Introduction to fuzzy arithmetics:
theory and applications. New York, NY, Van Nostrand Reinhold.
[5] Efimov-Soini, N., Kozlova, M., Luuka, P. and Collan M. (unpublished).
A multi-criteria decision-making tool with information redundancy
[6] Termotronic, product description. Available at:
http://termotronic.ru/products/ [Accessed 12.05.2016]
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Proceedings of NSAIS16 - 2016 Lappeenranta Finland - ISBN 978-952-265-986-6