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The use of improved TOPSIS method based on experimental design and Chebyshev regression in solving MCDM problems

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Abstract

Decision makers today are faced with a wide range of alternative options and a large set of conflicting criteria. How to make trade-off between these conflicting attributes and make a scientific decision is always a difficult task. Although a lot of multiple criteria decision making (MCDM) methods are available to deal with selection applications, it’s observed that in most of these methods the ranking results are very sensitive to the changes in the attribute weights. The calculation process is also ineffective when a new alternative is added or removed from the MCDM problem. This paper presents an improved TOPSIS method based on experimental design and Chebyshev orthogonal polynomial regression. A feature of this method is that it employs the experimental design technique to assign the attribute weights and uses Chebyshev regression to build a regression model. This model can help and guide a decision maker to make a reasonable judgment easily. The proposed methodology is particularized through an equipment selection problem in manufacturing environment. Two more illustrative examples are conducted to demonstrate the applicability of the proposed method. In all the cases, the results obtained using the proposed method almost corroborate with those derived by the earlier researchers which proves the validity, capability and potentiality of this method in solving real-life MCDM problems.

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Abbreviations

AHP:

Analytic hierarchy process

DM:

Decision maker

DoE:

Design of experiment

ELECTRE:

Elimination et choice translating reality

IC:

Integrated circuit

MCDM:

Multiple criteria decision making

MM:

Milling machine

MOORA:

Multi-objective optimization on the basis of ratio analysis

PROMETHEE:

Preference ranking organization method for enrichment evaluation

SAW:

Simple additive weighting

TOPSIS:

Technique for order preference by similarity to ideal solution

VIKOR:

VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian

\(a_{i}\) :

Coefficient of the Chebyshev term \(T_{i}\)

\(A^{+}\) :

The positive ideal solution

\(A^{-}\) :

The negative ideal solution

\(A_{i}\) :

The \(i\hbox {th}\) alternative

\(C_{j}\) :

The \(j\hbox {th}\) criterion

\(D_{i}^{+}\) :

The distance between the \(i\hbox {th}\) alternative and the positive ideal solution

\(D_{i}^{-}\) :

The distance between the \(i\hbox {th}\) alternative and the negative ideal solution

\(m\) :

The number of alternatives for a certain MCDM problem

\(n\) :

The number of criteria for a certain MCDM problem

\(r_{ij}\) :

The normalized value of \(j\hbox {th}\) criterion for the \(i\hbox {th}\) alternative

\(T_{i}\) :

Chebyshev orthogonal polynomial term

\(v_{ij}\) :

The weighted normalized value of \(j\hbox {th}\) criterion for the \(i\hbox {th}\) alternative

\(w_{j}\) :

The weight value assigned to the \(j\hbox {th}\) criterion

W :

The weight set

\(x_{ij}\) :

The value of the \(j\hbox {th}\) criterion for the alternative \(A_{i}\)

X :

The decision matrix

\(y\) :

Response or TOPSIS score

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Acknowledgments

The author is grateful to the editor and the anonymous referees for their insightful and constructive comments and suggestions, which have been very helpful for improving this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 51375389).

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Authors and Affiliations

  1. School of Marine Science and Technology, Northwestern Polytechnical University, No. 127 Youyi Road (West), Xi’an, 710072, People’s Republic of China

    Peng Wang, Zhouquan Zhu & Shuai Huang

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  1. Peng Wang
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  2. Zhouquan Zhu
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Correspondence to Peng Wang.

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Wang, P., Zhu, Z. & Huang, S. The use of improved TOPSIS method based on experimental design and Chebyshev regression in solving MCDM problems. J Intell Manuf 28, 229–243 (2017). https://doi.org/10.1007/s10845-014-0973-9

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