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A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

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Abstract

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.

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Abbreviations

n :

the number of alternatives

p :

the number of decision makers

D :

decision matrix

C ki :

relative closeness of alternative i by decision maker k

α kij :

weighted difference between alternatives i and j by decision maker k

α k :

weighted difference for decision maker k

φ ki :

preference ranking of alternative i by decision maker k

φ Gi :

preference ranking of alternative i by the group

β ki :

preference priorities of alternative i by decision maker k

\({\beta _i^{(G)}}\) :

preference priorities of alternative i by the group

G :

group decision matrix

\({C_{ki}^{(w)}}\) :

revised relative closeness of alternative i by decision maker k

G′:

weighted group decision matrix

v ki :

weighted relative closeness of alternative i by decision maker k

\({A_{G}^{\ast}}\) :

group positive ideal solution set

\({A_G ^{-}}\) :

group negative ideal solution set

\({v_{Gk}^{\ast}}\) :

best scores with respect to decision maker k by the group

\({v_{Gk}^{-}}\) :

worst scores with respect to decision maker k by the group

\({S_{Gi}^{\ast}}\) :

separation of alternative i with respect to group positive ideal solution by the group

\({S_{Gi}^{-}}\) :

separation of alternative i with respect to group negative ideal solution by the group

C Gi :

relative closeness of alternative i by the group

η ki :

differences of alternative i between decision maker k and the group

\({\eta _{ki}^{\prime}}\) :

normalized differences of alternative i between decision maker k and the

\({S_{Gi}^{-}}\) :

group

η k :

mean differentiation coefficient by decision maker k

ζ ki :

rank differences by alternative i between decision maker k and the group

a :

smoothing constant

r k :

revised rank correlation by decision maker k

a ki :

weight by smoothing constant of alternative i by decision maker k

\({r_{k}^{(d)}}\) :

decision’s rank correlation by decision maker k

τ k :

satisfaction index by decision maker k

τ :

satisfaction index by the group

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Authors and Affiliations

  1. Department of Industrial and Information Management, National Cheng Kung University, 1 University Rd., Tainan, 701, Taiwan

    Yeu-Shiang Huang & Wei-Hao Li

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  1. Yeu-Shiang Huang
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  2. Wei-Hao Li
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Correspondence to Yeu-Shiang Huang.

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Huang, YS., Li, WH. A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making. Group Decis Negot 21, 461–473 (2012). https://doi.org/10.1007/s10726-010-9218-2

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