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Mathematical Problems in Engineering
Volume 2015, Article ID 154848, 7 pages
http://dx.doi.org/10.1155/2015/154848
Research Article

Generalizing and Integrating TOPSIS and Cook-Seiford Method for Multicriteria Group Decision-Making with Both Cardinal and Ordinal Data

1School of Information and Communication Engineering, Hunan Institute of Science and Technology, Yueyang 414006, China
2School of Computer, Hunan Institute of Science and Technology, Yueyang 414006, China

Received 5 December 2014; Accepted 21 February 2015

Academic Editor: Tofigh Allahviranloo

Copyright © 2015 Wu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The TOPSIS and Cook-Seiford social choice function are generalized and integrated for multicriteria group decision-making (MCGDM) with both cardinal evaluations and ordinal preferences of the alternatives. Unlike traditional TOPSIS, at first, the group’s positive ideal solution and negative ideal solution under cardinal and ordinal preferences are defined, respectively. Thus the group rankings of the alternatives with respect to each criterion are derived from the individual preferences by the modified group TOPSIS considering the weights of decision makers under each criterion. Then the weighted distance function representing the total inconsistency between the comprehensive rankings of all alternatives and the ones under all criteria is presented after the criteria weights are taken into account. Form the perspective of minimizing the criteria-weighted distance of the rankings, a nonlinear integer programming is developed and transformed into an assignment problem to obtain the final rankings of all alternatives. An illustrative case is presented and some comparisons on the results show that the developed approach is practical and effective. This study extends TOPSIS to group decision-making with ordinal preferences and generalizes Cook-Seiford social choice function to multicriteria decision-making considering the criteria weights and can be a novel benchmark for MCGDM with both cardinal and ordinal data.