Title: The conversion of cost and benefit criteria in the TOPSIS method

Authors: Milan Houska; Ludmila Domeova; Martina Berankova

Addresses: Department of Systems Engineering, Faculty of Economics and Management, Czech University of Life Sciences Prague, Kamycka 129, 165 21 Prague 6, Czech Republic. ' Department of Systems Engineering, Faculty of Economics and Management, Czech University of Life Sciences Prague, Kamycka 129, 165 21 Prague 6, Czech Republic. ' Department of Systems Engineering, Faculty of Economics and Management, Czech University of Life Sciences Prague, Kamycka 129, 165 21 Prague 6, Czech Republic

Abstract: Multiple attribute decision making (MADM) models involve both cost and benefit criteria. However, it is convenient to unify criteria type; this means to convert the cost criteria into benefit criteria or vice versa. There are several procedures for criteria type conversion. Unfortunately, these procedures are usually outside of the MADM methods' algorithms and some combinations of criteria type conversion method and the MADM method provide incorrect results. We focus on the method 'technique for order preference by similarity to ideal solution' (TOPSIS method) and the subtraction-based conversion procedure, which converts criterion type using the differences between criterion values and the maximum value in the criterion column. We find that this widely used procedure for criteria conversion can completely distort the results of the analysis. In this paper, we suggest a new subtraction-based conversion procedure that is possible to combine with the TOPSIS method and receive correct results.

Keywords: multicriteria decision making; MCDM; multi-attribute decision making; MADM; TOPSIS; order preference; similarity; ideal situations; criteria type conversion; cost criterion; benefit criterion; criteria weights; ideal solutions; negative-ideal solutions; Euclidean distance; Euclid; unified criteria types; algorithms; incorrect results; subtraction-based procedures; conversion procedures; criterion values; maximum values; distortion; correct results; applied decision sciences.

DOI: 10.1504/IJADS.2012.050021

International Journal of Applied Decision Sciences, 2012 Vol.5 No.4, pp.329 - 341

Published online: 09 Aug 2014 *

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