Title: Investigation of the rank reversal problem in some novel objective weight-based MADM methods

Authors: Ravindra Singh Saluja; Varinder Singh

Addresses: Department of Mechanical Engineering, KK Birla Goa Campus, BITS Pilani, Goa, 403726, India ' Department of Mechanical Engineering, KK Birla Goa Campus, BITS Pilani, Goa, 403726, India

Abstract: Objective weight-based multi-attribute decision-making (OWMADM) methods are applied in decision situations where the weight values are not sought from decision-makers and are rather obtained based on the range or spread of attribute data. The present study develops three novel OWMADM methods, namely preference selection index proximity indexed value method (PSIPIVM), standard deviation proximity indexed value method (SDPIVM) and entropy proximity indexed value method (EPIVM), by combining the objective weights obtained through three different methods with the recently developed proximity indexed value method (PIVM), which is known to promote minimisation of the rank reversal problem. Two established criteria are adopted to evaluate the occurrence of rank reversal, one by removing the least preferred alternative from consideration while another involved splitting the considered alternatives into two sets and testing for the transitive property. The paper also attempts to identify suitable normalisation techniques for the proposed OWMADM methods to yield robust ranking orders, which may enhance the reliability of decision outcome.

Keywords: multi-attribute decision making; MADM; objective weight; PSI; SD; entropy; PIVM; rank reversal; decision analysis.

DOI: 10.1504/IJIDS.2023.134790

International Journal of Information and Decision Sciences, 2023 Vol.15 No.4, pp.431 - 456

Received: 26 Mar 2021
Accepted: 23 May 2021
Published online: 13 Nov 2023 *

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