The Problem of Rank Reversal in Combination with AHP and TOPSIS Applied to Image Fusion

Abstract

Selecting a method is a multi-criteria decision-making issue which includes both qualitative and quantitative aspects. In order to choose the best method or a solution,, it is necessary to make a transition between both visible and invisible aspects. The focus of this work is to expand a methodology to evaluate the best method based on Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). In this manuscript, by ‘method’ is meant an algorithm. The relevant criteria which affect the process of algorithmic selection are the image, the sensors, and the resources, and the available alternatives are discrete wavelet transform (DWT)-based image fusion, principal component analysis (PCA)-based image fusion, intensity hue saturation (IHS)-based image fusion, and Laplacian-based image fusion. The assessments of each criterion are calculated using pairwise comparisons based on analytic hierarchy process (AHP) and inserted to the TOPSIS method to rank the alternatives. The process of selecting the alternative and the drawback of an algorithm (AHP, TOPSIS) is demonstrated with the help of numerical example. This manuscript comprises the following section headings: Introduction, Concept of TOPSIS and AHP, Hybrid Method, A Numerical Example, Computation of TOPSIS, Occurrence of Rank Reversal, Conclusion, and References.