A Comparison between Two Types of Fuzzy TOPSIS Method

Abstract

Abstract-Multi Criteria Decision Making methods have been developed to solve complex real-world decision problems. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is currently one of the most popular methods and has been shown to provide helpful outputs in various application areas. In recent years, a variety of extensions, including fuzzy extensions of TOPSIS have been proposed. One challenge that has arisen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. Thus, in this paper, a comparison between the classical Fuzzy TOPSIS method proposed by Chen in 2000 and the recently Fuzzy TOPSIS proposed extension by Yuen in 2014 is made. The purpose of this comparative study is to show the difference between both methods and to provide context for their respective strengths and limitations both in complexity of application, and expressiveness of results. A detailed synthetic numeric example and comparison of both methods are provided.

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“…This method has been successfully used in various areas, requiring multi-criteria decision making. The fuzzy version of the TOPSIS, introduced in (Chen, 2000) and elaborated in the follow-up research and publications (Chu, (2002); Mahdavi et al, 2008;Wang and Lee, 2009;Kaya and Kahraman (2011); Madi et al, 2015;Nădăban et al, 2016;Palczewski and Sałabun, 2019), laid down a methodological foundation for applications of the Z-number based versions of the TOPSIS (Yaakob and Gegov, 2015;Krohling et al, 2016;Wang and Mao, 2019).…”

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“…The fuzzy set theory uses membership functions to permit the gradual assessment of element membership in a set. Thus, a fuzzy set in may be represented as [17],…”

“…According to Madi et al [17] -A fuzzy number M is a convex normal fuzzy set M of the real line R such that [18]: There exists exactly one with ( ) ( is called mean value of M) and ( ) is piecewise continuous.‖ Among various fuzzy numbers like triangular fuzzy number (TFN), trapezoidal fuzzy number, bell-shaped fuzzy number, etc., TFN is the most commonly used due to its computational simplicity and intuitiveness. TFN is a triplet of three real numbers ( ) (see Fig.…”