A novel approach based on similarity measure for the multiple attribute group decision-making problem in selecting a sustainable cryptocurrency

Abstract

Environmental impact and sustainability challenges in the cryptocurrencies has become increasingly examined in the literature. However, studies of the multiple attribute group decision making (MAGDM) method for major selection of cryptocurrencies in advancing sustainability are still at an early stage. In particular, research on the fuzzy-MAGDM method in the evaluation of sustainability in cryptocurrencies is scarce. This paper adds contributions by developing a novel MAGDM approach to evaluate the sustainability development of major cryptocurrencies. It proposes a similarity measure for interval-valued Pythagorean fuzzy numbers (IVPFNs) based on whitenisation weight function and membership function in grey systems theory for IVPFNs. It further developed a novel generalised interval-valued Pythagorean fuzzy weighted grey similarity (GIPFWGS) measure approach to provide a more rigorous evaluation in complex decision marking problem with embedding ideal solution and membership degree. It also conducts a sustainability evaluation model of major cryptocurrencies as a numerical application and performs a robustness assessment with different variations of the expert's weight to test how different values of parameter θ can affect the ranking results of alternatives. The results suggest that Stellar is the most sustainable cryptocurrency, while Bitcoin with its intensive energy consumption, high mining cost and high computing power provides the least effective support for its sustainable development. A comparative analysis with the average value method and Euclidean distance method was performed to validate the reliability of the proposed decision-making model and provides evidence that the GIPFWGS has better fault tolerance.

Keywords: Cryptocurrency; MAGDM; Sustainability evaluation.

Fig. 1

The changing value of $GIPFWGS\left({\mu }_i,{\nu }_i\right)$ with $\theta$ (4) Boundedness: let $\mu ={\left({\mu }_1,{\mu }_2,...,{\mu }_m\right)}^T$ and $\nu ={\left({\nu }_1,{\nu }_2,...,{\nu }_m\right)}^T$ be two sets of IPFMs, then in formula (18).

Figure 2

Flowchart of the proposed approach.

Fig. 3

Variations of comprehensive preference value $s_i$ with changing values of $\theta$ In addition, the comprehensive preference value of the eight cryptocurrencies varies when the values of parameter $\theta$ are chosen from 0 to 400. As shown in Fig. 3, the comprehensive preference value generally increases as $\theta$ increases. As $\theta$ approaches 400, the ranking of the eight cryptocurrencies becomes $s_6>s_4>s_5>s_2>s_7>s_3>s_8>s_1$. In particular, Stellar (X6) is now identified as the most sustainable cryptocurrency (from third to first place), Ripple (X3) decreases from fourth to sixth place, while Bitcoin (X1) remains the most pessimistic cryptocurrency in terms of its sustainability.

Fig. 4

Variations of the optimal expert’s weight with changing values of $\theta$.

Fig. 5

Variations of ${\hat{s}}_i$ with changing values of $\theta$ 6. Comparative analysis.

Fig. 6

Variations of comprehensive preference value $s_i$ with changing values of $\theta$.

Fig. 7

Variations of the optimal expert’s weight with changing values of $\theta$.

Fig. 8

Variations of ${\hat{s}}_i$ with changing values of $\theta$ Euclidean distance.

Fig. 9

Variations of comprehensive preference value $s_i$ with changing values of $\theta$ When revalidating the optimal expert weight according to the value of $\theta$, from Fig. 10, Fig. 11, it is not difficult to find that the final ranking of comprehensive evaluation value obtained by the Euclidean distance method is with the optimal expert’s weight $\hat{\omega }=\left({\hat{\omega }}_1,{\hat{\omega }}_2,{\hat{\omega }}_3\right)=\left(\mathrm{0.11,0.89,0}\right)$, where Litecoin (X4) remains the most sustainable cryptocurrency.

Fig. 10

Variations of the optimal expert’s weight with changing values of $\theta$.

Fig. 11

Variations of ${\hat{s}}_i$ with changing values of $\theta$.