Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear

The various diversity measures used tomeasure biodiversity include the Margalef index, McIntosh index, Simpson index,Brillouin index, and Shannon entropy. Of these measures, the most popular isShannon entropy (H). In this study, with respect to measuring biodiversity, wecompare Shannon entropy-the essential aspect of information theory-with theDeng and improved Deng entropies, as proposed within the framework of theDempster–Shafer evidential theory. To do so, we used a hypothetical dataset ofthree complexes. Based on this hypothetic data, ecologically speaking, weobtained the most reasonable result from the improved Deng entropy. There aretwo reasons for this result: 1) Mass functions cannot be used when computingthe Shannon entropy, and 2) Deng entropy does not take into consideration thescale of the frame of discernment.