Measures of extended fractional Deng entropy and extropy with applications

Recently, Zhang and Shang introduced modifications to the concept of fractional entropy and proved some properties based on the inverse Mittag-Leffler function (MLF). The Deng entropy serves as a valuable measure in the Dempster-Shafer evidence theory (DST) to tackle uncertainty. In this study, we extend the fractional Deng entropy measure, introducing two distinct versions: Efd1α(m) and Efd2α(m). We call this new measure the extended fractional Deng entropy, EFDEn. Additionally, we apply a similar approach to the fractional Deng extropy measure, resulting in EXfd1α(m) and EXfd2α(m). We call this new measure the extended fractional Deng extropy, EFDEx. These two measures are complementary, leading to provide a deeper analysis of known and unknown information. Subsequently, we conduct a comparative analysis of these measures within the DST framework. We also propose the decomposable fractional Deng entropy, an extension of the decomposable entropy for Dempster–Shafer evidence theory, which effectively decomposes fractional Deng entropy. Finally, we delve into a pattern recognition classification problem to highlight the importance of these new measures.