Fractional Deng Entropy and Extropy and Some Applications |
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| Authors: | Mohammad Reza Kazemi Saeid Tahmasebi Francesco Buono Maria Longobardi |
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| Institution: | 1.Department of Statistics, Faculty of Science, Fasa University, Fasa 746-168-6688, Iran;2.Department of Statistics, Persian Gulf University, Bushehr 751-691-3817, Iran;3.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Naples, Italy;4.Dipartimento di Biologia, Università degli Studi di Napoli Federico II, 80138 Naples, Italy |
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| Abstract: | Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures. |
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| Keywords: | measures of uncertainty fractional entropy Deng entropy and extropy classification and discrimination |
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