As an important tool to measure the degree of difficulty of predicting the realization of an uncertain set, entropy theory of uncertain set has been investigated by many scholars. In order to measure the uncertainty associated with some uncertain sets, this paper first proposes the arc entropy for an uncertain set. Then a computational arc entropy formula via inverse membership function is introduced to calculate the arc entropy more quickly, and some properties of arc entropy are studied. Furthermore, some applications are also provided to illustrate the superiority of the arc entropy.
LiuY. and LioW., A revision of sufficient and necessary condition of uncertainty distribution, Journal of Intelligent and FuzzySystems38(4) (2020), 4845–4854.
13.
LuR. and WangX., Triangular entropy of uncertain sets, International Information Institute16(2) (2013), 1249–1256.
14.
ShengY. and KarS., Some results of moments of uncertain variable through inverse uncertainty distribution, Fuzzy Optimization and Decision Making14(1) (2015), 57–76.
15.
ShnnonC., WeaverW., The Mathematical Theory of communications, The Univeraity of Illinois Press, Urbana, (1949).
16.
VaidaI., Bounds of the minimal error probability on checking a finite or countable number of hypotheses, Problemy Peredachi Informatsii4(1) (1968), 9–19.
17.
WangX. and HaM., Quadratic entropy of uncertain sets, Fuzzy Optimization and Decision Making12(1) (2013), 99–109.
18.
WrightT., Factors affecting the cost of airplanes, Journal of the Aeronautical Sciences3(4) (1936), 122–128.
19.
YaoK. and KeH., Entropy operator for membership function of uncertain set, Applied Mathematics and Computation242(2014), 898–906.
20.
YaoK., Sine entropy of uncertain sets and its applications, Applied Soft Computing22 (2014), 432–442.
21.
YuX., Expected payoff of trading strategies for uncertain financial markets, Information: An International InterdisciplinaryJournal14(10) (2012), 3175–3186.
22.
YuX., A stock model with jumps for uncertain markets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems20(3) (2012), 421–432.
