In this paper, we mainly propose a definition of partial entropy for uncertain random variables. In fact, partial entropy is a tool to characterize how much of entropy of an uncertain random variable belongs to the uncertain variable. Furthermore, some properties of partial quadratic entropy are investigated such as positive linearity. Finally, some other types of partial entropies are studied.
BhandariD. and PalN.R., Some new information for fuzzy sets, Information Science67(3) (1993), 209–228.
2.
ChenX.W. and DaiW., Maximum entropy principle for uncertain variables, International Journal of Fuzzy Systems13(3) (2011), 232–236.
3.
DaiW. and ChenX.W., Entropy of function of uncertain variables, Mathe-matical and Computer Modelling55(3-4) (2012), 754–760.
4.
De LucaA. and
TerminiS., A definition of nonprobabilitistic entropy in the setting of fuzzy sets theory, Information and Control20 (1972), 301–312.
5.
GaoR., Milne method for solving uncertain differential equations, Applied Mathematics and Computation274 (2016), 774–785.
6.
GaoR. and ChenX.W., Some concepts and properties of uncertain fields, Journal of Intelligent and Fuzzy Systems. DOI: 10.3233/JIFS-16314
7.
GaoR. and ShengY.H., Law of large numbers for uncertain random variables with different chance distributions, Journal of Intelligent and Fuzzy Systems31(3) (2016), 1227–1234.
8.
GaoR. and YaoK., Importance index of components in uncertain reliability systems, Journal of Uncertainty Analysis and Applications. DOI: 10.1186/s40467-016-0047-y
9.
GaoR. and YaoK., Importance index of components in uncertain random systems, Knowledge-Based Systems109 (2016), 208–217.
10.
GaoX.L., Regularity index of uncertain graph, Journal of Intelligent and Fuzzy Systems27(4) (2014), 1671–1678.
11.
HouY.C., Subadditivity of chance measure, Journal of Uncertainty Analysis and Applications2 (2014), Article 14.
12.
JaynesE., Information theory and statistical mechanics, Phisical Reviews106(4) (1957), 620–630.
13.
KaufmannA., Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975.
14.
KoskoB., Fuzzy entropy and conditioning, Information Sciences40 (1986), 165–174.
15.
KahnemanD. and TverskyA., Prospect theory: An analysis of decision under risk, Econometrica47(2) (1979), 263–292.
16.
KwakernaakH., Fuzzy random variables-1: Definitions and theorems, Information Sciences15(1) (1978), 1–29.
17.
KwakernaakH., Fuzzy random variables-2: Algorithms and examples for the discrete case, Information Sciences17(3) (1979), 253–278.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
20.
LiuB., Theory and practice of uncertain programming, 2nd ed., Springer, Berlin, 2009.
21.
LiuB., Why is there a need for uncertainty theory?Journal of Uncertain Systems6(1) (2012), 3–10.
22.
LiuY.H., Uncertain random variables: A mixture of uncertainty and randomness, Soft Computing17(4) (2013), 625–634.
23.
LiuY.H., Uncertain random programming with applications, Fuzzy Optimization and Decision Making12(2) (2013), 153–169.
24.
LiuY.K. and LiuB., Fuzzy random variables: A scalar expected value operator, Fuzzy Optimization and Decision Making2(2) (2003), 143–160.
25.
LiuY.K. and LiuB., Fuzzy randomprogramming with equilibrium chance constraints, Information Sciences170 (2005), 363–395.
26.
NingY.F., KeH. and FuZ.F., Triangular entropy of uncertain variables with application to portfolio selection, Soft Computing19(8) (2015), 2203–2209.
27.
PuriM. and RalescuA.D., Fuzzy random variables, Journal of Mathematical Analysis and Applications114 (1986), 409–422.
28.
KruseR. and MeyerK., Statistics with vague data. Reidel Publishing Company, Dordrecht, 1987.
29.
ShannonC., A mathematical theory of communication, Bell System Techcnical Journal27 (1948), 373–423.
30.
ShengY.H., ShiG. and RalescuD.A., Entropy of uncertain random variables with application to minimum spanning tree problem, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, to be published.
31.
ShengY.H. and WangC.G., Stability in p-th moment for uncertain differential equation, Journal of Intelligent and Fuzzy Systems26(3) (2014), 1263–1271.
32.
TangW.P. and GaoW.N., Triangular entropy of uncertain variables, Information: An International Interdisciplinary Journal16(2(A)) (2013), 1279–1282.
33.
YagerR.R., On measures of fuzziness and negation, Part I: Membership in the unit interval, International Journal of General Systems5 (1979), 221–229.
34.
YaoK., GaoJ.W. and DaiW., Sine entropy for uncertain variables, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems21(5) (2013), 743–753.
35.
ZhangZ.Q., GaoR. and YangX.F., The stability of multifactor uncertain differential equation, Journal of Intelligent and Fuzzy Systems30(6) (2016), 3281–3290.
36.
ZadehL., Fuzzy sets, Information and Control8 (1965), 338–353.
