Analytical properties of credibilistic expectation functions.
The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained.
Department of Industrial & Systems Engineering, National University of Singapore, Block E1A No. 05-19, 1 Engineering Drive 2, Singapore 117576.
Shuming
0000-0002-1080-8471
S
Wang
Graduate School of Information, Production & Systems, Waseda University, Hibikino 2-7, Wakamatsu-ku, Kitakyshu, Fukuoka, Japan.
Bo
B
Wang
Graduate School of Information, Production & Systems, Waseda University, Hibikino 2-7, Wakamatsu-ku, Kitakyshu, Fukuoka, Japan.
Junzo
J
Watada
D000465:Algorithms; D003198:Computer Simulation; D017143:Fuzzy Logic; D055641:Mathematical Concepts; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*