Entropy Optimization Model

Fuzzy entropy is used to characterize the uncertainty on the possible values of fuzzy variables, which has been studied by many researchers. Within the framework of credibility theory, Li and Liu presented a Shannon-like entropy for both discrete fuzzy variable and continuous fuzzy variable. Furthermore, Li and Liu proposed the maximum entropy principle, and proved that out of all the credibility functions with fixed expected value and variance, the normal credibility function has the maximum entropy. Based on the concept of fuzzy entropy, Li et al. proposed an entropy optimization model by minimizing the uncertainty of the fuzzy objective under certain expected constraints. This chapter mainly includes the definition of fuzzy entropy, maximum entropy theorems, entropy optimization model and its crisp equivalents, fuzzy simulation, and applications in portfolio selection problem.