Seyyed Hamed Abtahi - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Gholamhossein Yari - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
Farhad Hosseinzadeh Lotfi - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Rahman Farnoosh - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran

In this paper we introduce concepts of pseudo-triangular entropy as a supplement measure of uncertainty in the uncertain portfolio optimization. We first prove that logarithm entropy and triangular entropy for uncertain variables sometimes may fail to measure the uncertainty of an uncertain variable. Then, we propose a definition of pseudo-triangular entropy as a supplement measure to characterize the uncertainty of uncertain variables and we derive its mathematical properties. We also give a formula to calculate the pseudo-triangular entropy of uncertain variables via inverse uncertainty distribution. Moreover, we use the pseudo-triangular entropy to characterize portfolio risk and establish some uncertain portfolio optimization models based on different types of entropy. A genetic algorithm (GA) is implemented in MATLAB software to solve the corresponding problem. Numerical results show that pseudo-triangular entropy as a quantifier of portfolio risk outperforms logarithm entropy and triangular entropy in the uncertain portfolio optimization.

Entropy, Uncertain variable, Uncertainty theory, Pseudo-triangular entropy, uncertain portfolio optimization