LAUSR

The interval type-2 intuitionistic fuzzy random variable is an extension of the intuitionistic fuzzy random variable such that it can be a effective tool to determine some high-uncertainty phenomena. In this paper, the interval type-2 intuitionistic fuzzy random variable is introduced for the first time, and then, a scalar expected value operator of interval type-2 intuitionistic fuzzy random variable is proposed. Moreover, the new concepts of mean chance value at risk and mean chance conditional value at risk are discussed for the interval type-2 intuitionistic fuzzy random variables which have application in uncertain optimization, like fuzzy inverse location problems. Finally, it is proven that mean chance value at risk and mean chance conditional value at risk fulfill the convex risk metric properties.