While going through different methods of risk measure i came across AVaR/CVaR, while i was calculating AVaR/CVaR in credibilistic environment using VaR, i got stuck in the calculations

eg. For triangular fuzzy numbers $A =(a1,a2,a3)$ $$VaR(\alpha)= 2*(a1-a2)*\alpha -a1;$$ $$\alpha \leq 0.5$$ $$ = 2*(a2-a3)*\alpha +a3-2*a2; $$$$\alpha >0.5$$

Now, $$ AVaR(\alpha) = (1/\alpha) \int_0^\alpha Var(\beta)d\beta$$

which somehow results in $$AVaR(\alpha)= (a1-a2)*\alpha -a1;$$$$\alpha \leq 0.5$$ $$= (a2-a3)*\alpha +a3-2*a2-1/4*\alpha(a1-2*a2+a3)$$$$\alpha >0.5$$

Plz help me wd d term $$-1/4*\alpha(a1-2*a2+a3).$$ How to get it?


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