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Figure 2. The membership function for the established portfolio’s anticipated profit<br />

b) The membership function of the objective „the portfolio’s risk”:<br />

1<br />

μ w ( x)<br />

=<br />

1 + exp( α ( w(<br />

x)<br />

− w ))<br />

where w is the inflexion point where the membership function takes the value 0.5<br />

M<br />

and α can be given by the investor, according to its own degrees of satisfaction for<br />

r<br />

the anticipated profile. r represents the central aspiration level for the anticipated<br />

M<br />

profile returned by the portfolio. Figure 3 shows the membership function for the<br />

established risk objective.<br />

Figure 3. The membership function for the established risk portfolio<br />

c) The membership function of the objective „the portfolio’s liquidities”:<br />

1<br />

μ ˆ ( x)<br />

= l<br />

1+<br />

exp( −α<br />

( ( ˆ<br />

l E l ( x))<br />

− lM<br />

))<br />

where l is the inflexion point where the membership function takes the value 0.5 and<br />

M<br />

α can be given by the investor, according to its own degrees of satisfaction for the<br />

r<br />

anticipated profile. r represents the central aspiration level for the anticipated profile<br />

M<br />

returned by the portfolio. Figure 4 shows the membership function for the established<br />

liquidity objective.<br />

w<br />

~ 340 ~<br />

M

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