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We used a fuzzy alternative both to avoid solving a bi-objective model and mostly to<br />

highlight the decision taker’s expected satisfaction. In other words, because a<br />

nonlinear membership function may change its shape according to the parameter<br />

values, the function could better reflect the investor’s logic and expectations from this<br />

portfolio.<br />

Figure 6. Nonlinear membership function of the portfolio<br />

Table 6. Rate of return and involved risk on the selected portfolio<br />

Η ΑF ΑW<br />

PORTFOLIO RATE<br />

OF RETURN<br />

INVOLVED<br />

RISK<br />

30 600 800 0.09 0.00000002<br />

37 500 1000 0.115 0.00000001<br />

52.5 400 1200 0.215 0.000000014<br />

We consider that the first alternative is preferred by the investor, because it generates<br />

the highest degree of satisfaction after mathematically illustrating its logic regarding<br />

the investment decision. So, in order to find the portfolio structure in this case, we<br />

elaborate the following function with the aid of Wolfram Mathematica software:<br />

Figure 7. Mathematical expression of the portfolio structure<br />

We obtain the following optimal portfolio structure for maximizing the decision<br />

taker’s satisfaction:<br />

Table 7. Optimal portfolio structure<br />

MICROSOFT<br />

(M)<br />

GOOGLE<br />

(G)<br />

APPLE<br />

(A)<br />

YAHOO<br />

(Y)<br />

P1 P2<br />

7% 34% 37% 22% Yes No<br />

~ 344 ~

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