Engineering Tri: Bology by G.W. Stachowiak and A.W. Batchelor (Eds.)

By G.W. Stachowiak and A.W. Batchelor (Eds.)

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Now, let z˜j = c˜B B −1 aj = w ˜∗ aj be the fuzzy number corresponding to real −1 number zj = cB B aj with respect to a linear ranking function, where aj is the jth column of the coefficient matrix [A I] in (10). , m. , n, that is, wA ˜ c˜. , m, we have, z˜n+i − c˜n+i = c˜B B −1 ei − ˜0 = w ˜ ∗ ei = w ˜i∗ and A New Approach to Duality in Fuzzy Linear Programming 27 hence, w ˜∗ ˜ 0. , n + m implies ∗ ˜∗ ˜ 0, where w ˜∗ = c˜B B −1 . That is w ˜ ∗ is a feasible solution to that w ˜ A c˜ and w (6).

T. , n, where [ M , M ] and [l0 , l0 ] are constant. M is the pessimistic affordable risk level of investors, and M is the optimistic affordable risk level. l0 is pessimistic l0 is optimistic affordable liquidity level. The interval numbers of objective function in (LIPM ) represents portfolio affordable liquidity level, and uncertain profits, the left of (1) is risks of portfolio described by interval numbers of standard variance, the right represents affordable risk interval. The left of (2) represents uncertainty of liquidity, the right is affordable liquidity interval.

0100. 0145. 0147. ) 5 ( Conclusion These factors in securities investment all are uncertain. It is very consistent with real condition to describe the uncertainty by interval numbers. The author has converted the fuzzy portfolio selection problem with liquidity constraints into a linear programming problem with parameters. The numerical examples have shown the method for solving this problem is valid. By the results, we know that it has an obvious influence on investment whether or not to consider liquidity constraints, and different levels of liquidity have also significant implications.

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