The Multiple Objective Decision Making (MOD) is very important not only in the economic, political and other decisions, but in daily decisions too. The description of our fuzzy environment is impossible without the MOD. The consideration of only one objective leads often to erratic forecasting and decisions /11/.

The MOD is in practice mostly based on a crisp (certain) weighting of the given objectives. The result however, does not correspond to fuzzy data. Under the conditions of incomplete information it is mandatory to introduce the LPI-fuzzy weighting.

In the Table 1 with two investment strategies x1, x2 and three objectives O1, O2, O3, the corresponding units of the objectives O1, O2, O3 are given.

The case of normalized crisp weights of the objectives:

w1 = 1/8, w2 = 1/2, w3 = 3/8
By the MaxWmin-principle following weighting sums will be obtained:
WS(x1) = 3/8 + 1/2 + 3/2 = 2 3/8 ; WS(x2) = 1/4 + 3/2 + 9/8 = 2 7/8
Thus, x2 is the MaxWmin-optimal investment strategy with the guaranteed weighted sum:

WS(x2) = 2 7/8

The LPI-fuzziness assumption (more credible)

Only the linear restrictions for the weights are known (Graph 2):

LPI(w): w1 < w3 < w2

In accordance with the calculations /11/ theMaxWmin.optimal investment strategy is again x2, but with the guaranteed weighted sum  WS(x2) = 2 2/3