LPI-concept is of empirical character. By investigation of corresponding state time series, fuzzy statement about the state distributions or state weights, can be established. This way the credibility and degree of fuzziness of the LPI(s) can be determined. It concerns both, the optimality and stability of considered decisions and possibility of erratic decisions.

The more terms in the state time series are taken into account, the smaller the fuzziness of the results /6/.

This way the credibility and the degree of fuzziness can be tested.

On the contrary, the application of crisp distributions is of a small credibility and leads often to erratic decisions.

    Erratic decisions and the LPI-correction (A simple example)

Let us assume a risk decision situation shown in Table 1:

The crisp distribution (small credibility):

p1 = 3/4, p2 = 1/4; Expected values: E(y1) = 3 1/4, E(y2) = 2 1/2

The Bernoulli-optimal strategy: y1 with E(y1) = 3 1/4 (small credibility).

    The LPI-correction:

By the corresponding significant state time series for p1 we will obtain:

LPI(p): 1/2 < p1 < 4/5 with the credibility e.g. O > 75 %    /11/