Abstract: In this paper we address the following questions. Can we assume that choosing the best interval alternative by their pair-wise comparison, we thus choose the alternative that is preferable simultaneously all others in their given set (prefer ability “as a whole”)? Does the answer depend to this question from an amount of compared alternatives? It is shown that comparing interval alternatives "as a whole" reduces the values of chances of prefer ability for each alternative with respect to these values under pair-wise comparison. This in turn leads to a quantitative increasing risk of choice as preferred alternative the alternative, which will not be really such later, in future, when the uncertainty will be removed. The nature of this effect is that in the presence of intersection even for two comparable interval alternatives there is a non-zero risk of making the wrong decision. This risk increases with the amount of comparable alternatives, particularly if the chances of preferability for some of them are not very different from each other. Does generate the comparison "as a whole" other changes in the results of the pair-wise comparison of alternatives? Particularly important is the question of possible depending order of the alternatives in their set defined by preferebilities on using concrete approaches to comparing. The answer to this question is negative: the order established under the pair-wise comparison is the same as the order for comparing “as a whole”. However, an estimation of true value of the risk associated with decision-making is useful for decision-maker or expert. Mentioned risk is in fact greater than risk that was estimated by pair-wise comparison because is determined not only by the 168 International Journal “Information Theories and Applications”, Vol. 22, Number 2, 2015 configurations of the compared pairs of alternatives, but also the concrete set of compared alternatives i.e. the risk depends on the context. The presence of a large number of alternatives aimed at achieving the same goal is a characteristic of the upper hierarchical levels of decision-making. Perhaps this is why the risk of making not quit right decision is more likely to upper management levels. If because of some reasons it is necessary to select a number of alternatives to supporting, the delegation of authority to lower management levels with the assignment of appropriate rights of decision-making concerning corresponding subset of alternatives is presented in the framework of the considered here approach to comparing as the well-founded, because it reduces the risks of decision-making at each level of management.

Keywords: collective effect for comparing the interval alternatives, dependence of the risk of making the wrong decision about prefer ability on context, taking into account results comparing “as a whole” during deciding on preferebility

ACM Classification Keywords: H.1.2 Human information processing; G3 Distribution functions; I.2.3 Uncertainty, “fuzzy”, and probabilistic reasoning.

Link:

СРАВНЕНИЕ ИНТЕРВАЛЬНЫХ АЛЬТЕРНАТИВ “В ЦЕЛОМ”

(Comparing Interval Alternatives “As a Whole”)

Михаил Стернин, Геннадий Шепелев

http://www.foibg.com/ijita/vol22/ijita22-02-p05.pdf