Abstract: Problem of comparing alternatives with numerical quality indicators, which due to uncertainty have interval representations, is considered. It is demonstrated inevitability of presence in similar tasks of irremovable risk of making a wrong decision on preference of alternatives. It is emphasized necessity of the account in dealing with such problems both indicators of preference for analyzed alternative in comparison with other objects in their group and risk indicators of making wrong decision. Advantages and disadvantages of available methods of interval alternatives comparing are analyzed. Namely, methods of comparison are considered based on principles of dominance by probability, evaluation methods based on average indicators, new method of collective risk estimating, and methods of “mean – risk” approach. The arguments are given that methods of dominance by probability and methods based on average indicators as tools, which do not allow estimate risk of making a wrong decision explicitly, can play only an auxiliary role in decision-making. Advantages of the method of collective risk estimating consist in account of integral risk in concrete group of compared interval alternatives. Disadvantages are consequence of the fact that the method compares only relative preferences of alternative and permits take into account acceptability of separate alternative only after additional constructions. In the framework of “mean – risk” approach properties of such convenient for practice risk indicator as average semideviation were studied for some simple but important for applications distribution functions of preference chances. It is shown that in some cases instead of average semideviation indicator using of indicators of risk based on results of methods evaluating of deviation from target marks is more expedient. An advantage of methods of “mean – risk” approach is the possibility of calculating for each alternative pair of basic indicators needed for the evaluation interval alternatives, indicator of acceptability of alternatives and indicator of associated risk. The disadvantages include the fact that both of these indicators are calculated for an alternative as an independent object, which is not associated with others in compared group. Comparison of the alternatives on preference is based on values of these indicators but dependence of the risk on the context is not taken into account. Due to presence of both advantages and disadvantages of the methods is proposed to use a three-step approach to decision-making on the selection of interval alternatives, which is based on consistent using of different methods: A stage of the preliminary analysis of alternatives for the purpose of culling some of their number and reducing the dimension of the problem and size of collective risk by this is suggested to include in the procedure of decision making on the choice of the preferred objects. Method 304 International Journal “Information Theories and Applications”, Vol. 23, Number 4, © 2016 of average estimates is suggested to use at this stage. Using of the collective risk estimating techniques with isolating of a small number of alternatives as acceptable by the indicator of preference, as well as having the lowest risk of wrong estimates, is recommended at the following stage and methods of “mean – risk " approach at the final stage.

Keywords: comparing interval alternatives, methods of probabilistic dominance, collective risk estimating, “mean-risk” methods, joint using of the methods.

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

Link:

DECISION-MAKING IN GROUPS OF INTERVAL ALTERNATIVES

Gennady Shepelev

http://www.foibg.com/ijita/vol23/ijita23-04-p01.pdf