Background
Ordinary aggregated indices method allows comprehensive estimation of complex (multi-attribute) objects’ quality. Examples of such complex objects (decision alternatives, variants of a choice, etc.) may be found in diverse areas of business, industry, science, etc. (e.g., large-scale technical systems, long-time projects, alternatives of a crucial financial/managerial decision, consumer goods/services, and so on). There is a wide diversity of qualities under evaluation too: efficiency, performance, productivity, safety, reliability, utility, etc. The essence of the aggregated indices method consists in an aggregation (convolution, synthesizing, etc.) of some ''single indices (criteria)'' q(1),...,q(m), each single index being an estimation of a fixed quality of multiattribute objects under investigation, into one ''aggregated index (criterion)'' Q=Q(q(1),...,q(m)). In other words, in the aggregated indices method single estimations of an object, each of them being made from a single (specific) “point of view” (single criterion), is synthesized by ''aggregative function'' Q=Q(q(1),...,q(m)) in one aggregated (general) object's estimation Q, which is made from the general “point of view” (general criterion). Aggregated index Q value is determined not only by single indices’ values but varies depending on non-negative weight-coefficients w(1),...,w(m). ''Weight-coefficient'' (“weight”) w(i) is treated as a ''measure of relative significance'' of the corresponding single index q(i) for general estimation Q of the quality level.Summary
It is well known that the most subtle and delicate stage in a variant of the aggregated indices method is the stage of weights estimation because of usual shortage of information about exact values of weight-coefficients. As a rule, we have only ''non-numerical (ordinal) information'', which can be represented by a system of equalities and inequalities for weights, and/or ''non-exact (interval) information'', which can be represented by a system of inequalities, which determine only intervals for the weight-coefficients possible values. Usually ordinal and/or interval information is ''incomplete'' (i.e., this information is not enough for one-valued estimation of all weight-coefficients). So, one can say that there is only non-numerical (ordinal), non-exact (interval), and non-complete information (''NNN-information'') I about weight-coefficient. As information I about weights is incomplete, then ''weight-vector'' w=(w(1),...,w(m)) is ambiguously determined, i.e., this vector is determined with accuracy to within a set W(I) of all admissible (from the point of view of NNN-information I) weight-vectors. To model such ''uncertainty'' we shall address ourselves to the ''concept of BayesianApplications
*Support of crucial managerial decisions of high level, which characterized by a great volume of non-numeric and uncertain information *Estimation under uncertainty of complex technical systems efficiency, capacity and performance *Multi-criteria choice of alternatives under shortage of information about criteria priorities; revelation of decision-making person priorities *Synthesis of a collective opinion of an expert committee under deficiency of information about expert qualification *Construction of hierarchical systems of decision-making (hierarchical systems of evaluation of complex multilevel objects) under uncertainty *Multi-criteria pattern recognition and classification under shortage of information about significance and reliability of employed sources of data *Multi-criteria evaluation and prognosis of dynamic alternatives for economical, financial and insurance juncture *Allocation of resources (investments) when only nonnumeric, inexact and incomplete information about admissible investments is attainable. *Multilateral analysis of financial institutes (commercial banks, insurance companies, investment funds, etc.) efficiency and reliability under uncertainty; flexible multi-criteria express-rating of financial institutes.History
The aggregated indices method was explicitly represented by colonel Aleksey Krylov (the well known Russian specialist in applied mathematics, member of thePublications
* * * *{{cite conference , author1=Popovich V. , author2=Hovanov N. , author3=Schrenk M. , author4=Prokaev A. , author5=Smirnova A. , title=Situation assessment in everyday life , editor=Schrenk M. , conference=Proceedings of the 13th International Conference Urban Planning, Regional Development and Information Society , pages=637–652 , publisher=Real Corp 008 , year=2008 , location=Vienna , url=http://programm.corp.at/cdrom2008/papers2008/CORP2008_89.pdf , display-editors=etalSee also
* Decision-making software Multiple-criteria decision analysis