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In applied mathematics and decision making, the aggregated indices randomization method (AIRM) is a modification of a well-known aggregated indices method, targeting complex objects subjected to multi-criteria estimation under uncertainty. AIRM was first developed by the Russian naval applied mathematician Aleksey Krylov around 1908. The main advantage of AIRM over other variants of aggregated indices methods is its ability to cope with poor-quality input information. It can use non-numeric (ordinal), non-exact (interval) and non-complete expert information to solve multi-criteria decision analysis (MCDM) problems. An exact and transparent mathematical foundation can assure the precision and fidelity of AIRM results. ==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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Aggregated indices randomization method」の詳細全文を読む スポンサード リンク
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