|
Aggregated Indices Randomization Method
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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aleksey Krylov
, birth_date = O.S. (August 15, 1863 N.S.) , death_date = , image = Alexey Krylov 1910s.JPG , image_size = 200px , caption = Official portrait (1910) , birth_place = Alatyrsky uezd of Simbirsk Gubernia, Russian Empire , death_place = Leningrad, USSR , placeofburial = Leningrad, USSR , placeofburial_label = , allegiance = Russian Empire , branch = Imperial Russian Navy , serviceyears = 1878–1917 , rank = General of the fleet , unit = , commands = , battles = , awards = , relations = , laterwork = , signature = Signature of Aleksey Krylov.png , signature_size = 150px , signature_alt = Aleksey Nikolaevich Krylov (russian: Алексе́й Никола́евич Крыло́в; – October 26, 1945) was a Russian naval engineer, applied mathematician and memoirist. Biography Aleksey Nikolayevich Krylov was born on August 3 O.S., 1863 in Visyaga vill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Number
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used. To extend this process to various infinite sets, ordinal numbers are defined more generally as linearly ordered labels that include the natural numbers and have the property that every set of ordinals has a least element (this is needed for giving a meaning to "the least unused element"). This more general definition allows us to define an ordinal number \omega that is greater than every natural number, along with ordinal numbers \omega + 1, \omega + 2, etc., which are even greater than \omega. A linear order such that every subset has a least element is called a well-order. The axiom of choice implies that every set can be well-ordered, and given two well-ordered sets, one is isomorphic to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers satisfying is an interval which contains , , and all numbers in between. Other examples of intervals are the set of numbers such that , the set of all real numbers \R, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element). Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure. Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-criteria Decision Analysis
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine). Conflicting criteria are typical in evaluating options: cost or price is usually one of the main criteria, and some measure of quality is typically another criterion, easily in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider – it is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, managers are interested in getting high returns while simultaneously reducing risks; however, the stocks that have the potential of bringing high returns typically carry high risk of losing money. In a service industry, customer satisfaction and the cost of providing service are fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity
Fidelity is the quality of faithfulness or loyalty. Its original meaning regarded duty in a broader sense than the related concept of ''fealty''. Both derive from the Latin word ''fidēlis'', meaning "faithful or loyal". In the City of London financial markets it has traditionally been used in the sense encompassed in the motto "My word is my bond". Audio and electronics In audio, "fidelity" denotes how accurately a copy reproduces its source. In the 1950s, the terms " high fidelity" or "hi-fi" were popularized for equipment and recordings which exhibited more accurate sound reproduction. For example, a worn gramophone record will have a lower fidelity than one in good condition, and a recording made by a low budget record company in the early 20th century is likely to have significantly less audio fidelity than a good modern recording. Similarly in electronics, fidelity refers to the correspondence of the output signal to the input signal, rather than sound quality, as in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Probability
Bayesian probability is an Probability interpretations, interpretation of the concept of probability, in which, instead of frequentist probability, frequency or propensity probability, propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with Hypothesis, hypotheses; that is, with propositions whose truth value, truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomization
Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with nonprobability sampling where arbitrary individuals are selected. In various contexts, randomization may involve: * generating a random permutation of a sequence (such as when shuffling cards); * selecting a random sample of a population (important in statistical sampling); * allocating experimental units via random assignment to a treatment or control condition; * generating random numbers (random number generation); or * transforming a data stream (such as when using a scrambler in telecommunications). Applications Randomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Academy Of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals. Peter the Great established the Academy (then the St. Petersburg Academy of Sciences) in 1724 with guidance from Gottfried Leibniz. From its establishment, the Academy benefitted from a slate of foreign scholars as professors; the Academy then gained its first clear set of goals from the 1747 Charter. The Academy functioned as a university and research center throughout the mid-18th century until the university was dissolved, leaving research as the main pillar of the institution. The rest of the 18th century continuing on through the 19th century consisted of many published academic works from Academy scholars and a few Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision-making Software
Decision-making software (DM software) is software for computer applications that help individuals and organisations make choices and take decisions, typically by ranking, prioritizing or choosing from a number of options. An early example of DM software was described in 1973.Dyer, JS (1973), "A time-sharing computer program for the solution of the multiple criteria problem", ''Management Science'', 19: 1379-83.Wallenius, J, Dyer, JS, Fishburn, PC, Steuer, RE, Zionts, S and Deb, K (1992), "Multiple criteria decision making, multiattribute utility theory: The next ten years", ''Management Science'', 38: 645-54. Before the advent of the World Wide Web, most DM software was spreadsheet-based, with the first web-based DM software appearing in the mid-1990s.Koksalan, M, Wallenius, J, and Zionts, S, ''Multiple Criteria Decision Making: From Early History to the 21st Century'', World Scientific Publishing: Singapore, 2011. Nowadays, many DM software products (mostly web-based) are available ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
