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A radically different approach of dealing with the uncertainty than the traditional probabilistic and the statistical methods. The necessary feature of the fuzzy set is a membership function which assigns the grade of membership between 0 and 1 to each and every member of the set.
Mathematically the membership function of a fuzzy set A is a mapping from a space χ to unit interval As the memberships take their values in the unit interval, it is appealing to think of them as probabilities; though, memberships do not follow the laws of probability and it is possible to permit an object to simultaneously hold the nonzero degrees of membership in sets traditionally considered to be mutually exclusive.
The methods which are derived from the theory have been proposed as an alternatives to traditional statistical methods in areas like quality linear regression, control and forecasting, though they have not met with the universal acceptance and a number of statisticians have commented that they could not found any solution using such an approach which could not have been achieved as least as effectively using the probability and statistics.
1) Consider an antenna with a pattern: G(θ,φ) = sinn(θ/θ0) cos(θ/θ0) where θ0 = Π/1.5 (a) What is the 3-dB bandwidth? (b) What is the 10-dB beam width? (c) What is t
The distribution free or technique which is the analogue of the analysis of variance for the design with two factors. It can be applied to data sets which do not meet the assumptio
Initial data analysis (IDA): The first phase in the examination of the data set which comprises number of informal steps including the following steps * checking the quality o
Hazard function : The risk which an individual experiences an event in a small time interval, given that the individual has survived up to the starting of the interval. It is th
This is given by common network e.g. Phone Company. The public networks are those networks, which are given by common carriers. It can be a telephone company or an other organizati
The Null Hypothesis - H0: γ 1 = γ 2 = ... = 0 i.e. there is no heteroscedasticity in the model The Alternative Hypothesis - H1: at least one of the γ i 's are not equal
Nearest-neighbour methods are the methods of discriminant analysis are based on studying the training set subjects much similar to the subject to be classified. Classification mig
Poisson regression In case of Poisson regression we use ηi = g(µi) = log(µi) and a variance V ar(Yi) = φµi. The case φ = 1 corresponds to standard Poisson model. Poisson regre
Bayes factor : A summary of evidence for the modelM1 against the another modelM0 provided by the set of data D, which can be used in the model selection. Given by the ratio of post
Computer-aided diagnosis : The computer programs which are designed to support clinical decision making. In common, such systems are based on the repeated application of the Bay
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