Fuzzy set theory, Advanced Statistics

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

2335_fuzzy set theory].png 

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.

Posted Date: 7/28/2012 2:50:38 AM | Location : United States







Related Discussions:- Fuzzy set theory, Assignment Help, Ask Question on Fuzzy set theory, Get Answer, Expert's Help, Fuzzy set theory Discussions

Write discussion on Fuzzy set theory
Your posts are moderated
Related Questions
Omitted covariates is a term generally found in the connection with regression modelling, where the model has been incompletely specified by not including significant covariates.

Window variables are the variables measured during the constrained interval of an observation period which is accepted as the proxies for the information over the whole period. Fo

Growth curve analysis is t he general term for methods dealing with development of the individuals over time. A classic instance includes recordings made on a group of children, sa

Weighted least squares  is the method of estimation in which the estimates arise from minimizing the weighted sum of squares of the differences between response variable and its pr

Bivariate boxplot : A bivariate analogue of boxplot in which the inner area contains 50%of the data, and a 'fence' helps to identify the potential outliers. Robust methods or techn

Kleiner Hartigan trees is a technique for displaying the multivariate data graphically as the 'trees' in which the values of the variables are coded into length of the terminal br

Particlefilters is a simulation method for tracking moving target distributions and for reducing computational burden of the dynamic Bayesian analysis. The method uses a Markov ch

Codominance : The relationship between genotype at the locus and a phenotype to which it in?uences. If an individuals with heterozygote (such as, AB) genotype is phenotypically dif

The division of a sample of observations into several classes, together with the number of observations in each of them.  It acts as a useful summary of the main features of the da

Procedures for estimating the probability distributions without supposing any particular functional form. Constructing the histogram is perhaps the easiest example of such type of