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
Response feature analysis is the approach to the analysis of longitudinal data including the calculation of the suitable summary measures from the set of repeated measures on each

Option-3 scheme is a scheme of measurement used in the situations investigating possible changes over the time in longitudinal data. The scheme is planned to prevent measurement o

Odds ratio is the ratio of the odds for the binary variable in two groups of the subjects, such as, males and females. If the two possible states of variable are labeled as 'succe

Over dispersion is the phenomenon which occurs when empirical variance in the data exceeds the nominal variance under some supposed model. Most often encountered when the modeling

Nuisance parameter : The parameter of the model in which there is no scienti?c interest but whose values are generally required (but in usual are unknown) to make inferences about

Literature controls : The patients with the disease of interest who have received, in the past, one of two treatments under the investigation, and for whom the results have been pu

The computer programs designed to mimic the role of the expert human consultant. This type of systems are capable to cope with the complex problems of the medical decision makin

Behrens Fisher problem : The difficulty of testing for the equality of the means of the two normal distributions which do not have the equal variance. Various test statistics have

cholscores Treatment income ($000) Patient ID low Income? 0.6 Old 21.3 2 Yes 0.17 Old 27.2 13 Yes 0.69 New 27.1 16 Yes 1.09 Old 94.8

Higher criticism is a multiple-comparison test concept arising from the situation where there are number of independent tests of significance and interest lies in the rejecting jo