A membership function is a slice we cut off a pie: 0.2 of one pie may be a different size piece of 0.2 of another pie!

It has been proposed by Sasikala and Petrou that the membership functions are allowed to take values higher than 1, up to a value that reflects the relative importance between the different factors that are to be combined.

In their paper in Fuzzy Sets and Systems, Sasikala and Petrou proposed a training based scheme, where the appropriate operators for combining information at the disjunctive and the conjunctive levels of reasoning as well as the relative importance of the different factors are learned using training data classified by experts. During the operational stage of such a system the operators used and the relative weights of the various factors are fixed. To read more on this, click here for the acrobat version of this paper.

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