Hello 

In Boolean logic, the truth values of variables may only be 0 or 1; Thus, the fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false.

Let take the example of data clustering  which is the process of dividing data elements from original images into classes or clusters so that items in the same class are as similar as possible, and items in different classes are as dissimilar as possible. In hard clustering, data is divided into distinct clusters, where each data element belongs to exactly one cluster. In fuzzy clustering (also referred to as soft clustering), data elements can belong to more than one cluster, and associated with each element  a set of membership levels. (e.g. Kmeans VS Fuzzy c-means)

Best,

Refer the paper  Mathematical computation of fuzzy statistics for sensory evaluation

international journal of information and management sciences

Refer to

http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html

The article " Mathematical computation of  fuzzy statistics for sensory evaluation "  answer  your question   It appears in the journal  international journal of information and management  sciences

Well. I am not sure if that is exactly what you are looking for, but I made a very simple model mixing a fuzzy membership function and normal distribution a few years ago, that I used to classify 3d human motions. It worked pretty well. Detail and explanation in my thesis. See: http://eprints.port.ac.uk/1668/

Statistical modeling is used to describe variability of quantities and errors in observations.But these models assume the observations to be numbers or vectors with out any uncertainty in them.  However, for data with uncertainity, the conventional statistics does't hold water. Therefore, fuzzy statistics is a suitable method only for that kind of data with all the savageness.

Reference on this link is highly useful. Because it provides a nice starting point:

http://www.statistik.tuwien.ac.at/forschung/MS/SM-2007-1complete.pdf