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Suppose the system will give output either 1 or 0 based on the following independent variables: 

(1) variable_a: a float variable in the range of [0, 1], which can be called confidence a 
(2) varaible_b: a float variable in the range of [0, 1], which can be called confidence b
(3) varaible_c: a float variable in the range of [0, 1], which can be called confidence c

For these three confidence levels, the higher they are, the more possible the system's output is 1. The lower they are, the more possible the system's output is 0. Then the question is how I can set up a function to determine the system's output based on these variables. Any ideas will be appreciated.

feelfree
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    You could just multiply all three confidence levels ? You could also apply a suitable weighting factor to each if you wanted to control their relative contributions to the output. – Paul R Jun 16 '14 at 11:14
  • the problem is that you do not know the weights ... to solve such systems there is usually applied PCA analysis (http://en.wikipedia.org/wiki/Principal_component_analysis). The PCA it self identify input values responsible for output state and determine the transfere function (if exists). Cant help you further (never did this in praxis) ... If you want to avoid this and stick to your approach you need corelation coefficients not fuzzy probability variables – Spektre Jun 16 '14 at 12:03

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