.. _step1:

Creating fuzzy sets and fuzzy variables
=======================================

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Fuzzy Sets
-----------------
Ex-Fuzzy supports different kinds of fuzzy sets, but the procedure to use them all is the same.
Fuzzy sets have a name, a domain range and a membership function::
    
    import ex_fuzzy.fuzzy_sets as fs

    cold = fs.FS('Cold', [0, 0, 5, 15] , [0,40])

This code creates a fuzzy set named "Cold", with a trapezoidal membership function and a domain that ranges from 0 to 40 degrees.
A fuzzy membership can be computed easily using the newly-created fuzzy set::

    cold(8.2)

This would be the code to do the same thing using interval-valued fuzzy sets::

    cold2 = fs.IVFS('Cold', [0, 0, 5, 10], [0, 0, 5, 15], [0,40], 0.8)

This code would create an interval-valued fuzzy set defined using a lower and upper membership function, 
the same domain and name as before, and a maximum certainty of 0.8 for the lower membership.
The membership is computed just as an ordinary fuzzy set::

    cold2(8.2)

We could use any of these kinds of fuzzy sets (or even general-type 2 fuzzy sets) to construct all the linguistic variables
for our temperature domain::

    cold = fs.FS('Cold', [0, 0, 5, 15] , [0,40])
    warm = fs.FS('Warm', [15, 20, 25, 30] , [0,40])
    hot = fs.FS('Hot', [25, 30, 40, 40] , [0,40])

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Fuzzy Variables
-----------------
Once we have the linguistic variables, we can construct a fuzzy variable. A fuzzy variable consists of a list of fuzzy sets
of the same kind and a proper name::

    temperature = fs.fuzzyVariable('Temperature', [cold, warm, hot])

We do not need to specify domain or fuzzy set type, because the ``fuzzyVariable`` class deduces it from the fuzzy sets given in the list. 
We can use a ``fuzzyVariable`` object to compute the memberships for a value to all the linguistic variables in the fuzzy variable::

    temperature(8.2)

Once we have defined the fuzzy variables, we can use them to construct a fuzzy rule base. This step is described in :ref:`step2`.