If P, Q, R are Fuzzy propositions defined on sets A, B, C of their respective universe of discourses, then the fuzzy propositions P, Q, R are given by

P : x is A, A ⊂ X

Q : y is B, B ⊂ Y

R : y is C, C ⊂ Y

P : x is A, A ⊂ X

Q : y is B, B ⊂ Y

R : y is C, C ⊂ Y

P → Q : Max [ 1 – T(P), T(Q) ]

If A, then B (in linguistic rule form)

In set theoretic form, it is given by the relation

R = (A X B) V (A^{c} X Y)

It membership function is given by

for the linguistic “If A then B else C”, the set theoretic form is given by

R = (A X B) V (A^{c} X C)

Its membership function is given by –