To implement fuzzy properties using Matlab

Aim  – To implement fuzzy properties.

Tools – MATLAB                                                                                             

Theory – Fuzzy Properties are as follows-

·         Commutative:

Ø  Union of sets is commutative: that is,
A ∪ B = B ∪ A

Ø  Intersection of sets is commutative: that is,
A ∩ B = B ∩ A

·         Associativity:

Ø  Union of sets is associative: that is,
A ∪ (B ∪ C) = (A ∪B) ∪ C

Ø  Intersection of sets is associative: that is,
A ∩ (B ∩ C) = (A ∩ B) ∩ C

·         Distributivite:

Ø  Union distributes over intersection: that is,
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Ø  Intersection distributes over union: that is,
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

·         Idempotence:

Ø  Sets are idempotent under union: that is, for all sets A,
A ∪ A = A

Ø  Sets are idempotent under intersection: that is, for all sets A,

A ∩ A = A

·         Identity:

Ø  A ∪ ∅ = A

Ø  A ∩ ∅= A

·         Involution:

Ø  (A ) =A

Program –

clc

a=[0.4 0.5 0.6 0.4]

b=[0.4 0.6 0.6 0.3]

c=[0.5 0.3 0.6 0.1]

fi=[0 0 0 0]

disp('=====================================================================');

disp('Comutative Law');

union=max(a,b)

union1=max(b,a)

if(union == union1)   

        disp('Comutative Law is Satisfied for Union');   

end 

inter=min(a,b)

inter1=min(b,a)

if(inter == inter1)

        disp('Comutative Law is Satisfied Intersect');   

end

disp('=====================================================================');

disp('Associativity Law');

assou=max(a,max(b,c))

assou1=max(max(a,b),c)

if(assou == assou1)

    disp('Associative Law is Satisfied for Union');

end

assoi=min(a,min(b,c))

assoi1=min(min(a,b),c)

if(assoi == assoi1)

     disp('Associative Law is Satisfied for Intersect');

end

disp('=====================================================================');

disp('Distributive Law');

disu=max(a,min(b,c))

disu1=min(max(a,b),max(a,c))

if(disu == disu1)

    disp('Distributive Law is Satisfied for Union');

end

disi=min(a,max(b,c))

disi1=max(min(a,b),min(a,c))

if(disi == disi1)

    disp('Distributive Law is Satisfied Intersect');

end

disp('=====================================================================');

disp('Idempotance Law');

ideu=max(a,a)

a

if(ideu == a)

    disp('Idempotance Law is Satisfied for Union');

end

idei=min(a,a)

a

if(idei == a)

    disp('Idempotance Law is Satisfied for Intersect');

end

disp('=====================================================================');

disp('Identity Law');

ideu=max(a,fi)

if(ideu == a)

    disp('Identity Law is Satisfied for Union');

end

idei=min(a,fi)

if(idei == fi)

    disp('Identity Law is Satisfied for Intersect');

end

disp('=====================================================================');

disp('Involution Law');

inv=(1-(1-a))

a

if(inv == a)

    disp('Involution Law is Satisfied');

end

Output –