Discrete Mathematics

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Definition (a) The support

of

a fuzzy subset, since fuzzy subsets are mappings, is defined in the usual way as

Supp(A) = {x;

A(x)

:;to

0}

that is, it is a classical set.

(b) The

kernel

of

a fuzzy subset A is a classical set

Ker(A) = {x;

A(x)

= l}

(c) The height

of

a fuzzy subset A is defined as

hgt(.4)

=sup

{A(x) ;

xES}

that is, the least upper bound

of

A(x).

(d) A fuzzy subset is nonnal

if

Ker(A)

:;to

0,

that is, hgt(A) = l and it is subnormal otherwise. A non-

empty subset

A can always be normalized by dividing

A(x)

by

hgt(A).

As a matter

of

convenience we will

generally ...