Abstract: A generalization of fuzzy
set theory is discussed in this paper. We define a weak Boolean algebra with two
distinct operations and Then we suppose that a weak Boolean Algebra is assigned to each x
in X and let H
denote Each modern set A is
characterized by a membership function such that for each assigns an element When A is a set in
the ordinary sense of the term its membership function can take on only two values and with or according to whether x
does or does not belong to A. The
operations and coincide with the set
operations Èand Ç respectively, in Some examples of modern sets are included. Some possibilities
of its applications are discussed.
Keywords and phrases: fuzzy set, L-fuzzy set, generalized fuzzy set.
