L-fuzzy Subgroups, L-vague Ideals and Boolean Vague Sets. Dr.t.eswarlal: Study of L-fuzzy and L-vague Theory

The concept of Fuzzy set was opened up a new horizon in Mathematical Sciences. In fuzzy set theory, a fuzzy set which assigns to each object a grade of membership ranking between 0 and 1. This single value combines both evidence and nonevidence without indicating howmuch there is of each. But it is felt by several decission makers and researchers that proper decission making the evidence and non evidence both necessary. To counter this problem, the vague set theory is introduced which it has both the grade of membership and grade of nonmembership functions and these are generalization of fuzzy sets. The object of thesis, author is to generalize the fuzzy algebra in terms of L-fuzzy and vague algebra with complete version. The author introduced and studied Boolean vague sets and its algebra, this type of Booleanisation of vague sets has the advantages of representing such Boolean vague sets as a pair of arrays where each array consists of 0,s & 1's, in view of famous Stone theorem that any Boolean algebra is a subalgebra of direct product of two element Boolean algebra. Further, the author introduced and studied L-vague sets and its algebra, where L is a complete Brouwerian lattice.