Ph.D. Tezi Görüntüleme

      There are many generalizations of fuzzy subgroups. Generalized subgroups and TL- subgroups are the ones which have great importance in literature. In this thesis, the concept of generalized subgroups of a group is introduced and the fundamental properties of these subgroups are investigated. A necessary and sufficient condition is obtained for a generalized subgroup of Cartesian product of some groups to be written as the generalized product of generalized subgroups. On the other hand, it is shown that the lattice of (normal) generalized subgroups of a group is a complete lattice. Some results for special cases of these lattices are given and so that some new results on the classification of groups are obtained. One of these results is that the lattice of (normal) generalized subgroups of a group is a modular lattice. As a further result, a necessary and sufficient condition for distributivity of the lattice of generalized subgroups of a group is shown as being locally cyclic group. Also it is obtained that the lattice of generalized subgroups is pseudo complemented and the pseudo complementation of the lattice of generalized subgroups is investigated. On the other side, the lattice of TL-subgroups of a group is investigated and a characterization is obtained for modularity of this lattice. Finally, pseudo complementation of the lattice of T-fuzzy subgroups of a group is characterized by t-norms without zero-divisors.