This paper introduces the concept of LM-G-filter spaces as a generalization of LM-filters and studies the notions of sum, subspace, product and quotient of these spaces. The application potential of this generalization in connection with various decision making situations is brought out. Moreover, certain known theorems on stratified L-filters are disproved and efforts to correct them resulted in the introduction of stratified LM-G-filters. It is proved that the category of stratified LM-G-filters is an isomorphism closed bicoreflective full subcategory of the category of LM-G-filters. Finally, some relation between the categories of LM-filters and LM-G-filters are also obtained. [ABSTRACT FROM AUTHOR]