Weights And Their Use Of Them In Mathmatics

We　introduce　the　notion　of　weight　in　this　paper,　we　have　shown　that　many　fuzzy　structures　can　be　characterized　by　making　use　of　weight.　Furthermore,　we　have　given　a　concrete　description　of　many　structures　using　the　notion　of　weight.　First,　we　introduce　the　definition　of　weight,　anti-fuzzy　subgroup　and　intuitionistic　fuzzy　subgroup　.　And　discuss　the　one　to　one　relations　between　weight　and　anti-fuzzy　subgroup　,　intuitionistic　weight　and　　intuitionistic　fuzzy　subgroup　.　secondly,　regular　weight　is　introduced　on　the　base　of　the　definition　of　regular　fuzzy　subgroup.　And　regular　fuzzy　subgroup　which　can　be　characterized　by　making　use　of　weight　is　proved.　Thirdly,　we　introduce　the　definition　of　convex　fuzzy　set　and　convex　　intuitionistic　fuzzy　set.　And　discuss　the　characters　of　them　.we　proved　the　one　to　one　relations　between　them.　Finally,we　introduce　the　notions　of　fuzzifying　topology　and　intuitionistic　fuzzifying　topology,　discuss　the　using　of　weight　and　regular　weight　in　the　fuzzifying　topology　and　intuitionistic　fuzzifying　topology.