Variable Weighted Synthesis Forecasting Of Violent Event Early-warning Grade Based On A New Fuzzy Distance

The comprehensive forecasting of violent event early-warning grade under uncertainty environment is studied. A variable weighted synthesis forecasting model is set up based on a new fuzzy distance of fuzzy numbers. The main content concludes:First, a new priority-degree for comparing a pair of interval numbers were introduced. We proved that it can avoid the unreasonable phenomenon of denominator will turn to zero when interval numbers degrade into real numbers, which were found in several possibility degrees usually used for interval number comparison. Then, some important interval number comparison related concepts, such as "totally greater than", "greater than", "exactly equal to" and "equal to" etc., were redefined based on the priority-degree. It was proved that interval numbers are reducible for addition and subtraction operations according to the redefined "equal to" relation. Finally, a method for multi-criteria decision making problems with interval data was given by using priority-degree and its validation was examined by an example.Second, the deficiences of several widely used interval distances of interval number or fuzzy distance of fuzzy number for they does not hold some usually used axiomatic conditions, such as " d(A,B)= 0<=> A= B " etc, were analyzed. Then, a new interval distance for interval numbers was defined based on the priority-degree. Further, the axiomatic definition of fuzzy distance is redefined. A new fuzzy distance for fuzzy number were proposed by using the interval distances of their cut sets. It was proved that it holds all of the axiomatic conditions of distance measure.Finally, a new membership function construction method for the single feature early-warning grade was given based on the typical history data and approximate inference. A formula based on fuzzy distance was introduced for computing the membership degree of a violent event to certain early-warning grade considering a given feature. A fuzzy distance based state-weight adapter was designed and a new mode for variable weight construction was given by adding a fuzzy distance based state-weight adapter to the usually used feature constant weight. A variable weighted synthesis forecasting model and its processes of actualizing were put forward for violent event early-warning grade. Finally, the validity of this model were examined by simulation analysis of an example.