This question is not very clear, there are an unlimited number of possible solutions, here are two of them:

public class WeirdQuestion {

    // Assuming 0<=threshold<=1
    public static double ThresholdRoundMethodOne(double value, double threshold) {
        return Math.round(value-(1.0-threshold));
    }

    // No limitations for threshold
    public static double ThresholdRoundMethodTwo(double value, double threshold) {
        threshold = threshold-(int)threshold;
        return Math.round(value-(1.0-threshold));
    }


    public static void main(String[] args) {
        double threshold = 0.8;
        System.out.println("MethodOne: 1.08: "+ThresholdRoundMethodOne(1.08, threshold));
        System.out.println("MethodOne: 1.56: "+ThresholdRoundMethodOne(1.56, threshold));
        System.out.println("MethodOne: 1.67: "+ThresholdRoundMethodOne(1.67, threshold));
        System.out.println("MethodOne: 1.98: "+ThresholdRoundMethodOne(1.98, threshold));
        System.out.println("MethodOne: 1.89: "+ThresholdRoundMethodOne(1.89, threshold));
        System.out.println("MethodOne: 1.8 : "+ThresholdRoundMethodOne(1.8, threshold));
        threshold = 1.8;
        System.out.println("------------------------------------------------------------");
        System.out.println("MethodTwo: 1.08: "+ThresholdRoundMethodTwo(1.08, threshold));
        System.out.println("MethodTwo: 1.56: "+ThresholdRoundMethodTwo(1.56, threshold));
        System.out.println("MethodTwo: 1.67: "+ThresholdRoundMethodTwo(1.67, threshold));
        System.out.println("MethodTwo: 1.98: "+ThresholdRoundMethodTwo(1.98, threshold));
        System.out.println("MethodTwo: 1.89: "+ThresholdRoundMethodTwo(1.89, threshold));
        System.out.println("MethodTwo: 1.8 : "+ThresholdRoundMethodTwo(1.8, threshold));
        System.out.println("Done!");
    }


}