/* 开始时间 */
  Date leftStartDate = feesPreferential.getPreferentialStartTime();
   /* 结束时间 */
  Date leftEndDate = feesPreferential.getPreferentialEndTime();

 /*比较的时间段*/
 Date rightStartDate = (Date) feesPreferentialList.get(i).get("preferentialStartTime");
 Date rightEndDate = (Date) feesPreferentialList.get(i).get("preferentialEndTime");

/*判断*/
if (((leftStartDate.getTime() >= rightStartDate.getTime())
                                    && leftStartDate.getTime() < rightEndDate.getTime())
                            || ((leftStartDate.getTime() > rightStartDate.getTime())
                                    && leftStartDate.getTime() <= rightEndDate.getTime())
                            || ((rightStartDate.getTime() >= leftStartDate.getTime())
                                    && rightStartDate.getTime() < leftEndDate.getTime())
                            || ((rightStartDate.getTime() > leftStartDate.getTime())
                                    && rightStartDate.getTime() <= leftEndDate.getTime())){
System.out.println("两段时间存在交集");
}
System.out.println("两段时间不存在交集");