/* 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");