15. Huáshì Supermarket offers discounts to customers, with the following rules:
(1) If a single shopping trip is less than 200 yuan, no discount is given;
(2) If a single shopping trip is between 200 yuan and 500 yuan, a 10% discount is given;
(3) If a single shopping trip exceeds 500 yuan, the first 500 yuan is given a 10% discount, and the amount exceeding 500 yuan is given a 20% discount.

Xiaoming went to the supermarket twice and paid 198 yuan and 554 yuan respectively. Now Xiaoliang decides to buy the same amount of items in one trip that Xiaoming bought in two trips. How much does he need to pay?
Three, 15. The first payment of 198 yuan might be the actual price of the purchased items without any discount; it could also be the amount paid after a 10% discount. Therefore, we should discuss two scenarios.
(1) When 198 yuan is the amount paid for shopping without a discount, the original price of the purchased items is 198 yuan.

Also, $554=450+104$, where 450 yuan is the amount paid for 500 yuan worth of items at a 10% discount, and 104 yuan is the amount paid for items at a 20% discount, $104 \div 0.8 = 130$ (yuan).

Therefore, the original price of the items purchased for 554 yuan is $130+500=630$ (yuan). Thus, for purchasing items originally priced at $198+630=828$ (yuan) in one go, Xiao Liang should pay
$$
500 \times 0.9 + (828 - 500) \times 0.8 = 712.4 \text{ (yuan). }
$$
(2) When 198 yuan is the amount paid for shopping at a 10% discount, the original price of the purchased items is $198 \div 0.9 = 220$ (yuan).

Following the discussion in (1), for purchasing items originally priced at $220 + 630 = 850$ (yuan) in one go, the payment should be
$$
500 \times 0.9 + (850 - 500) \times 0.8 = 730 \text{ (yuan). }
$$

In summary, if Xiao Liang goes to the supermarket to purchase the same amount of items that Xiao Ming has already bought, he should pay 712.4 yuan or 730 yuan.