It depends on what you mean by "advanced". Even just focusing on economic development, it still depends on which definition you want.
China is the largest, in pure gross domestic product terms (GDP), which is the most commonly-cited measure of any country's economy, and GDP purchasing power parity-adjusted (PPP), which is GDP adjusted for exchange rates; I tend to use GDP PPP-adjusted because it more accurately shows the level of economic activity in a country, and is a better measure for the standard of living. Japan is right now a close second, but you can expect the gap between them to widen. South Korea is third, also in both, with Singapore, small as it is, in fourth place.
The rankings change quite a bit when looking at per capita, or per person, GDP. Singapore and Japan are very close to one another, in a virtual tie for first place by nominal (non-PPP) figures. South Korea is in third by this measure, at about have of the GDP-nominal per capita of Japan and Singapore. However the distance between Singapore and Japan widens significantly on a PPP per capita measure, with Singapore rising a little, Japan falls significantly, and South Korea rising enough to be at a virtual tie with Japan. China is a very distant fourth on both versions of the per capita measurement by virtue of a population that dwarfs the other three countries combined.
Here are the figures from 2010:
GDP nominal GDP PPP GDP nom. per capita GDP PPP per capita
China-5.7 trillion 9.9 trillion 4,500 7,200
Japan- 5.4 trillion 4.3 trillion 41,000 32,000
South Korea- 987 billion 1.5trillion 20,000 30,000
Singapore-215 billion 292billion 52,000 57,000
http://en.wikipedia.org/wiki/List_of_countries_by_GDP_(PPP)_per_capita
I use wikipedia for this information because it has direct links to the original source material cited, where you can go to learn more about the development of each of these countries as well.
Again, I tend to rely most on the PPP per capita figure to best understand the standard of living in other countries. But if what you want to know is how advanced a country is, there are numerous other metrics to do this with.
My personal preferences, to visit and live in, would probably be from hgihest to lowest South Korea, Japan, China, then Singapore, but that's a matter of personal interest, really.
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