No-free-lunch result for interval and fuzzy computing: when bounds are unusually good, their computation is unusually slow

Authors:
Martine Ceberio;Vladik Kreinovich
Affiliations:
Computer Science Dept., University of Texas at El Paso, El Paso, TX;Computer Science Dept., University of Texas at El Paso, El Paso, TX
Venue:
MICAI'11 Proceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II
Year:
2011

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Abstract

On several examples from interval and fuzzy computations and from related areas, we show that when the results of data processing are unusually good, their computation is unusually complex. This makes us think that there should be an analog of Heisenberg's uncertainty principle well known in quantum mechanics: when we an unusually beneficial situation in terms of results, it is not as perfect in terms of computations leading to these results. In short, nothing is perfect.