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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty in Measurement: Significant Figures03:34

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All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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An Inexact Optimization Model for Crop Area Under Multiple Uncertainties.

Chongfeng Ren1,2, Hongbo Zhang3,4

  • 1Key Laboratory of Subsurface Hydrology and Ecological Effect in Arid Region, Ministry of Education, Xi'an 710054, Shaanxi Province, China.

International Journal of Environmental Research and Public Health
|July 25, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a new model for optimizing crop areas and irrigation, considering uncertainties in water resources. The findings aid in making informed decisions for sustainable agriculture and resource management.

Keywords:
chance constrained programmingcrop area optimizationmultiple uncertaintiestype-2 fuzzy interval programmingwater-saving scenarios

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Area of Science:

  • Agricultural Economics
  • Operations Research
  • Environmental Management

Background:

  • Optimizing crop area and irrigation is crucial for food security and resource management.
  • Uncertainties in water availability and economic factors pose significant challenges to agricultural planning.
  • Existing optimization models often struggle to adequately address complex, fuzzy uncertainties.

Purpose of the Study:

  • To develop an integrated optimization model for crop area and irrigation planning.
  • To incorporate type-2 fuzzy interval programming and chance-constrained programming to handle uncertainties.
  • To maximize economic benefits under various water-saving irrigation scenarios.

Main Methods:

  • Developed a type-2 fuzzy interval chance-constrained programming (T2FI-CCP) model.
  • Applied the T2FI-CCP model to a case study in Wuwei City, Gansu Province, China.
  • Analyzed optimal irrigation water and planting structures under different violation probabilities and water-saving modes.

Main Results:

  • The model successfully generated optimal irrigation water and planting structure schemes.
  • Results demonstrated the trade-offs between economic benefits and violation probabilities across different scenarios.
  • Identified effective strategies for land and water resource allocation under uncertainty.

Conclusions:

  • The developed T2FI-CCP model provides a robust framework for agricultural optimization under uncertainty.
  • The study offers valuable insights for decision-makers in agricultural planning, resource management, and water conservation.
  • Findings support sustainable agricultural development by balancing economic objectives with environmental considerations.