Editing Uncertainty (section)

===Risk and uncertainty===
For example, if it is unknown whether or not it will rain tomorrow, then there is a state of uncertainty. If probabilities are applied to the possible outcomes using weather forecasts or even just a [[calibrated probability assessment]], the uncertainty has been quantified. Suppose it is quantified as a 90% chance of sunshine. If there is a major, costly, outdoor event planned for tomorrow then there is a risk since there is a 10% chance of rain, and rain would be undesirable. Furthermore, if this is a business event and $100,000 would be lost if it rains, then the risk has been quantified (a 10% chance of losing $100,000). These situations can be made even more realistic by quantifying light rain vs. heavy rain, the cost of delays vs. outright cancellation, etc.

Some may represent the risk in this example as the "expected opportunity loss" (EOL) or the chance of the loss multiplied by the amount of the loss (10% × $100,000 = $10,000). That is useful if the organizer of the event is "risk neutral", which most people are not. Most would be willing to pay a premium to avoid the loss. An insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add onto that other operating costs and profit. Since many people are willing to buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk.

Quantitative uses of the terms ''uncertainty'' and ''risk'' are fairly consistent among fields such as [[probability theory]], [[actuarial science]], and [[information theory]]. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, [[surprisal]] is a variation on uncertainty sometimes used in [[information theory]]. But outside of the more mathematical uses of the term, usage may vary widely. In [[cognitive psychology]], uncertainty can be real, or just a matter of perception, such as [[Expectation (epistemic)|expectations]], threats, etc.

[[Vagueness]] is a form of uncertainty where the analyst is unable to clearly differentiate between two different classes, such as 'person of average height' and 'tall person'. This form of vagueness can be modelled by some variation on [[Lotfi A. Zadeh|Zadeh]]'s [[fuzzy logic]] or [[subjective logic]].<ref>{{Cite book |author=Williamson, Timothy |url=http://worldcat.org/oclc/254215717 |title=Vagueness |year=1994 |publisher=Psychology Press |isbn=0-415-03331-4 |oclc=254215717}}</ref>

[[Ambiguity]] is a form of uncertainty where even the possible outcomes have unclear meanings and interpretations. The statement ''"He returns from the bank"'' is ambiguous because its interpretation depends on whether the word 'bank' is meant as ''"the side of a river"'' or ''"a financial institution"''. Ambiguity typically arises in situations where multiple analysts or observers have different interpretations of the same statements.<ref>{{Citation |last=Winkler |first=Susanne |title=Exploring Ambiguity and the Ambiguity Model from a Transdisciplinary Perspective |url=http://dx.doi.org/10.1515/9783110403589-002 |work=Ambiguity |year=2015 |pages=1–26 |access-date=2023-04-02 |place=Berlin, München, Boston |publisher=DE GRUYTER|doi=10.1515/9783110403589-002 |isbn=9783110403589 }}</ref>

At the subatomic level, uncertainty may be a fundamental and unavoidable property of the universe. In [[quantum mechanics]], the [[Heisenberg uncertainty principle]] puts limits on how much an observer can ever know about the position and velocity of a particle. This may not just be ignorance of potentially obtainable facts but that there is no fact to be found. There is some controversy in physics as to whether such uncertainty is an irreducible property of nature or if there are "hidden variables" that would describe the state of a particle even more exactly than Heisenberg's uncertainty principle allows.<ref name=":1">{{Cite journal |last1=Soloviev |first1=V. |last2=Solovieva |first2=V. |last3=Saptsin |first3=V. |date=2014 |title=Heisenberg uncertainity principle and economic analogues of basic physical quantities |doi=10.31812/0564/1306 |s2cid=248741767 |doi-access=free }}</ref>