Certainty and precision are much too often used as an absolute standard in reasoning and decision making. Fuzzy logic, created by Dr. Lotfi Zadeh, can deal with information that is uncertain, imprecise, vague, partially true, or without sharp boundaries. In crisp logic, a numerical value has a membership of either 0 or 1 in crisp sets. In fuzzy logic, a numerical value can have a partial membership from 0 to 1 in fuzzy sets. This mathematics of uncertainty and imprecision is extremely useful in approximate reasoning and decision making.
With his question, Warren wanted to know an exact number at which an individual becomes rich. He specifically asked McCain and Obama whether incomes of $50,000, $100,000, or $200,000 are the dividing lines between rich and not rich. According to Warren's crisp logic for his dividing line of $100,000, an individual with an income of $99,999 is not rich whereas an individual with an income of $100,001 is rich.
In responding to Warren's question, Obama essentially defined anyone making $150,000 or less as being in the middle class or being poor and he defined anyone making $250,000 or more as doing well. He didn't assign a linguistic qualifier for those making an income between $150,000 and $250,000. According to Obama's crisp logic, an individual with an income of $149,999 is middle class or poor whereas an individual with an income of $150,001 is undefined.
An individual's annual income does not solely determine whether or not he is rich. There are many different factors related to an individual's circumstances that affect his financial well-being and affect what annual income is needed to be rich: number of dependents, family income, geographical location, assets, savings, expenses, debts, investments, inheritances, and time period. For example, an individual with no annual income, no dependents, no debts, and $10,000,000 in savings would be considered rich.
However, to answer Warren's question about annual income, one needs to make an assumption about the other factors affecting an individual's financial well-being. The assumption can be made that the individual's circumstances other than annual income are equivalent to that of the average American adult.
There is no specific income level at which an individual goes from being not rich to being rich. Rich should be defined as a range of incomes in which different incomes have different degrees of richness associated with them. In fuzzy logic, a linguistic qualifier like rich is a fuzzy set and different incomes have different degrees of membership in this fuzzy set.
In questioning McCain and Obama about the annual income needed for an individual to be rich, Warren first needed to specify in detail the individual's other circumstances affecting his financial well-being. Alternatively, he could have said that the individual's other circumstances were equivalent to that of the average American adult. Then Warren should have separately asked for an income below which an individual is definitely not rich, a range of incomes between which an individual is rich to some degree, and an income above which an individual is definitely rich.
This could be phrased as follows: "In the following questions, assume that all of the circumstances affecting an individual's prosperity are equivalent to that of the average American adult. Give me an annual income below which an individual is definitely not rich. Give me a range of annual incomes between which an individual is rich to some degree. Give me an annual income above which an individual is definitely rich. To avoid overwhelming Obama, McCain, and the audience with too many queries at once, Warren could have waited for a response after each query before proceeding to the subsequent query.
Obama and McCain first needed to make clear that the definition of rich varies considerably depending on many factors affecting an individual's financial well-being other than annual income. They should have stated their assumptions regarding the other factors or asked Warren for more details. Then they could have given their perception of what annual income is needed to be rich for the average American by providing an income below which an individual is definitely not rich, providing a range of incomes between which an individual is rich to some degree, and providing an income above which an individual is definitely rich.
This could be articulated as follows: "There are many different factors other than annual income that affect an individual's prosperity. If we make the assumption that these other factors are equivalent to that of the average American adult, then in my perception, an individual with an income less than $100,000 per year is definitely not rich. As an individual's income rises from $100,000 to $250,000 per year, he is rich to some degree and his degree of being rich steadily increases. An individual with an income greater than $250,000 per year is definitely rich.
People think in imprecise and vague terms. Consequently, human language is inherently imprecise and vague. A major problem arises when people try to bring precision into situations where it doesn't apply, such as defining human linguistic terms like rich as being greater than a single precise annual income. An understanding of the basic principles of fuzzy logic can be extremely useful in asking proper questions and giving proper answers about numerically defining imprecise linguistic terms. Furthermore, fuzzy logic can be extremely useful in public policy and law, which are full of uncertainties and imprecision.
Further reading:
A. M. G. Solo et al., "Obama, McCain, and Warren Needed Fuzzy Logic to Define 'Rich' by Income, Proceedings of the 2009 International Conference on e-Learning, e-Business, Enterprise Information Systems, and e-Government (EEE'09), Las Vegas, July 13-16, 2009, CSREA, pp. 265-270.
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