Abstract
During a presidential forum in the 2008 U.S. presidential campaign, the moderator, Pastor Rick Warren, wanted Senator John McCain and then-Senator Barack Obama to define “rich” with a specific number. Warren wanted to know at what specific income level a person goes from being not rich to rich. The problem with this question is that there is no specific income at which a person makes the leap from being not rich to being rich. This is because “rich” is a fuzzy set, not a crisp set, with different incomes having different degrees of membership in the “rich” fuzzy set. Similarly, “middle class” and “poor” are fuzzy sets. Fuzzy logic is needed to properly ask and answer Warren's question about quantitatively defining “rich.” Similarly, fuzzy logic is needed to properly ask and answer queries about quantitatively defining imprecise linguistic terms in politics and public policy like “middle class,” “poor,” “low inflation,” “medium inflation,” and “high inflation.” Imprecise terms like these in natural languages should be considered to have “qualitative definitions,” “quantitative definitions,” “crisp quantitative definitions,” and “fuzzy quantitative definitions.” This chapter provides much more information on the preceding.
Top2. Types Of Imprecision And Uncertainty
There are various types of uncertainty and imprecision. However, they can be classified under two broad categories: type one uncertainty and type two uncertainty (Solo & Gupta, 2007; Gupta & Solo, 2010).
Type one uncertainty deals with information that arises from the random behavior of physical systems. The pervasiveness of this type of uncertainty can be witnessed in random vibrations of a machine, random fluctuations of electrons in a magnetic field, diffusion of gases in a thermal field, random electrical activities of cardiac muscles, uncertain fluctuations in the weather pattern, and turbulent blood flow through a damaged cardiac valve. Type one uncertainty has been studied for centuries. Complex statistical mathematics has evolved for the characterization and analysis of such random phenomena.
Type two uncertainty deals with information or phenomena that arise from human perception and cognitive processes or from cognitive information in general. This subject has received relatively little attention. Perception and cognition through biological sensors (eyes, ears, nose, etc.), perception of pain, and other similar biological events throughout our nervous system and neural networks deserve special attention. The perception and cognition phenomena associated with these processes are characterized by many great uncertainties and cannot be described by conventional statistical theory. A person can linguistically express perceptions experienced through the senses, but these perceptions cannot be described using conventional statistical theory.
Fuzzy logic has proven to be a very promising tool for dealing with type two uncertainty. Stochastic theory is only effective in dealing with type one uncertainty. The theory of fuzzy logic is based on the notion of relative graded membership, as inspired by the processes of human perception and cognition.