A type-two fuzzy set allows the inclusion of uncertainty in the parameters of a membership function. The membership function of a type-two fuzzy set is in itself a fuzzy set. A type-two fuzzy set is three-dimensional where the third dimension indicates the degree of membership of the two-dimensional membership function at each point in its two-dimensional domain. A type-two fuzzy set has a footprint of uncertainty with an upper membership function and lower membership function.
Published in Chapter:
Type-One and Interval Type-Two Fuzzy Logic for Quantitatively Defining Imprecise Linguistic Terms in Politics and Public Policy
Ashu M. G. Solo (Maverick Trailblazers Inc., USA)
Copyright: © 2020
|Pages: 28
DOI: 10.4018/978-1-7998-0377-5.ch002
Abstract
During a presidential forum in the 2008 U.S. presidential campaign, the moderator, Pastor Rick Warren, wanted Sen. John McCain and then-Sen. 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. Type-one or interval type-two fuzzy logic can be used for quantitatively defining imprecise linguistic terms. This chapter shows how to use type-one fuzzy logic and interval type-two fuzzy logic for this purpose, as well as the advantages and disadvantages of each. Imprecise terms in natural languages should be considered to have qualitative definitions, quantitative definitions, crisp quantitative definitions, fuzzy quantitative definitions, type-one fuzzy quantitative definitions, and interval type-two fuzzy quantitative definitions.