Sources of Uncertainty and Membership Functions

This chapter examines the kinds of uncertainties that motivate the use of type-2 fuzzy sets and systems and how data about words can be collected from a group of subjects so that two kinds of linguistic uncertainties can then be modeled using fuzzy sets. Its coverage includes: general discussions about the occurrence, causes, and nature of uncertainty; uncertainties and sets; uncertainties in a fuzzy system; collecting word data from a group of subjects to demonstrate that (maxim #1) words mean different things to different people; how to make use of word (linguistic) uncertainties (intra-uncertainty—the uncertainty that a person has about a word—and inter-uncertainty—the uncertainty that a group of people have about the word); why type-1 fuzzy sets cannot model both kinds of linguistic uncertainties but interval type-2 fuzzy sets can; (maxim #2) words must also mean similar things to different people or else people are not communicating effectively; and a method for mapping a data interval (collected from a subject) into a type-1 fuzzy set (leading to an ensemble of type-1 fuzzy sets for a group of subjects). Modeling words using type-2 fuzzy sets is continued in Chap. 6 .