Type-2 fuzzy sets and systems

Type-2 fuzzy sets and systems generalize standard <a href="/facts/Fuzzy_sets/BGWudHJq">Type-1 fuzzy sets</a> and <a href="/facts/Fuzzy_sets_and_systems/SMamr5qY">systems</a> so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of much uncertainty. So, what does one do when there is uncertainty about the value of the membership function? The answer to this question was provided in 1975 by the inventor of fuzzy sets, <a href="/facts/Lotfi_A._Zadeh/WojTlG4Y">Lotfi A. Zadeh</a>, when he proposed more sophisticated kinds of fuzzy sets, the first of which he called a "type-2 fuzzy set". A type-2 fuzzy set lets us incorporate uncertainty about the membership function into fuzzy set theory, and is a way to address the above criticism of type-1 fuzzy sets head-on. And, if there is no uncertainty, then a type-2 fuzzy set reduces to a type-1 fuzzy set, which is analogous to probability reducing to determinism when unpredictability vanishes.
Type1 fuzzy systems are working with a fixed <a href="/facts/Membership_function/QEuh04NM">membership function</a>, while in type-2 fuzzy systems the membership function is fluctuating. A fuzzy set determines how input values are converted into fuzzy variables.

Type-2 fuzzy sets and systems open-in-new

Type-2 fuzzy sets and systems