Intuitionistic fuzzy sets

Spiritia: /* Formal definition */

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'''Intuitionistic fuzzy sets''' (IFSs) are an extension of the concept of Lotfi Zadeh's fuzzy sets, introduced originally in 1983 by the Bulgarian mathematician [[Krassimir Atanassov]].

While in the case of fuzzy sets, a ''membership'' function <math>\mu</math> defines the level of [[Membership function (mathematics)|membership]] of an element to a (fuzzy) set, the intuitionistic fuzzy set extends the fuzzy set by the introduction of a second function <math>\nu</math> which defines the level of ''non-membership'' of the element to the (intuitionistic fuzzy) set. Since both the membership and the non-membership function can be evaluated in the <math>[0,1]</math> interval, but do not obligatory sum up to 1, the complement to 1 is defined as ''degree of uncertainty'' or ''hesitation margin''.

In this way, IFSs render a better account of uncertainty than fuzzy sets.

== Formal definition ==

== Relations, operations, operators ==

== Extensions of IFS ==

== History of development ==

== References ==

[[Category:Fuzzy logic]]

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