Intuitionistic fuzzy sets. (English) Zbl 0597.03033

Atanassov, K.; Stoeva, S.

Interval and fuzzy mathematics, Proc. Polish Symp., Poznań/Pol. 1983, 23-26 (1985).

[For the entire collection see Zbl 0587.00015.]
An intuitionistic fuzzy set A in the authors’ sense is characterized through a membership degree \(\mu_ A(x)\) and a nonmembership degree \(\nu_ A(x)\) in each point x of a universe of discourse, with \(0\leq \mu_ A(x)+\nu_ A(x)\leq 1\) as a standard restriction. Some elementary set algebra for such intuitionistic fuzzy sets is sketched, and two operators – denoted \(\square\) and \(\diamond\) – are introduced making ordinary fuzzy sets out of intuitionistic ones and having essential properties of modal operators.

Reviewer: S. D. Latow

MSC:

03E72	Theory of fuzzy sets, etc.
03B45	Modal logic (including the logic of norms)

Keywords:

generalized fuzzy sets; membership degree; set algebra; modal operators

Citations:

Zbl 0587.00015