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Interval valued intuitionistic fuzzy sets. (English) Zbl 0674.03017
The intuitionistic fuzzy sets (IFS’s) of the first author [Fuzzy Sets Syst. 20, 87–96 (1986; Zbl 0631.03040)] are at each point of a given universe of discourse characterized by a pair of degrees: one for membership and the other for non-membership. Here the rather obvious fact first is proven that there is a 1-1 correspondence of such IFS’s with interval valued fuzzy sets, a special kind of fuzzy sets of type 2. Later on the IFS’s are generalized by allowing the membership as well as the non-membership degrees to be intervals. Fundamental operations are defined and some basic properties proven.

MSC:
03E72 Theory of fuzzy sets, etc.
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References:
[1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy sets and systems, 20, 87-96, (1986) · Zbl 0631.03040
[2] Gorzalczany, M., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987) · Zbl 0635.68103
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