Interval valued intuitionistic fuzzy sets.

*(English)*Zbl 0674.03017The 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.

Reviewer: Siegfried J. Gottwald (Leipzig)

##### MSC:

03E72 | Theory of fuzzy sets, etc. |

##### Keywords:

interval valued degrees of membership and non-membership; intuitionistic fuzzy sets; interval valued fuzzy sets; fuzzy sets of type 2
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\textit{K. Atanassov} and \textit{G. Gargov}, Fuzzy Sets Syst. 31, No. 3, 343--349 (1989; Zbl 0674.03017)

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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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