The General Type 1 and Interval Type 2 Fuzzy Sets Addition Based on the Yager T-norms with Entropy as Degree of Fuzziness

The classical fuzzy operation that was based on the minimum t-norm would lead to uncontrollable fuzziness. The generalized t-norm based fuzzy arithmetic can better control the fuzziness. In this paper, the Yager t-norms based additions of the general type 1 fuzzy set and interval type 2 fuzzy set (IT2FS) are developed. Firstly, the T1FS additions based on the Yager t-norms are developed. Then, the general T1FS t-norm based developed expressions will extend to the IT2FS t-norm based additions. We define the entropy of the addition results of the general T1FS and the degree of fuzziness of IT2FS. The multiple criteria decision making (MCDM) aggregation is one of the Yager t-norms based applications. A linguistic MCDM numerical example is performed to verify the developed expressions.