Extended Bonferroni Mean Under Intuitionistic Fuzzy Environment Based on a Strict t-Conorm

The Bonferroni mean (BM) operator, originally introduced by Bonferroni, assumes homogeneous relationship among the input arguments. Recently, extended BM (EBM) operator is developed to capture heterogeneous relationship among real arguments and linguistic 2-tuple data. In this paper, we investigate the EBM operator with Atanassov’s intuitionistic fuzzy sets (AIFSs) by using additive generators of strict t-conorms in the operations of AIFSs. This new operator is referred to as AIF-EBM operator. We also define weighted AIF-EBM (WAIF-EBM) operator by using the said operations. Moreover, we investigate several desirable properties of the proposed operators and we prove that some known specific intuitionistic fuzzy aggregation operators are special cases of the proposed AIF-EBM and WAIF-EBM operators. Subsequently, by utilizing the proposed operators, we develop a new approach for determining criteria weights, where criteria are heterogeneously interrelated. The contribution ends by introducing a numerical example with a comparative analysis of the proposed approach and the existing processes. The results of the numerical example are also analyzed with parameterized strict t-conorms.