Hybrid Atanassov intuitionistic fuzzy Bonferroni means for multi-criteria aggregation

This study proposes the hybrid Atanassov intuitionistic fuzzy number (HAIFN) to effectively and accurately represent membership and non-membership degrees in an Atanassov's intuitionistic fuzzy environment. The HAIFN is obtained by combining the crisp number with the interval-valued number, in which decision makers provide only an interval-valued membership degree, thereby avoiding the intricate and difficult evaluation of the non-membership degree. Based on the HAIFN, the hybrid Atanassov intuitionistic fuzzy Bonferroni mean and the generalized hybrid Atanassov intuitionistic fuzzy Bonferroni mean are introduced to aggregate the hybrid Atanassov intuitionistic fuzzy information and capture their interrelationship. The hybrid Atanassov intuitionistic fuzzy weighted Bonferroni mean, the generalized hybrid Atanassov intuitionistic fuzzy weighted Bonferroni mean, and their desired properties are further investigated given the distinct importance of each criterion. A practical case is provided at the end to demonstrate the application of the proposed fuzzy numbers and aggregation operators.