Covering-based compound mean operators arising from Heronian and Bonferroni mean operators in fuzzy and intuitionistic fuzzy environments

Both Heronian mean (HM) operators and Bonferroni mean (BM) operators can capture the interrelationship between input arguments and have been a hot research topic as a useful aggregation technique in fuzzy and intuitionistic fuzzy environments. In this paper, associated with the common characters of these operators we propose the covering-based compound mean operators in fuzzy environments to capture various interrelationships between input arguments, some desirable properties and special cases of the proposed mean operators are provided. Then, conditions under which these covering-based compound mean operators can be directly used to aggregate the membership degrees and nonmembership degrees of intuitionistic fuzzy information, are provided. In particular, novel intuitionistic fuzzy HM operators and intuitionistic fuzzy BM operators are directly derived from the classical ones. We list the detailed steps of multiple attribute decision making with the developed aggregation operators, and give a comparison of the new extensions of BM operators by this paper with the corresponding existing ones to prove the rationality and effectiveness of the proposed method.