Abstract: In information aggregation of multiple attribute decision making, some aggregation operators are defined based on the hypothesis in which all the attributes are mutually indenpent, resulting in unreasonable information aggregation and decision result. Heronian mean operator is an aggregation opeator in which can deal with the situation of interrelationshiop between attributes, and from the theoretical and and practical points of view, it is worth to study and generalize Heronian mean operator. Firstly, aiming at weighted Heronian mean operator without reducibility in related reference, the generalized weighted Heronian mean operator(GWHM) with reducibility is introduced. And then, the three parameters Heronian mean operator(TPHM) and the three parameters weighted Heronian mean operator(TPWHM) are defined, and their basic properties such as idempotency, monotonicity and boundness are studied. Further, in order to fulfill applications of Heronian mean operator in linguistic multiple attribute decision making, linguistic weighted Heronian mean operator(LWHM), three parameters linguisitic Heronian mean operator(TPLWHM) and three parameters linguisitic weighted Heronian mean operator(TPLHM) are dedined, and their properties such as idempotency, monotonicity and boundness are also discussed. Finally, an approach to multiple attribute decision making based on the (linguisitic) Heronian mean operators is proposed, and two practical examples are given to illustrate our results.

Key words: aggregation operator, Heronian mean operator, linguistic Heronian mean operator, decision making