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In actual multiple attribute decision making, people often use language to evaluate attributes of the object, and sometimes there are associations between the attributes. Therefore, the study of multiple attribute decision making with language as attributes and associations between attributes is of great theoretical significance and practical value. The Heronian mean is not only an operator which reflects the associations between attributes, but also has excellent properties, including idempotency, monotonicity, boundedness, parameter symmetry, and alternate symmetry. In this paper, firstly a new linguistic generalized weighted Heronian mean (LGWHM) was provided, and its properties including idempotency, monotonicity, boundedness, and limit were studied. Then, a new three-parameter linguistic generalized weighted Heronian mean (TPLGWHM) and its idempotency, monotonicity, and boundedness properties were proposed. Finally, multi-attribute decision making methods based on the new linguistic generalized weighted Heronian mean were given, and an example was analyzed and compared with other methods.

Multiple Attribute Decision Making Based on Linguistic Generalized Weighted Heronian Mean