A Model Based on Linguistic 2-Tuples for Dealing With Heterogeneous Relationship Among Attributes in Multi-expert Decision Making

Classical Bonferroni mean, defined by Bonferroni in 1950, assumes homogeneous relation among the attributes, i.e., each attribute A(i) is related to the rest of the attributes A \ {A(i)}, where A = {A(1), A(2),..., A(n)} denotes the attribute set. In this paper, we emphasize the importance of having an aggregation operator, which we will refer to as the extended Bonferroni mean (EBM) operator to capture heterogeneous interrelationship among the attributes. We provide an interpretation of "heterogeneous interrelationship" by assuming that some of the attributes, which are denoted as A(i), are related to a subset B-i of the set A \ {A(i)}, and others have no relation with the remaining attributes. We provide an interpretation of this operator as computing different aggregated values for a given set of inputs as interrelationship pattern is changed. We also investigate the behavior of the proposed EBM aggregation operator. Furthermore, to investigate a multiattribute group decision making (MAGDM) problem with linguistic information, we analyze the proposed EBM operator in linguistic 2-tuple environment and develop three new linguistic aggregation operators: 2-tuple linguistic EBM, weighted 2-tuple linguistic EBM, and linguistic weighted 2-tuple linguistic EBM. A concept of linguistic similarity measure of 2-tuple linguistic information is introduced. Subsequently, an MAGDM technique is developed, in which the attributes' weights are in the form of 2-tuple linguistic information and experts' weights information is completely unknown. Finally, a practical example is presented to demonstrate the applicability of our results.