2-dimension linguistic computational model with 2-tuples for multi-attribute group decision making

Abstract

The 2-dimension linguistic information includes two common linguistic labels. One dimension is used for describing the evaluation result of alternatives provided by the decision maker, and the other is used for describing the self-assessment of the decision maker on the reliability of the given evaluation result. In order to deal with comparability and incomparability of 2-dimension linguistic labels (2DLLs), a 2-dimension linguistic lattice implication algebra (2DL-LIA) is constructed as a linguistic evaluation set with lattice structure. In this paper, a 2DLL is firstly represented by two 2-tuples in a 2DL-LIA for more precise computing and aggregating 2-dimension linguistic information. This model allows a continuous representation of 2DLL on its domain, therefore, it can represent any continuous 2-dimension linguistic information obtained in the aggregation process. Next, two new 2-dimension linguistic aggregation operators, including 2-dimension linguistic weighted arithmetic aggregation (2DLWAA) operator and 2-dimension linguistic ordered weighted arithmetic aggregation (2DLOWAA) operator, are developed, and then some desirable properties of the operators are studied. Subsequently, based on 2DLWAA and 2DLOWAA operators, a decision making approach is provided to solve multi-attribute group decision making (MAGDM) problem with 2DLL assessment. Finally, an illustrative example is provided to show the concrete steps of the developed decision making approach and to demonstrate the practicality and the flexibility of this proposal by comparing with existing decision making approaches.