Analysis of Ranking Consistency in Linguistic Multiple Attribute Decision Making: The Roles of Granularity and Decision Rules

Linguistic multiple attribute decision making (LMADM) has been widely used in different decision contexts to achieve a final solution, e.g., obtaining the ranking of alternatives. Evaluation information using linguistic scales in LMADM is usually expressed in simple discrete linguistic terms. In this article, we consider that each simple linguistic term in LMADM actually has a continuous representation (denoted as a linguistic two tuples) whose rounding operation matches the linguistic term. Under such conditions, the ranking of alternatives based on the simple linguistic terms may not be consistent with that based on the linguistic two tuples. Thus, this article studies the linguistic scale ranking consistency issue in LMADM under seven classical and commonly used decision rules: weighted averaging, ordered weighted averaging, weighted geometric averaging, ordered weighted geometric averaging, preference ranking organization method for enrichment evaluation, technique for order preference by similarity to an ideal solution, and elimination et choice translating reality. We first define the concept of the linguistic scale ranking consistency in LMADM. Afterward, several consistency conditions are presented analytically for the selected decision rules to guarantee the linguistic scale ranking consistency. Finally, we present the detailed theoretical and simulation-based comparisons. The theoretical comparisons show the roles of decision rules and granularity in the consistency conditions, and the simulation-based comparisons demonstrate the performance of the selected decision rules in defending against the ranking inconsistency in LMADM.