Aggregation Weights for Linguistic Hybrid Geometric Averaging Operator

Abstract

This paper tries to point out that the aggregation weights in linguistic hybrid geometric averaging operator will dominate the final result of the ranking for alternatives. We examined the linguistic hybrid geometric averaging operator that was proposed by previous studies and found it contained several questionable results. The major defect of the previous approach was that it failed to demonstrate two core factors: accuracy and speed, both of which have been explicitly uncovered and discussed in the study. With previous work the pivotal and dominant element, distribution of weights, in finding subjectively by decision maker of linguistic hybrid geometric averaging operators for group decision-making problems, lacks solid foundation and is unjustified. Here we provide the mathematical rationale and reliable advices, to point out that deficiency. In addition, we have detected and rectified some redundancies of operational laws in the procedure of previous study due to the improper utilization of negative operators. It certainly should be noted that the careless applications of those highly dependant operators may significantly diminish the efficiency and performance of entire mechanism for decision making under fuzzy environment. We develop an easy aggregation approach based on the arithmetic mean to solve the most favorable alternative problem. A comprehensive numerical examination of 1296 tests supports our result.

Keywords

• Decision-making
• Linguistic preference relation