An improved similarity measure of generalized trapezoidal fuzzy numbers and its application in multi-attribute group decision making

Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric distance, center of gravity, area and perimeter after analyzing the limitations of previous methods. Then comparative analysis is conducted with existing similarity measures, and the results show that the novel similarity measure has better distinguishability and lower invalidity. Furthermore, a general process, which combines the new similarity measure of GTFNs with compromise methods, is developed to deal with multi-attribute group decision making (MAGDM) problem. Finally, we combine fuzzy VIKOR with the general process as illustrated example, which proves the superiority of the developed similarity measure in solving MAGDM problem.

Keywords:

Generalized trapezoidal fuzzy numbers , Similarity measure , MAGDM , fuzzy VIKOR , cosine similarity