Generalized similarity measures under linguistic q-rung orthopair fuzzy environment with application to multiple attribute decision-making

Abstract

The similarity measures have been extensively used as an efficient tool to analyze the degree of similarity between two sets of objects. The linguistic q-rung orthopair fuzzy set provides a flexible model to represent uncertain qualitative information more precisely. This paper defines some new generalized trigonometric similarity measures between two linguistic q-rung orthopair fuzzy sets. We use the linguistic scaling function to accommodate the different semantic levels of the linguistic terms during the similarity measuring process. Several basic and advanced mathematical properties are proved in detail. Next, we present a generalized hybrid trigonometric similarity measure between two linguistic q-rung orthopair fuzzy sets. The weighted version of the developed similarity measures is also defined and extends them to a continuous domain. It is worth mentioning that all the proposed similarity measures are reduced into the similarity measures between linguistic intuitionistic fuzzy sets and the linguistic Pythagorean fuzzy sets when we take $$q=1$$\n and $$q=2$$\n , respectively. A new decision-making method based on developed generalized hybrid trigonometric similarity measure is formulated to solve multiple attribute decision-making problems under the linguistic q-rung orthopair fuzzy environment. Finally, a numerical example is given to illustrate the flexibility and effectiveness of the developed method in solving real-world decision problems.