On new operational laws of 2-tuple linguistic information using Archimedean t-norm and s-norm

The aim of this paper is to develop some novel operational laws of linguistic 2-tuples based on the Archimedean t-norm and s-norm. The most advantage of such operational laws is that the operations are closed. The properties of such operational laws are studied, such as the commutative, associative, and distribution law of scalar-multiplication. We propose the successive weighted arithmetic and geometric operations of 2-tuple linguistic terms based on these new operational laws, which is also appropriate for cases of uncertain linguistic variables. Finally, a ranking problem of white wines is developed to illustrate the application of the proposed method.