Group operations and isomorphic relation with the 2-tuple linguistic variables

This paper aims to put forth the theory of 2-tuple linguistic groups concerning the binary operation in the conventional sense. For this, a formal methodology has been introduced to prove that a predefined nonempty linguistic term set, LT, and the interval, [-1/2, 1/2], forms a group. Further, we have proved that a set of all 2-tuple linguistic information, (LT) over bar = LT x[-1/2, 1/2], and numerical interval, [-n, n], where n is presumed to be a positive integer, also forms a group. Later on, we develop a oneto-one correspondence and homomorphic group relation between the set of all 2-tuple linguistic information and numerical interval, [-n, n]. Henceforth, a similarity relation between the two groups is obtained. Finally, a practical application is defined by proposing the notion of a 2-tuple linguistic bipolar graph to illustrate the usefulness and practicality of the group isomorphic relation.