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

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Abstract

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, \([\frac{-1}{2},\frac{1}{2}]\), forms a group. Further, we have proved that a set of all 2-tuple linguistic information, \(\overline{LT} \equiv LT \times [\frac{-1}{2},\frac{1}{2}]\), and numerical interval, \([-n,n]\), where n is presumed to be a positive integer, also forms a group. Later on, we develop a one-to-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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Tanya Malhotra & Anjana Gupta

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  1. Tanya Malhotra
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  2. Anjana Gupta
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Correspondence to Anjana Gupta.

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Malhotra, T., Gupta, A. Group operations and isomorphic relation with the 2-tuple linguistic variables. Soft Comput 24, 18287–18300 (2020). https://doi.org/10.1007/s00500-020-05367-9

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