Some Properties of Anti Imprecise Subgroup and its Application

Various authors from around the world have extended the fuzzy concept to study the uncertainty condition and define its degree of certainty in various real-life experiments. At the same time, many authors have discussed the shortcomings of the definition of fuzzy sets that currently exist. However, no author has properly highlighted the problem of not following the two main classical set theories logically. To address this issue, an imprecise set definition is introduced as an extended definition of fuzzy sets, where the new concept applies two parameters, namely the functions of membership and reference, instead of one, and is helpful in defining the uncertainty problem in a more convenient manner than the existing one. In our previous work, we have studied imprecise subgroup using this new concept addressed by Baruah. In this paper, using the concept of complement of imprecise subgroup, we have introduced anti imprecise subgroup and some properties of anti imprecise subgroup with examples. Imprecise subgroup is an extended version of fuzzy group theory developed using the definition of imprecise set defined by Baruah. In addition, we expected an application developed from an anti imprecise subgroup that can be used to resolve various networking problems.