CAUCHY –Jurnal Matematika Murni dan Aplikasi Volume 7(3) (2022), Pages 354-361 p-ISSN: 2086-0382; e-ISSN: 2477-3344 Submitted: December 23, 2021 Reviewed: May 25, 2022 Accepted: July 17, 2022 DOI: http://dx.doi.org/10.18860/ca.v7i3.14555 −    Mustika Ana Kurfia * , Noor Hidayat, Corina Karim Mathematics Department, Universitas Brawijaya, Malang, Indonesia Email: muzematika@gmail.com ABSTRACT The fuzzy set theory was introduced by Zadeh in 1965 and the soft set theory was introduced by Molodtsov in 1999. Recently, many researchers have developed these two theories and combined the theory of fuzzy set and soft set became the fuzzy soft set. In this research, we present the idea of the −intuitionistic fuzzy soft group defined on the −intuitionistic fuzzy soft set. The main purpose of this research is to create a new concept, which is an −intuitionistic fuzzy group. To achieve this, we combine the concept of −intuitionistic fuzzy group and intuitionistic fuzzy soft group. As the main result, we prove the correlation between intuitionistic fuzzy soft group and −intuitionistic fuzzy soft group along with some properties of −intuitionistic fuzzy soft group. Also, we prove some properties of subgroup of an −intuitionistic fuzzy soft group. An −intuitionistic fuzzy soft homomorphism is also proved. Keywords: intuitionistic fuzzy group; intuitionistic fuzzy soft group; −intuitionistic fuzzy group; −intuitionistic fuzzy soft group INTRODUCTION The theory of fuzzy has been studied by many researchers in various fields. Zadeh introduced the fuzzy set theory in [1] by defining a membership function that maps each member of a set to a closed interval of 0 and 1. Then Atanassov formed the intuitionistic fuzzy set that consist of membership function and nonmembership function in [2]. The theory of fuzzy set and intuitionistic fuzzy set was developed into group theory became fuzzy subgroup in [3] and intuitionistic fuzzy subgroup in [4]. The intuitionistic fuzzy subgroup was studied in various types. For example, the intuitionistic L-fuzzy subgroups formed in [5], the (  , ] −intuitionistic fuzzy subgroups defined in [6], definition of (  , )cut of intuitionistic fuzzy subgroups in [7], and t-intuitionistic fuzzy subgroups in [8]. Doda and Sharma studied the finite groups of different orders and gave the idea of recording the count of intuitionistic fuzzy subgroups in [9]. Zhou and Xu extended the intuitionistic fuzzy sets based on the hesitant fuzzy membership in [10]. The concept of the (  , ) −intuitionistic fuzzy subgroups and normal subgroups were defined in [11]. Then the fundamental properties of t-intuitionistic fuzzy abelian subgroup along with the homomorphism of t-intuitionistic fuzzy abelian subgroup were studied in [12]. Latif, et al. studied the fundamental theorems of t-intuitionistic fuzzy isomorphism of t-intuitionistic fuzzy subgroup in [13]. Moreover, the concept of  −intuitionistic fuzzy subgroup,  −intuitionistic fuzzy cosets, and  −intuitionistic fuzzy normal subgroup were characterized in [14]. Based on those research, Shuaib, et al. in [15] formed a concept