The Studies Of Several Intuitionistic Fuzzy Subgroups

In the paper,based on the(?,?)-intuitionistic fuzzy subgroups,various definitions and properties of its cut sets,we define and study the(?,?)-intuitionistic fuzzy subgroups and(?,?)-intuitionistic fuzzy subgroups,We have a more extensive discussion of several intuitionistic fuzzy subgroups.This paper is divided into two parts,the details are as follows:The first part studies(?,?)-intuitionistic fuzzy subgroups.Based on the definition of(?,?)-intuitionistic fuzzy subgroups and its various cut sets,we propose the definition of(?,?)-intuitionistic fuzzy subgroups,where ? and ? respectively take ?,q,??q,??q4 kinds of situations.Therefore,(?,?)-intuitionistic fuzzy subgroups have 16 types,and we have extensively studied the part of(?,?)-intuitional fuzzy subgroups.First of all,if ?? ??q,we research A0 is fuzzy subgroup.Then,when(?,?)-intuitionistic fuzzy subgroups satisfies x?G,vA(x)>0,for(?,?)? ?(?,q),(?,??q),(??q,q),(??q,??q),(q,?),(q,??q),(??q,?)?,We prove A(x)=(0,1).After,we discuss the rest of(?,?)-intuitionistic fuzzy subgroups,conclude some the relationships between(?,?)-intuitionistic fuzzy subgroups and ?(x),v(x).In turn,we have a deep understanding of the(?,?)-intuitionistic fuzzy subgroups.The second part studies(?,?)-intuitionistic fuzzy subgroups.First of all,based on the(?,?)-intuitionistic fuzzy subgroups and its cut sets.From the perspective of its ?-the upper cut set A?,?-strong upper Q-cut set A[?],We make further characterization of(?,?)-intuitionistic fuzzy subgroups.We present the definition of(?,?)-intuitionistic fuzzy subgroups,introduce some properties of(?,?)-intuitionistic fuzzy subgroups,respectively study properties of(?,?)-intuitionistic fuzzy subgroup,(q,q)-intuitionistic fuzzy subgroup,(? ?q,??q)-intuitionistic fuzzy subgroup,(? ?q,? ?q)-intuitionistic fuzzy subgroup.Then,according to the definition of the intuitionistic fuzzy normal subgroup,we give the definition of(?,?)-intuitionistic fuzzy normal subgroups and the equivalent conditions of its existence.We separately discuss the relationships between(?,?)-intuitionistic fuzzy subgroup and As,(As)?,(As)(?),between(q,q)-intuitionistic fuzzy subgroup and A[s],(A[s])?,(A[s])(?),between(??q,??q)-intuitionistic fuzzy subgroup and As?A[s].(As?A[s])?,(As?A[s])(?),between(?? q,??q)-intuitionistic fuzzy subgroup and As ?A[s],(As ?A[s])?,(As ? A[s])(?).