On direct product of a fuzzy subgroup with an anti-fuzzy subgroup

Abstract

We have introduced and analysed some new refreshing concepts in the field of fuzzy abstract algebra. The main contributions of this paper are fivefold: (1) we have introduced the notion of dual-fuzzy subgroup, (2) we have defined the direct product of a fuzzy subgroup with an anti-fuzzy subgroup, (3) Furthermore, we have defined mixed level subset and mixed level subgroup, (4) we have also developed some new theories as well as propositions based on these newly defined notions and lastly (5) we have redefined these notions using general T-norm and T* conorm.