Revisiting some fuzzy algebraic structures

Abstract

Following our investigations on particular fuzzy algebraic structures, we revisit fuzzy subgroups and fuzzy ideals and introduce some numerical examples. As usual, we associated relations to fuzzy subgroup and fuzzy ideal. Consequently, right and left cosets modulo a fuzzy relation were introduced. This work and the our previous works can be considered as a continuation of investigations initiated by Abu Osman and Antony in the 1980s. Toward our investigation, we have in mind that by introducing these new definitions, the results that we can get should represent a real generalization of classical and commonly known concepts of algebra.