In this paper, we introduce the notions of essential ideals and 0-essential
ideals of ternary semigroups and the concept of their fuzzifications. This study examines
relationships between essential ideals and their fuzzifications and relationships between
0-essential ideals and their fuzzications. In addition, we propose the concept of minimal (prime, semiprime) essential ideals and minimal (prime, semiprime) essential fuzzy
ideals of ternary semigroups and provide the relationships between them. Moreover, we
investigate in the same manner in the case of 0-essential ideals and 0-essential fuzzy
ideals.