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Abstract

The aim of this study is to introduce the concept of implication-based fuzzy ternary subsemigroups in ternary semigroups. Using the four implication operators, that is, Gaines-Rescher implication operator, Gödel implication operator, the contraposition of Gödel implication operator and the Luckasiewicz implication operator, the implication-based fuzzy ternary subsemigroups are considered. Furthermore, based on this novel idea, relationships between fuzzy [resp.(ϵ,ϵ Vԛ)-fuzzy] ternary subsemigroups and implication-based fuzzy ternary subsemigroups are discussed. Finally, conditions for a fuzzy ternary subsemigroup with thresholds 0 and 0.5 to be an implication-based fuzzy ternary subsemigroups under the Luckasiewicz implication operator are provided. 

Keywords: Fuzzifying ternary semigroup, fuzzy ternary subsemigroup, t- implication-based fuzzy ternary subsemigroup.