Abstract
AbstractBy combining \( R- \) implication operators and fuzzy prime ideals of a ring, the concept of a new fuzzy algebra structure, such \( R- \) generalized fuzzy completely prime ideal, is introduced. And we obtain the related theorie and deduction that the union of finite even infinite \( R- \) generalized fuzzy completely prime ideal is still a \( R-\)generalized fuzzy completely prime ideal when \( R(x, y) \) is increasing on the variable \( x \). Based on the definition of ring homomorphism, we deduce that the full homomorphic image or homomorphic preimage of a \( R- \) generalized fuzzy completely prime ideal is still a \( R-\)generalized fuzzy completely prime ideal. Furthermore, eight concrete implication operations of such fuzzy completely prime ideal are given.Keywords \( R-\)generalized fuzzy completely prime idealRingImplication operator
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