Abstract
This paper introduces the concept of lattices of prime fuzzy ideals, which extends the classical theory of lattices of prime ideals in ring theory to the fuzzy setting. In this paper, we propose some examples and properties related to lattices of prime fuzzy ideals, contributing to the knowledge in fuzzy algebra. Think about an ordered semigroup ℛ. Plotting the function f from ℛ to the closed interval [0,1] defines a fuzzy subset of ℛ, where [0,1] ϵ ℛ. In order to explore prime ideals in rings, semigroups, and ordered semigroups in terms of fuzzy subsets, we build an ordered semigroup ℛ with ordered fuzzy points. To study, we presented the thoughts of ℒ-fuzzy prime ideals of an ordered semigroups ℛ, which forms a completelattice obeying the law relating the operations of multiplication and addition.
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