Q-代数中具有界限的模糊子代数(英文)

Fuzzy Subalgebras with Thresholds in Q-algebras

摘要: 引入了Q-代数中具有界限的模糊子代数的概念,获得了它的一些相关性质,给出了具有界限的模糊子代数与(∈,∈∨q)-模糊子代数的关系.在Q-代数中,引入了t-蕴含的模糊子代数的概念,讨论了具有界限的模糊子代数与分别基于Gaines-Rescher蕴涵算子、Godel蕴涵算子和Godel蕴涵算子的换质算子的0.5-蕴含的模糊子代数之关系.

Abstract: The concept of a fuzzy subalgebra with thresholds of Q-algebra is introduced, and some related properties are obtained. The relations between a fuzzy subalgebra with thresholds of Q-algebra and an(∈,∈∨q)-fuzzy subalgebra of Q-algebra are provided. The notion of t-implication-based fuzzy subalgebra of Q-algebra is also introduced, and the relations between fuzzy subalgebra with thresholds of Q-algebras and 0.5-implication–based fuzzy subalgebra of Q-algebra based respectively on Gaines-Rescher implication operator, Godel implication operator and the contraposition of Godel implication operator are discussed.