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Abstract
Characterizations of a (⋶, ⋶ ∨ q̄)-fuzzy subalgebra (ideal) are considered. Given an ∈-soft set, an (⋶, ⋶ ∨ q̄)-fuzzy subalgebra is established. Using the notion of (t, s)-fuzzy subalgebras, characterizations for an∈-soft set to be a (idealistic) soft BCK/BCI-algebra are provided. Using the notion of fuzzy p-ideals, a characterization of an∈-soft set to be a p-idealistic soft BCI-algebra is constructed. An equivalent condition for a q-soft set to be a p-ideal is given. Characterizations of a (∈,∈ ∨ q)-fuzzy p-ideal are initiated. Conditions for a (∈,∈∨ q)-fuzzy ideal to be a (∈,∈∨ q)-fuzzy p-ideal are stated.
Acknowledgements
The authors are extremely grateful to the referees for giving them many valuable comments and helpful suggestions which helps to improve the presentation of this paper.
This work was supported by a grant of the National Natural Science Foundation of China (60875034); a grant of the Innovation Term of Educational Department of Hubei Province of China (No.T201109); and also the support of the National Science Foundation of Hubei Province, China (2009CDB340).