A new form of fuzzy set and its application in $BCK$-algebras and $BCI$-algebras
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The notion of the J-operator in the closed interval $[0,1]$ is introduced and several properties are investigated. Using the J-operator, a new fuzzy set called the $Y_J^{\varepsilon}$-fuzzy set is established and it is applied it to subalgebras in $BCK/BCI$-algebras. The concept of the $Y_J^{\varepsilon}$-fuzzy subalgebra is introduced and its properties are discussed. Conditions for a fuzzy set to be a $Y_J^{\varepsilon}$-fuzzy subalgebra are provided, and the relationship between the fuzzy subalgebra and the $Y_J^{\varepsilon}$-fuzzy subalgebra is discussed.
Abstract
The notion of the J-operator in the closed interval $[0,1]$ is introduced and several properties are investigated. Using the J-operator, a new fuzzy set called the $Y_J^{\varepsilon}$-fuzzy set is established and it is applied it to subalgebras in $BCK/BCI$-algebras. The concept of the $Y_J^{\varepsilon}$-fuzzy subalgebra is introduced and its properties are discussed. Conditions for a fuzzy set to be a $Y_J^{\varepsilon}$-fuzzy subalgebra are provided, and the relationship between the fuzzy subalgebra and the $Y_J^{\varepsilon}$-fuzzy subalgebra is discussed.
참고문헌 (9)
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