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The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
The concepts of a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.
In this paper, we introduce a more general form of neutrosophic ideal, and investigate their properties.
The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set , intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
The notion of commutative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal are considered. Characterizations of commutative MBJ-neutrosophic ideal are discussed.
Neutrosophic set (NS) developed by Smarandache [11, 12,13] is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set. Neutrosophic set theory is applied to various part which is refered to the site http://fs.gallup.unm.edu/neutrosophy.htm. Jun, Borumand Saeid and Ozturk studied neutrosophic subalgebras/ideals in BCK/BCI-algebras based on neutrosophic points (see [1], [6]and [10]).
The concepts of a positive implicative BMBJ-neutrosophic ideal is introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a (positive implicative) BMBJ-neutrosophic ideal are provided. Relations between BMBJ-neutrosophic ideal and positive implicative BMBJ-neutrosophic ideal are discussed. Characterizations of positive implicative BMBJ-neutrosophic ideal are displayed.
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In the fuzzy set which is introduced by Zadeh, the membership degree is expressed by only one function so called the truth function. As a generalization of fuzzy set, intuitionistic fuzzy set is introduced by Atanassove by using membership function and nonmembership function.