Abstract:Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed.
“…In 2012, Y.B. Jun et al [1] introduced cubic sets, and then this notion is applied to several algebraic structures (see [2,3,4,5,7,8,10,11,12,13]). In 2017, extending the concept of a cubic set, Y.B.…”
In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.
“…In 2012, Y.B. Jun et al [1] introduced cubic sets, and then this notion is applied to several algebraic structures (see [2,3,4,5,7,8,10,11,12,13]). In 2017, extending the concept of a cubic set, Y.B.…”
In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.
“…Jun [6] applied the notion of soft set to BCK/BCI-algebras, and Jun et al [8] considered applications of soft set theory in the ideals of d-algebras. Also, Muhiuddin et al studied the soft set theory on various aspects (see for e.g., [1], [16], [17]), [18], [19]). A (crisp) set A in a universe X can be defined in the form of its characteristic function µ A : X → {0, 1} yielding the value 1 for elements belonging to the set A and the value 0 for elements excluded from the set A.…”
In this paper, using the notion of soft sets and N-structures, the notion of N-soft p-ideals in BCI-algebras is introduced, and related properties are investigated. Relations between N-soft ideals and N-soft p-ideals are discussed. Conditions for an N-soft ideal to be an N-soft p-ideal are established.
“…Jun et al [6] introduced the cubic set. Mohiuddin et al [7] showed that the union of two internal cubic soft sets might not be internal. Turksen [8] showed that the proposed representation (1) exists for certain families of the conjugate pairs of t-norms and t-norms, and (2) resolves some of the difficulties associated with particular interpretations of conjunction, disjunction, and implication in fuzzy set theories.…”
In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.