2014
DOI: 10.1155/2014/458638
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Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

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.

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Cited by 36 publications
(18 citation statements)
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References 26 publications
(29 reference statements)
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“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%