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.
Highlights
Zadeh [1] made an extension of the concept of a fuzzy set by an interval-valued fuzzy set, that is, a fuzzy set with an interval-valued membership function
Uncertainties could be dealt with the help of a wide range of contemporary mathematical theories such as probability theory, theory of fuzzy sets [4], interval mathematics [5], and rough set theory [6, 7]
Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties based on the viewpoint of parameterization
Summary
Zadeh [1] made an extension of the concept of a fuzzy set by an interval-valued fuzzy set, that is, a fuzzy set with an interval-valued membership function. Using a fuzzy set and an interval-valued fuzzy set, Jun et al [2] introduced a new notion, called a (internal, external) cubic set, and investigated several properties. They dealt with P-union, P-intersection, R-union, and R-intersection of cubic sets and investigated several related properties. The Scientific World Journal (internal, external) cubic soft sets, P-cubic (resp., R-cubic) soft subsets, R-union (resp., R-intersection, P-union, and Pintersection) of cubic soft sets, and the complement of a cubic soft set They investigated several related properties and applied the notion of cubic soft sets to BCK/BCI-algebras. We investigate several properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter
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