Crossing octahedron sets and their applications to Q-algebras
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A crossing octahedron set is composed of three components : interval-valued fuzzy set, intuitionistic fuzzy set and negative-valued function. In this paper, we first introduce the concept of crossing octahedron set and investigate its properties. Further, we define a crossing octahedron Q-ideal, Q-subalgebra and BCK-ideal of a Q-algebra, and we deal with their relationships. In addition, the homomorphic images and pre-images of a crossing octahedron Q-ideal are also studied. Related properties of crossing octahedron Q-ideals are explored and discussed. Finally, the Cartesian product of two crossing octahedron Q-ideals is investigated.
Abstract
A crossing octahedron set is composed of three components : interval-valued fuzzy set, intuitionistic fuzzy set and negative-valued function. In this paper, we first introduce the concept of crossing octahedron set and investigate its properties. Further, we define a crossing octahedron Q-ideal, Q-subalgebra and BCK-ideal of a Q-algebra, and we deal with their relationships. In addition, the homomorphic images and pre-images of a crossing octahedron Q-ideal are also studied. Related properties of crossing octahedron Q-ideals are explored and discussed. Finally, the Cartesian product of two crossing octahedron Q-ideals is investigated.
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