Cubic relations

다국어 초록 (Multilingual Abstract)

Various relations of fuzzy types has been applied to decision makings, graph theories, congruence problems in algebras and quotient spaces in topological spaces, etc. Then in this paper, we deal with cubic relations as one of various fuzzy type's relations. First, we define a cubic point and obtained some of its properties. Second, we introduce the notions of cubic reflexive [resp. symmetric and transitive] relations, and we define the composition of two cubic relations and the inverse of a cubic relation. And investigate some of each properties and give some examples. Third, we define the concepts of cubic equivalence relations, cubic equivalence classes and cubic partitions, and obtain some of each properties, respectively. Finally, we define a $<\widetilde{a},\alpha>$-level relation of a cubic relation and study some of its properties.

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