N-Hyper Sets

Abstract

To deal with the uncertainties, fuzzy set theory can be considered as one of the mathematical tools by Zadeh. As a mathematical tool to deal with negative information, Jun et al. introduced a new function, which is called a negative-valued function, and constructed -structures in 2009. Since then, -structures are applied to algebraic structures and soft sets, etc. Using the -structures, the notions of (extended) -hyper sets, -substructures of type 1, 2, 3 and 4 are introduced, and several related properties are investigated in this research paper.