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\(\mathcal N\)-hyper sets. (English) Zbl 1402.06009
Summary: To deal with the uncertainties, fuzzy set theory can be considered as one of the mathematical tools by L. A. Zadeh [Inf. Control 8, 338–353 (1965; Zbl 0139.24606)]. As a mathematical tool to deal with negative information, Y. B. Jun et al. introduced a new function, which is called a negative-valued function, and constructed \(\mathcal N\)-structures in [“\(\mathcal N\)-ideals of BCK/BCI-algebras”, J. Chungcheong Math. Soc. 22, No. 3, 417–437 (2009)]. Since then, \(\mathcal N\)-structures are applied to algebraic structures and soft sets, etc. Using the \(\mathcal N\)-structures, the notions of (extended) \(\mathcal N\)-hyper sets, \(\mathcal N\)-substructures of type 1, 2, 3 and 4 are introduced, and several related properties are investigated in this research paper.
MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
03E72 Theory of fuzzy sets, etc.
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