Hesitant fuzzy rough sets through hesitant fuzzy relations

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived. Hesitant Fuzzy Rough sets are introduced using the lower approximation and upper approximation of a hesitant fuzzy set. A relation between the approximation operators is proved. 2010 AMS Classification: 03E72, 94D99, 68T37

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