Document Type : Research Paper


1 Research Scholar, Annamalai university, Annamalai nagar - 608002

2 Department of Mathematics, Mohamed Sathak AJ College of Engineering, Chennai, Tamilnadu, India.

3 Department of Mathematics, Govt. Arts and Science College, Nagercoil-629 004,Tamil Nadu, India.

4 3University of New Mexico, 705 Gurley Ave., Gallup, NM 87301


This paper is mainly intended to verify whether the basic laws of set theory are applicable in the Neutrosophic soft set. The laws that have been examined in this paper for NSS include Commutative law, Associative law, Distributive law, Involution law, Idempotent law, Negation law (law of contradiction and law of excluded middle), it has also been illustrated with sufficient examples. In addition, extending that to the hypersoft set, we have proved if H is a Neutrosophic hypersoft Subgroup (NHSSG) of a group G and N is a normal subgroup of G, then HN is a Neutrosophic hypersoft Subgroup (NHSSG) of G.

Keywords: Neutrosophic Set: Neutrosophic Soft Set: Complement set: Neutrosophic hypersoft set


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